Science.gov

Sample records for experimental chaos conference

  1. Experimental Evidence of Chaos from Memristors

    NASA Astrophysics Data System (ADS)

    Gambuzza, Lucia Valentina; Fortuna, Luigi; Frasca, Mattia; Gale, Ella

    Until now, most memristor-based chaotic circuits proposed in the literature are based on mathematical models which assume ideal characteristics such as piecewise-linear or cubic nonlinearities. The idea, illustrated here and originating from the experimental approach for device characterization, is to realize a chaotic system exploiting the nonlinearity of only one memristor with a very simple experimental set-up using feedback. In this way, a simple circuit is obtained and chaos is experimentally observed and is confirmed by the calculation of the largest Lyapunov exponent. Numerical results using the Strukov model support the existence of robust chaos in our circuit. To our knowledge, this is the first experimental demonstration of chaos in a real memristor circuit and suggests that memristors are well placed for hardware encryption.

  2. Experimental chaos detection in the Duffing oscillator

    NASA Astrophysics Data System (ADS)

    Eyebe Fouda, J. S. Armand; Bodo, Bertrand; Djeufa, Guy M. D.; Sabat, Samrat L.

    2016-04-01

    This paper presents a comparative study of four algorithms namely the maximal Lyapunov exponent (MLE), 0-1 test, conditional entropy of ordinal patterns (CPE) and recently developed permutation largest slope entropy (PLSE) algorithm for experimental chaos detection in the Duffing oscillator. We consider an electrical model of the Duffing oscillator and its equivalent electronic circuit for generating the data to validate the effectiveness of the algorithms. The performance of the PLSE is compared with the 0-1 test and the CPE algorithms on the data set obtained from the simulated circuit; and with the MLE for the data collected from the experimental circuit. The experimental data are acquired using a digital oscilloscope with 1 MHz sampling frequency. From the comparison of the experimental spectra of the four methods with the analog phase portraits of the real system, it appears that the PLSE is the more reliable algorithm for chaos detection from experimental data.

  3. "Chaos."

    ERIC Educational Resources Information Center

    Samson, Ilan

    1997-01-01

    Discusses what is meant by a process being described as chaotic and how such situations come about. Argues that clarifying this concept is particularly important because understanding chaos helps cure far more fundamental common misconceptions. (ASK)

  4. Experimental validation of wireless communication with chaos

    NASA Astrophysics Data System (ADS)

    Ren, Hai-Peng; Bai, Chao; Liu, Jian; Baptista, Murilo S.; Grebogi, Celso

    2016-08-01

    The constraints of a wireless physical media, such as multi-path propagation and complex ambient noises, prevent information from being communicated at low bit error rate. Surprisingly, it has only recently been shown that, from a theoretical perspective, chaotic signals are optimal for communication. It maximises the receiver signal-to-noise performance, consequently minimizing the bit error rate. This work demonstrates numerically and experimentally that chaotic systems can in fact be used to create a reliable and efficient wireless communication system. Toward this goal, we propose an impulsive control method to generate chaotic wave signals that encode arbitrary binary information signals and an integration logic together with the match filter capable of decreasing the noise effect over a wireless channel. The experimental validation is conducted by inputting the signals generated by an electronic transmitting circuit to an electronic circuit that emulates a wireless channel, where the signals travel along three different paths. The output signal is decoded by an electronic receiver, after passing through a match filter.

  5. Experimental validation of wireless communication with chaos.

    PubMed

    Ren, Hai-Peng; Bai, Chao; Liu, Jian; Baptista, Murilo S; Grebogi, Celso

    2016-08-01

    The constraints of a wireless physical media, such as multi-path propagation and complex ambient noises, prevent information from being communicated at low bit error rate. Surprisingly, it has only recently been shown that, from a theoretical perspective, chaotic signals are optimal for communication. It maximises the receiver signal-to-noise performance, consequently minimizing the bit error rate. This work demonstrates numerically and experimentally that chaotic systems can in fact be used to create a reliable and efficient wireless communication system. Toward this goal, we propose an impulsive control method to generate chaotic wave signals that encode arbitrary binary information signals and an integration logic together with the match filter capable of decreasing the noise effect over a wireless channel. The experimental validation is conducted by inputting the signals generated by an electronic transmitting circuit to an electronic circuit that emulates a wireless channel, where the signals travel along three different paths. The output signal is decoded by an electronic receiver, after passing through a match filter. PMID:27586613

  6. Experimental evidence of wave chaos from a double slit experiment with water surface waves.

    PubMed

    Tang, Yunfei; Shen, Yifeng; Yang, Jiong; Liu, Xiaohan; Zi, Jian; Li, Baowen

    2008-10-01

    In this paper, we report experimental evidence of wave chaos using the double slit water surface wave experiment. We demonstrate that classical dynamics of a domain manifests itself in the interference patterns after the diffraction behind the double slit. For a domain whose classical dynamics is integrable clear interference fringes can be observed behind the double slits; for a domain whose classical dynamics is chaotic, however, interference fringes can totally disappear. Our experimental results clearly demonstrate that the centuries-old double slit experiment can render an excellent tool to observe the manifestations of wave chaos.

  7. Controlling chaos experimentally in systems exhibiting large effective Lyapunov exponents

    NASA Astrophysics Data System (ADS)

    Hübinger, B.; Doerner, R.; Martienssen, W.; Herdering, M.; Pitka, R.; Dressler, U.

    1994-08-01

    We investigate experimentally the performance of the Ott, Grebogi, and Yorke [Phys. Rev. Lett. 64, 1196 (1989)] feedback concept to control chaotic motion. The experimental systems are a driven pendulum and a driven bronze ribbon. Both setups have unstable periodic orbits characterized by large effective Lyapunov exponents. All control vectors for the feedback control are extracted from the experimental data. To do this for the pendulum a global model obtained by the flow field analysis of Cremers and Hübler [Z. Naturforsch. 42a, 797 (1987)] is used, and for the bronze ribbon linear approximations in embedding space are exploited. We analyze the problems that arise due to the amplification of noise by large effective Lyapunov exponents in the determination of the control values as well as in the performance of the experimental control. Successful control can be achieved in our experiments by applying the ``local control method'' which allows a quasicontinuous adjustment of the control parameter in contrast to adjusting the control parameter only once per return time of the Poincaré map.

  8. Is there chaos in the brain? II. Experimental evidence and related models.

    PubMed

    Korn, Henri; Faure, Philippe

    2003-09-01

    The search for chaotic patterns has occupied numerous investigators in neuroscience, as in many other fields of science. Their results and main conclusions are reviewed in the light of the most recent criteria that need to be satisfied since the first descriptions of the surrogate strategy. The methods used in each of these studies have almost invariably combined the analysis of experimental data with simulations using formal models, often based on modified Huxley and Hodgkin equations and/or of the Hindmarsh and Rose models of bursting neurons. Due to technical limitations, the results of these simulations have prevailed over experimental ones in studies on the nonlinear properties of large cortical networks and higher brain functions. Yet, and although a convincing proof of chaos (as defined mathematically) has only been obtained at the level of axons, of single and coupled cells, convergent results can be interpreted as compatible with the notion that signals in the brain are distributed according to chaotic patterns at all levels of its various forms of hierarchy. This chronological account of the main landmarks of nonlinear neurosciences follows an earlier publication [Faure, Korn, C. R. Acad. Sci. Paris, Ser. III 324 (2001) 773-793] that was focused on the basic concepts of nonlinear dynamics and methods of investigations which allow chaotic processes to be distinguished from stochastic ones and on the rationale for envisioning their control using external perturbations. Here we present the data and main arguments that support the existence of chaos at all levels from the simplest to the most complex forms of organization of the nervous system. We first provide a short mathematical description of the models of excitable cells and of the different modes of firing of bursting neurons (Section 1). The deterministic behavior reported in giant axons (principally squid), in pacemaker cells, in isolated or in paired neurons of Invertebrates acting as coupled

  9. Chaos and simple determinism in reversed field pinch plasmas: Nonlinear analysis of numerical simulation and experimental data

    SciTech Connect

    Watts, C.A.

    1993-09-01

    In this dissertation the possibility that chaos and simple determinism are governing the dynamics of reversed field pinch (RFP) plasmas is investigated. To properly assess this possibility, data from both numerical simulations and experiment are analyzed. A large repertoire of nonlinear analysis techniques is used to identify low dimensional chaos in the data. These tools include phase portraits and Poincare 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 date 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 low 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. Experimental Determination of One-Atmosphere Phase Relations of Rhyodacite Pumice Erupted from Chaos Crags, Lassen Volcanic Center, California

    NASA Astrophysics Data System (ADS)

    Quinn, E. T.; Schwab, B. E.

    2012-12-01

    A series of one-atmosphere high-temperature anhydrous phase equilibrium melting experiments was performed on a natural rhyodacite pumice from the 1103±13 years BP pyroclastic flow from the Chaos Crags, Lassen Volcanic Center, California. The pumice (CCP) is the most silicic product known of the 1103 eruption of Chaos Crags. All experimental runs were performed in a Deltech VT-31 one-atmosphere gas-mixing furnace at the Experimental Petrology Lab, Humboldt State University, Arcata, California. Six ~90-99 hour runs were conducted at 35-55°C intervals, with target temperatures from 1000°C to 1200°C at the Ni-NiO buffer. The nominally anhydrous liquidus of the rhyodacite pumice is >1196°C and solidus is <998°C, outside the investigated temperature range. All experimental run products contain glass, plagioclase, quartz, and Fe-Ti oxides. Amphibole with breakdown textures is observed at temperatures ≤1159°C, and appears more stable in lower temperature runs. At 998°C, amphibole appears most stable, with only minor breakdown texture. Biotite, a major phase in starting material, is not observed in any run products. Based on comparison between experimental and natural phase assemblages and glass, plagioclase, and amphibole compositions, the Chaos Crags rhyodacite pumice erupted at a temperature <998°C, the lowest experimental run temperature investigated. Additional experimental runs at temperatures <998°C are currently being conducted.

  11. Experimental investigation of linear and nonlinear wave systems: A quantum chaos approach

    NASA Astrophysics Data System (ADS)

    Neicu, Toni

    2002-09-01

    An experimental and numerical study of linear and nonlinear wave systems using methods and ideas developed from quantum chaos is presented. We exploit the analogy of the wave equation for the flexural modes of a thin clover-shaped acoustic plate to the stationary solutions of the Schrodinger wave equation for a quantum clover-shaped billiard, a generic system that has regular and chaotic regions in its phase space. We observed periodic orbits in the spectral properties of the acoustic plate, the first such definitive acoustic experiment. We also solved numerically the linear wave equation of the acoustic plate for the first few hundred eigenmodes. The Fourier transform of the eigenvalues show peaks corresponding to the principal periodic orbits of the classical billiard. The signatures of the periodic orbits in the spectra were unambiguously verified by deforming one edge of the plate and observing that only the peaks corresponding to the orbits that hit this edge changed. The statistical measures of the eigenvalues are intermediate between universal forms for completely integrable and chaotic systems. The density distribution of the eigenfunctions agrees with the Porter-Thomas formula of chaotic systems. The viscosity dependence and effects of nonlinearity on the Faraday surface wave patterns in a stadium geometry were also investigated. The ray dynamics inside the stadium, a paradigm of quantum chaos, is completely chaotic. The majority of the observed patterns of the orbits resemble three eigenstates of the stadium: the bouncing ball, longitudinal, and bowtie patterns. We observed many disordered patterns that increase with the viscosity. The experimental results were analyzed using recent theoretical work that explains the suppression of certain modes. The theory also predicts that the perimeter dissipation is too strong for whispering gallery modes, which contradicts our observations of these modes for a fluid with low viscosity. Novel vortex patterns were

  12. Between chaos and petrification: a summary of the Fifth IPA Conference of Training Analysts.

    PubMed

    Wallerstein, R S

    1993-02-01

    The Fifth IPA Conference of Training Analysts was devoted to the problems in the integration of different theoretical and clinical perspectives in the formation of psychoanalysts, the dialectical tensions between rigidity and stultification on the one hand, and a chaotic 'anything goes' on the other. Seven presentations, from the three major geographical regions and representing a range of theoretical perspectives, though drawing upon common and shared clinical and training experiences, were widely divergent in both their descriptions and their prescriptions. The presentations by Janice de Saussure of Geneva, by Charles Kligerman of Chicago, by Marcio de Freitas Giovanetti of São Paulo, Raquel Zak de Goldstein of Buenos Aires, André Green of Paris, José Infante of Chile and André Lussier of Montreal, are arrayed along a spectrum from the most conservative to the most sweepingly radical critique of our organisations and our practices; what is shared by these seven quite disparate presentations from so many ideologically and geographically diverse quarters is a widespread dissatisfaction with so many aspects of, and so many consequences of, the operation or our extant tripartite training structure bequeathed to us by Eitingon and his colleagues almost 75 years ago and hardly changed at all ever since. PMID:8454399

  13. Between chaos and petrification: a summary of the Fifth IPA Conference of Training Analysts.

    PubMed

    Wallerstein, R S

    1993-02-01

    The Fifth IPA Conference of Training Analysts was devoted to the problems in the integration of different theoretical and clinical perspectives in the formation of psychoanalysts, the dialectical tensions between rigidity and stultification on the one hand, and a chaotic 'anything goes' on the other. Seven presentations, from the three major geographical regions and representing a range of theoretical perspectives, though drawing upon common and shared clinical and training experiences, were widely divergent in both their descriptions and their prescriptions. The presentations by Janice de Saussure of Geneva, by Charles Kligerman of Chicago, by Marcio de Freitas Giovanetti of São Paulo, Raquel Zak de Goldstein of Buenos Aires, André Green of Paris, José Infante of Chile and André Lussier of Montreal, are arrayed along a spectrum from the most conservative to the most sweepingly radical critique of our organisations and our practices; what is shared by these seven quite disparate presentations from so many ideologically and geographically diverse quarters is a widespread dissatisfaction with so many aspects of, and so many consequences of, the operation or our extant tripartite training structure bequeathed to us by Eitingon and his colleagues almost 75 years ago and hardly changed at all ever since.

  14. An Experimental Realization of a Chaos-Based Secure Communication Using Arduino Microcontrollers.

    PubMed

    Zapateiro De la Hoz, Mauricio; Acho, Leonardo; Vidal, Yolanda

    2015-01-01

    Security and secrecy are some of the important concerns in the communications world. In the last years, several encryption techniques have been proposed in order to improve the secrecy of the information transmitted. Chaos-based encryption techniques are being widely studied as part of the problem because of the highly unpredictable and random-look nature of the chaotic signals. In this paper we propose a digital-based communication system that uses the logistic map which is a mathematically simple model that is chaotic under certain conditions. The input message signal is modulated using a simple Delta modulator and encrypted using a logistic map. The key signal is also encrypted using the same logistic map with different initial conditions. In the receiver side, the binary-coded message is decrypted using the encrypted key signal that is sent through one of the communication channels. The proposed scheme is experimentally tested using Arduino shields which are simple yet powerful development kits that allows for the implementation of the communication system for testing purposes. PMID:26413563

  15. An Experimental Realization of a Chaos-Based Secure Communication Using Arduino Microcontrollers

    PubMed Central

    Zapateiro De la Hoz, Mauricio; Acho, Leonardo; Vidal, Yolanda

    2015-01-01

    Security and secrecy are some of the important concerns in the communications world. In the last years, several encryption techniques have been proposed in order to improve the secrecy of the information transmitted. Chaos-based encryption techniques are being widely studied as part of the problem because of the highly unpredictable and random-look nature of the chaotic signals. In this paper we propose a digital-based communication system that uses the logistic map which is a mathematically simple model that is chaotic under certain conditions. The input message signal is modulated using a simple Delta modulator and encrypted using a logistic map. The key signal is also encrypted using the same logistic map with different initial conditions. In the receiver side, the binary-coded message is decrypted using the encrypted key signal that is sent through one of the communication channels. The proposed scheme is experimentally tested using Arduino shields which are simple yet powerful development kits that allows for the implementation of the communication system for testing purposes. PMID:26413563

  16. An Experimental Realization of a Chaos-Based Secure Communication Using Arduino Microcontrollers.

    PubMed

    Zapateiro De la Hoz, Mauricio; Acho, Leonardo; Vidal, Yolanda

    2015-01-01

    Security and secrecy are some of the important concerns in the communications world. In the last years, several encryption techniques have been proposed in order to improve the secrecy of the information transmitted. Chaos-based encryption techniques are being widely studied as part of the problem because of the highly unpredictable and random-look nature of the chaotic signals. In this paper we propose a digital-based communication system that uses the logistic map which is a mathematically simple model that is chaotic under certain conditions. The input message signal is modulated using a simple Delta modulator and encrypted using a logistic map. The key signal is also encrypted using the same logistic map with different initial conditions. In the receiver side, the binary-coded message is decrypted using the encrypted key signal that is sent through one of the communication channels. The proposed scheme is experimentally tested using Arduino shields which are simple yet powerful development kits that allows for the implementation of the communication system for testing purposes.

  17. Pioneering through chaos.

    PubMed

    Warshawsky, Nora E; Joseph, M Lindell; Fowler, Debra L; Edmonson, Cole; Nelson-Brantley, Heather V; Kowalski, Karren

    2015-03-01

    The 2014 International Nursing Administration Research Conference, "Pioneering Through Chaos: Leadership for a Changing World," was held at the Texas Woman's University in Dallas, Texas, in the fall of 2014. The program drew more than 100 attendees from 4 countries. The conference informed attendees from both academe and practice about the role of nursing administration in navigating the dynamic healthcare climate. This article will report on the insights from the conference presenters. PMID:25689497

  18. Routes towards the experimental observation of the large fluctuations due to chaos-assisted tunneling effects with cold atoms

    NASA Astrophysics Data System (ADS)

    Dubertrand, R.; Billy, J.; Guéry-Odelin, D.; Georgeot, B.; Lemarié, G.

    2016-10-01

    In the presence of a complex classical dynamics associated with a mixed phase space, a quantum wave function can tunnel between two stable islands through the chaotic sea, an effect that has no classical counterpart. This phenomenon, referred to as chaos-assisted tunneling, is characterized by large fluctuations of the tunneling rate when a parameter is varied. To date, the full extent of this effect as well as the associated statistical distribution have never been observed in a quantum system. Here, we analyze the possibility of characterizing these effects accurately in a cold-atom experiment. Using realistic values of the parameters of an experimental setup, we examine through analytical estimates and extensive numerical simulations a specific system that can be implemented with cold atoms, the atomic modulated pendulum. We assess the efficiency of three possible routes to observe in detail chaos-assisted tunneling properties. Our main conclusion is that due to the fragility of the symmetry between positive and negative momenta as a function of quasimomentum, it is very challenging to use tunneling between classical islands centered on fixed points with opposite momentum. We show that it is more promising to use islands symmetric in position space, and characterize the regime where it could be done. The proposed experiment could be realized with current state-of-the-art technology.

  19. Colored chaos

    SciTech Connect

    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.

  20. 14 CFR 437.17 - Rights not conferred by an experimental permit.

    Code of Federal Regulations, 2011 CFR

    2011-01-01

    ... 14 Aeronautics and Space 4 2011-01-01 2011-01-01 false Rights not conferred by an experimental permit. 437.17 Section 437.17 Aeronautics and Space COMMERCIAL SPACE TRANSPORTATION, FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION LICENSING EXPERIMENTAL PERMITS General Information § 437.17 Rights not conferred by an experimental...

  1. 14 CFR 437.17 - Rights not conferred by an experimental permit.

    Code of Federal Regulations, 2014 CFR

    2014-01-01

    ... 14 Aeronautics and Space 4 2014-01-01 2014-01-01 false Rights not conferred by an experimental permit. 437.17 Section 437.17 Aeronautics and Space COMMERCIAL SPACE TRANSPORTATION, FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION LICENSING EXPERIMENTAL PERMITS General Information § 437.17 Rights not conferred by an experimental...

  2. 14 CFR 437.17 - Rights not conferred by an experimental permit.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 14 Aeronautics and Space 4 2010-01-01 2010-01-01 false Rights not conferred by an experimental permit. 437.17 Section 437.17 Aeronautics and Space COMMERCIAL SPACE TRANSPORTATION, FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION LICENSING EXPERIMENTAL PERMITS General Information § 437.17 Rights not conferred by an experimental...

  3. 14 CFR 437.17 - Rights not conferred by an experimental permit.

    Code of Federal Regulations, 2012 CFR

    2012-01-01

    ... 14 Aeronautics and Space 4 2012-01-01 2012-01-01 false Rights not conferred by an experimental permit. 437.17 Section 437.17 Aeronautics and Space COMMERCIAL SPACE TRANSPORTATION, FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION LICENSING EXPERIMENTAL PERMITS General Information § 437.17 Rights not conferred by an experimental...

  4. Experimental evidence of intermittent chaos in a glow discharge plasma without external forcing and its numerical modelling

    SciTech Connect

    Ghosh, S. Kumar Shaw, Pankaj; Sekar Iyengar, A. N.; Janaki, M. S.; Saha, Debajyoti; Michael Wharton, Alpha

    2014-03-15

    Intermittent chaos was observed in a glow discharge plasma as the system evolved from regular type of relaxation oscillations (of larger amplitude) to an irregular type of oscillations (of smaller amplitude) as the discharge voltage was increased. Floating potential fluctuations were analyzed by different statistical and spectral methods. Features like a gradual change in the normal variance of the interpeak time intervals, a dip in the skewness, and a hump in the kurtosis with variation in the control parameter have been seen, which are strongly indicative of intermittent behavior in the system. Detailed analysis also suggests that the intrinsic noise level in the experiment increases with the increasing discharge voltage. An attempt has been made to model the experimental observations by a second order nonlinear ordinary differential equation derived from the fluid equations for an unmagnetized plasma. Though the experiment had no external forcing, it was conjectured that the intrinsic noise in the experiment could be playing a vital role in the dynamics of the system. Hence, a constant bias and noise as forcing terms were included in the model. Results from the theoretical model are in close qualitative agreement with the experimental results.

  5. Tandem antioxidant enzymes confer synergistic protective responses in experimental filariasis.

    PubMed

    Prince, P R; Madhumathi, J; Anugraha, G; Jeyaprita, P J; Reddy, M V R; Kaliraj, P

    2014-12-01

    Helminth parasites use antioxidant defence strategies for survival during oxidative stress due to free radicals in the host. Accordingly, tissue-dwelling filarial parasites counteract host responses by releasing a number of antioxidants. Targeting these redox regulation proteins together, would facilitate effective parasite clearance. Here, we report the combined effect of protective immune responses trigged by recombinant Wuchereria bancrofti thioredoxin (WbTRX) and thioredoxin peroxidase (WbTPX) in an experimental filarial model. The expression of WbTRX and WbTPX in different stages of the parasite and their cross-reactivity were analysed by enzyme-linked immunosorbent assay (ELISA). The immunogenicity of recombinant proteins and their protective efficacy were studied in animal models when immunized in single or cocktail mode. The antigens showed cross-reactive epitopes and induced high humoral and cellular immune responses in mice. Further, parasite challenge against Brugia malayi L3 larvae in Mastomys coucha conferred significant protection of 57% and 62% against WbTRX and WbTPX respectively. The efficacy of L3 clearance was significantly higher (71%) (P <  0.001) when the antigens were immunized together, showing a synergistic effect in multiple-mode vaccination. Hence, the study suggests WbTRX and WbTPX to be attractive vaccine candidates when immunized together and provides a tandem block for parasite elimination in the control of lymphatic filariasis.

  6. "Student Evaluation of an Experimental Course Conducted Via Conference Telephone."

    ERIC Educational Resources Information Center

    Gold, Ben K.

    This study summarizes student responses to an evaluation questionnaire and some performance statistics for a special "conference telephone" class in organization and management theory offered by Los Angeles City College to employees of the Pacific Telephone Company. The conference telephone setup permitted the students to take the class at their…

  7. Ergodic theory and experimental visualization of chaos in 3D flows

    NASA Astrophysics Data System (ADS)

    Sotiropoulos, Fotis; Mezic, Igor

    2000-11-01

    In his motivation for the ergodic hypothesis Gibbs invoked an analogy with fluid mixing: “…Yet no fact is more familiar to us than that stirring tends to bring a liquid to a state of uniform mixture, or uniform densities of its components…”. Although proof of the ergodic hypothesis is possible only for the simplest of systems using methods from ergodic theory, the use of the hypothesis has led to many accurate predictions in statistical mechanics. The problem of fluid mixing, however, turned out to be considerably more complicated than Gibbs envisioned. Chaotic advection can indeed lead to efficient mixing even in non-turbulent flows, but many non-mixed islands are known to persist within well-mixed regions. In numerical studies, Poincaré maps can be used to reveal the structure of such islands but their visualization in the laboratory requires laborious experimental procedures and is possible only for certain types of flows. Here we propose the first non-intrusive, simple to implement, and generally applicable technique for constructing experimental Poincaré maps and apply it to a steady, 3D, vortex breakdown bubble. We employ standard laser-induced fluorescence (LIF) and construct Poincaré maps by time averaging a sufficiently long sequence of instantaneous LIF images. We also show that ergodic theory methods provide a rigorous theoretical justification for this approach whose main objective is to reveal the non-ergodic regions of the flow.

  8. Evidence of low dimensional chaos in renal blood flow control in genetic and experimental hypertension

    NASA Astrophysics Data System (ADS)

    Yip, K.-P.; Marsh, D. J.; Holstein-Rathlou, N.-H.

    1995-01-01

    We applied a surrogate data technique to test for nonlinear structure in spontaneous fluctuations of hydrostatic pressure in renal tubules of hypertensive rats. Tubular pressure oscillates at 0.03-0.05 Hz in animals with normal blood pressure, but the fluctuations become irregular with chronic hypertension. Using time series from rats with hypertension we produced surrogate data sets to test whether they represent linearly correlated noise or ‘static’ nonlinear transforms of a linear stochastic process. The correlation dimension and the forecasting error were used as discriminating statistics to compare surrogate with experimental data. The results show that the original experimental time series can be distinguished from both linearly and static nonlinearly correlated noise, indicating that the nonlinear behavior is due to the intrinsic dynamics of the system. Together with other evidence this strongly suggests that a low dimensional chaotic attractor governs renal hemodynamics in hypertension. This appears to be the first demonstration of a transition to chaotic dynamics in an integrated physiological control system occurring in association with a pathological condition.

  9. Defining chaos

    SciTech Connect

    Hunt, Brian R.; Ott, Edward

    2015-09-15

    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.

  10. Chaos in Environmental Education.

    ERIC Educational Resources Information Center

    Hardy, Joy

    1999-01-01

    Explores chaos theory, the evolutionary capacity of chaotic systems, and the philosophical implications of chaos theory in general and for education. Compares the relationships between curriculum vision based on chaos theory and critical education for the environment. (Author/CCM)

  11. 14 CFR 437.17 - Rights not conferred by an experimental permit.

    Code of Federal Regulations, 2013 CFR

    2013-01-01

    ... 14 Aeronautics and Space 4 2013-01-01 2013-01-01 false Rights not conferred by an experimental permit. 437.17 Section 437.17 Aeronautics and Space COMMERCIAL SPACE TRANSPORTATION, FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION LICENSING EXPERIMENTAL PERMITS General Information § 437.17...

  12. Quantum Chaos

    NASA Astrophysics Data System (ADS)

    Casati, Giulio; Chirikov, Boris

    2006-11-01

    Preface; Acknowledgments; Introduction: 1. The legacy of chaos in quantum mechanics G. Casati and B. V. Chirikov; Part I. Classical Chaos and Quantum Localization: 2. Stochastic behaviour of a quantum pendulum under a periodic perturbation G. Casati, B. V. Chirikov, F. M. Izrailev and J. Ford; 3. Quantum dynamics of a nonintegrable system D. R. Grempel, R. E. Prange and S. E. Fishman; 4. Excitation of molecular rotation by periodic microwave pulses. A testing ground for Anderson localization R. Blümel, S. Fishman and U. Smilansky; 5. Localization of diffusive excitation in multi-level systems D. K. Shepelyansky; 6. Classical and quantum chaos for a kicked top F. Haake, M. Kus and R. Scharf; 7. Self-similarity in quantum dynamics L. E. Reichl and L. Haoming; 8. Time irreversibility of classically chaotic quantum dynamics K. Ikeda; 9. Effect of noise on time-dependent quantum chaos E. Ott, T. M. Antonsen Jr and J. D. Hanson; 10. Dynamical localization, dissipation and noise R. F. Graham; 11. Maximum entropy models and quantum transmission in disordered systems J.-L. Pichard and M. Sanquer; 12. Solid state 'atoms' in intense oscillating fields M. S. Sherwin; Part II. Atoms in Strong Fields: 13. Localization of classically chaotic diffusion for hydrogen atoms in microwave fields J. E. Bayfield, G. Casati, I. Guarneri and D. W. Sokol; 14. Inhibition of quantum transport due to 'scars' of unstable periodic orbits R. V. Jensen, M. M. Sanders, M. Saraceno and B. Sundaram; 15. Rubidium Rydberg atoms in strong fields G. Benson, G. Raithel and H. Walther; 16. Diamagnetic Rydberg atom: confrontation of calculated and observed spectra C.-H. Iu, G. R. Welch, M. M. Kash, D. Kleppner, D. Delande and J. C. Gay; 17. Semiclassical approximation for the quantum states of a hydrogen atom in a magnetic field near the ionization limit M. Y. Kuchiev and O. P. Sushkov; 18. The semiclassical helium atom D. Wintgen, K. Richter and G. Tanner; 19. Stretched helium: a model for quantum chaos

  13. Quantum Chaos

    NASA Astrophysics Data System (ADS)

    Casati, Giulio; Chirikov, Boris

    1995-04-01

    Preface; Acknowledgments; Introduction: 1. The legacy of chaos in quantum mechanics G. Casati and B. V. Chirikov; Part I. Classical Chaos and Quantum Localization: 2. Stochastic behaviour of a quantum pendulum under a periodic perturbation G. Casati, B. V. Chirikov, F. M. Izrailev and J. Ford; 3. Quantum dynamics of a nonintegrable system D. R. Grempel, R. E. Prange and S. E. Fishman; 4. Excitation of molecular rotation by periodic microwave pulses. A testing ground for Anderson localization R. Blümel, S. Fishman and U. Smilansky; 5. Localization of diffusive excitation in multi-level systems D. K. Shepelyansky; 6. Classical and quantum chaos for a kicked top F. Haake, M. Kus and R. Scharf; 7. Self-similarity in quantum dynamics L. E. Reichl and L. Haoming; 8. Time irreversibility of classically chaotic quantum dynamics K. Ikeda; 9. Effect of noise on time-dependent quantum chaos E. Ott, T. M. Antonsen Jr and J. D. Hanson; 10. Dynamical localization, dissipation and noise R. F. Graham; 11. Maximum entropy models and quantum transmission in disordered systems J.-L. Pichard and M. Sanquer; 12. Solid state 'atoms' in intense oscillating fields M. S. Sherwin; Part II. Atoms in Strong Fields: 13. Localization of classically chaotic diffusion for hydrogen atoms in microwave fields J. E. Bayfield, G. Casati, I. Guarneri and D. W. Sokol; 14. Inhibition of quantum transport due to 'scars' of unstable periodic orbits R. V. Jensen, M. M. Sanders, M. Saraceno and B. Sundaram; 15. Rubidium Rydberg atoms in strong fields G. Benson, G. Raithel and H. Walther; 16. Diamagnetic Rydberg atom: confrontation of calculated and observed spectra C.-H. Iu, G. R. Welch, M. M. Kash, D. Kleppner, D. Delande and J. C. Gay; 17. Semiclassical approximation for the quantum states of a hydrogen atom in a magnetic field near the ionization limit M. Y. Kuchiev and O. P. Sushkov; 18. The semiclassical helium atom D. Wintgen, K. Richter and G. Tanner; 19. Stretched helium: a model for quantum chaos

  14. Iani Chaos

    NASA Technical Reports Server (NTRS)

    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.

  15. Does chaos assist localization or delocalization?

    SciTech Connect

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

    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.

  16. Docosahexaenoic acid confers enduring neuroprotection in experimental stroke.

    PubMed

    Hong, Sung-Ha; Belayev, Ludmila; Khoutorova, Larissa; Obenaus, Andre; Bazan, Nicolas G

    2014-03-15

    Recently we demonstrated that docosahexaenoic acid (DHA) is highly neuroprotective when animals were allowed to survive during one week. This study was conducted to establish whether the neuroprotection induced by DHA persists with chronic survival. Sprague-Dawley rats underwent 2h of middle cerebral artery occlusion (MCAo) and treated with DHA or saline at 3h after MCAo. Animals received neurobehavioral examination (composite neuroscore, rota-rod, beam walking and Y maze tests) followed by ex vivo magnetic resonance imaging and histopathology at 3 weeks. DHA improved composite neurologic score beginning on day 1 by 20%, which persisted throughout weeks 1-3 by 24-41% compared to the saline-treated group. DHA prolonged the latency in rota-rod on weeks 2-3 by 162-178%, enhanced balance performance in the beam walking test on weeks 1 and 2 by 42-51%, and decreased the number of entries in the Y maze test by 51% and spontaneous alteration by 53% on week 2 compared to the saline-treated group. DHA treatment reduced tissue loss (computed from T2-weighted images) by 24% and total and cortical infarct volumes by 46% and 54% compared to the saline-treated group. These results show that DHA confers enduring ischemic neuroprotection. PMID:24433927

  17. Chronic exercise confers neuroprotection in experimental autoimmune encephalomyelitis.

    PubMed

    Pryor, William M; Freeman, Kimberly G; Larson, Rebecca D; Edwards, Gaylen L; White, Lesley J

    2015-05-01

    Multiple sclerosis (MS) is an autoimmune disease that affects the CNS, resulting in accumulated loss of cognitive, sensory, and motor function. This study evaluates the neuropathological effects of voluntary exercise in mice with experimental autoimmune encephalomyelitis (EAE), an animal model of MS. Two groups of C57BL/6J mice were injected with an emulsion containing myelin oligodendrocyte glycoprotein and then randomized to housing with a running wheel or a locked wheel. Exercising EAE mice exhibited a less severe neurological disease score and later onset of disease compared with sedentary EAE animals. Immune cell infiltration and demyelination in the ventral white matter tracts of the lumbar spinal cord were significantly reduced in the EAE exercise group compared with sedentary EAE animals. Neurofilament immunolabeling in the ventral pyramidal and extrapyramidal motor tracts displayed a more random distribution of axons and an apparent loss of smaller diameter axons, with a greater loss of fluorescence immunolabeling in the sedentary EAE animals. In lamina IX gray matter regions of the lumbar spinal cord, sedentary animals with EAE displayed a greater loss of α-motor neurons compared with EAE animals exposed to exercise. These findings provide evidence that voluntary exercise results in reduced and attenuated disability, reductions in autoimmune cell infiltration, and preservation of axons and motor neurons in the lumbar spinal cord of mice with EAE.

  18. Network inference from functional experimental data (Conference Presentation)

    NASA Astrophysics Data System (ADS)

    Desrosiers, Patrick; Labrecque, Simon; Tremblay, Maxime; Bélanger, Mathieu; De Dorlodot, Bertrand; Côté, Daniel C.

    2016-03-01

    Functional connectivity maps of neuronal networks are critical tools to understand how neurons form circuits, how information is encoded and processed by neurons, how memory is shaped, and how these basic processes are altered under pathological conditions. Current light microscopy allows to observe calcium or electrical activity of thousands of neurons simultaneously, yet assessing comprehensive connectivity maps directly from such data remains a non-trivial analytical task. There exist simple statistical methods, such as cross-correlation and Granger causality, but they only detect linear interactions between neurons. Other more involved inference methods inspired by information theory, such as mutual information and transfer entropy, identify more accurately connections between neurons but also require more computational resources. We carried out a comparative study of common connectivity inference methods. The relative accuracy and computational cost of each method was determined via simulated fluorescence traces generated with realistic computational models of interacting neurons in networks of different topologies (clustered or non-clustered) and sizes (10-1000 neurons). To bridge the computational and experimental works, we observed the intracellular calcium activity of live hippocampal neuronal cultures infected with the fluorescent calcium marker GCaMP6f. The spontaneous activity of the networks, consisting of 50-100 neurons per field of view, was recorded from 20 to 50 Hz on a microscope controlled by a homemade software. We implemented all connectivity inference methods in the software, which rapidly loads calcium fluorescence movies, segments the images, extracts the fluorescence traces, and assesses the functional connections (with strengths and directions) between each pair of neurons. We used this software to assess, in real time, the functional connectivity from real calcium imaging data in basal conditions, under plasticity protocols, and epileptic

  19. Noisy Chaos

    NASA Astrophysics Data System (ADS)

    Crutchfield, James Patrick, Jr.

    Deterministic dynamics often leads to complex, unpredictable behavior. This randomness or chaos produces information and limits one's ability to predict future events. There are two components to this imposed ignorance. The first arises in a mathematical context from highly convoluted orbit structures in state space. These allow a system to rapidly visit many regions of state space. In a physical context, the second comes from the coupling of the system -under-study to other systems that provide information to it. Extrinsic information sources preclude the exact determination of the system's state. By the mechanism of their complex orbits, chaotic systems amplify this uncertainty into unpredictable macroscopic behavior. The physical study of chaotic dynamical systems is incomplete without an appreciation of how external fluctuations affect their predictability. Using information theory we describe how to measure the unpredictability of (i) deterministic chaotic systems (without extrinsic noise), and (ii) nondeterministic chaotic systems (coupled to extrinsic noise). Scaling concepts are invaluable tools in this. Scaling reveals that extrinsic noise acts as a disordering field for chaos. Furthermore, even for systems with extrinsic noise, scaling captures fundamental features of chaotic behavior. It provides a unified framework for the topological, metric, and Renyi dimensions and entropies. The physical relevance of these concepts lies in their ability to analyze noisy chaotic signals. The information theoretic approach to temporally complex behavior is applied to chaotic signals from two hydrodynamic experiments. In addition, the dynamic aspects of pattern evolution and the possible breakdown of (naive) dynamical systems theory is discussed for experiments with an image processing system. The first appendix contains descriptions of algorithms for dynamical systems studies. The second discusses a movie on the geometric structure of chaotic driven oscillators using

  20. Advanced chaos forecasting

    NASA Astrophysics Data System (ADS)

    Doerner, R.; Hübinger, B.; Martienssen, W.

    1994-07-01

    The exponential separation of initially adjacent trajectories restricts the predictability of deterministic chaotic motions. The predictability depends on the initial state from where the trajectory starts that shall be forecasted. By calculating the predictability simultaneously with the forecast, we are able to reject forecasts with low reliability immediately, thereby decreasing drastically the average forecast error. We test this scheme experimentally on Chua's circuit [Komuro, Tokunaga, Matsumoto, Chua, and Hotta, Int. J. Bifurc. Chaos 1, 139 (1991)], basing all calculations only on a time series of a single scalar variable.

  1. Controlling chaos with simple limiters

    PubMed

    Corron; Pethel; Hopper

    2000-04-24

    New experimental results demonstrate that chaos control can be accomplished using controllers that are very simple relative to the system being controlled. Chaotic dynamics in a driven pendulum and a double scroll circuit are controlled using an adjustable, passive limiter-a weight for the pendulum and a diode for the circuit. For both experiments, multiple unstable periodic orbits are selectively controlled using minimal perturbations. These physical examples suggest that chaos control can be practically applied to a much wider array of important problems than initially thought possible. PMID:11019218

  2. Chaos and Fractals.

    ERIC Educational Resources Information Center

    Barton, Ray

    1990-01-01

    Presented is an educational game called "The Chaos Game" which produces complicated fractal images. Two basic computer programs are included. The production of fractal images by the Sierpinski gasket and the Chaos Game programs is discussed. (CW)

  3. Embrace the Chaos

    ERIC Educational Resources Information Center

    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 some degree…

  4. The Case for Chaos.

    ERIC Educational Resources Information Center

    Bedford, Crayton W.

    1998-01-01

    Outlines a course on fractal geometry and chaos theory. Discusses how chaos theory and fractal geometry have begun to appear as separate units in the mathematics curriculum and offers an eight unit course by pulling together units related to chaos theory and fractal geometry. Contains 25 references. (ASK)

  5. Physics and applications of laser diode chaos

    NASA Astrophysics Data System (ADS)

    Sciamanna, M.; Shore, K. A.

    2015-03-01

    This Review Article provides an overview of chaos in laser diodes by surveying experimental achievements in the area and explaining the theory behind the phenomenon. The fundamental physics underpinning laser diode chaos and also the opportunities for harnessing it for potential applications are discussed. The availability and ease of operation of laser diodes, in a wide range of configurations, make them a convenient testbed for exploring basic aspects of nonlinear and chaotic dynamics. It also makes them attractive for practical tasks, such as chaos-based secure communications and random number generation. Avenues for future research and development of chaotic laser diodes are also identified.

  6. Using the sensitive dependence of chaos (the butterfly effect'') to direct trajectories in an experimental chaotic system

    SciTech Connect

    Shinbrot, T.; Ditto, W.; Grebogi, C.; Ott, E.; Spano, M.; Yorke, J.A. Department of Physics, The College of Wooster, Wooster, Ohio 44691 Naval Surface Warfare Center, Silver Spring, Maryland 20902 )

    1992-05-11

    In this paper we present the first experimental verification that the sensitivity of a chaotic system to small perturbations (the butterfly effect'') can be used to rapidly direct orbits from an arbitrary initial state to an arbitrary accessible desired state.

  7. Effective suppressibility of chaos.

    PubMed

    López, Álvaro G; Seoane, Jesús M; Sanjuán, Miguel A F

    2013-06-01

    Suppression of chaos is a relevant phenomenon that can take place in nonlinear dynamical systems when a parameter is varied. Here, we investigate the possibilities of effectively suppressing the chaotic motion of a dynamical system by a specific time independent variation of a parameter of our system. In realistic situations, we need to be very careful with the experimental conditions and the accuracy of the parameter measurements. We define the suppressibility, a new measure taking values in the parameter space, that allows us to detect which chaotic motions can be suppressed, what possible new choices of the parameter guarantee their suppression, and how small the parameter variations from the initial chaotic state to the final periodic one are. We apply this measure to a Duffing oscillator and a system consisting on ten globally coupled Hénon maps. We offer as our main result tool sets that can be used as guides to suppress chaotic dynamics. PMID:23822472

  8. Chaos and microbial systems

    SciTech Connect

    Kot, M.

    1991-01-01

    Much of the recent work in nonlinear dynamics has centered on new techniques for identifying order in seemingly chaotic systems. To determine the robustness of these techniques, chaos must, to some extent, be brought into the laboratory. Preliminary investigations of the forded double-Monod equations, a model for a predator and a prey in a chemostat with periodic variation of inflowing substrate, suggested that simple microbial systems might provide the perfect framework for determining the efficacy and relevance of the new nonlinear dynamics in dealing with complex population dynamics. Progress in two areas of research, mathematical analysis and computer simulation of the periodically forced double-Monod equations and of related models; and experimental (chemostat) population studies that evaluate the accuracy and generality of the models, (and also judge the usefulness of various new techniques of nonlinear dynamics to the study of populations) is reported.

  9. Unpredictable points and chaos

    NASA Astrophysics Data System (ADS)

    Akhmet, Marat; Fen, Mehmet Onur

    2016-11-01

    It is revealed that a special kind of Poisson stable point, which we call an unpredictable point, gives rise to the existence of chaos in the quasi-minimal set. The existing definitions of chaos are formulated in sets of motions. This is the first time in the literature that description of chaos is initiated from a single motion. The theoretical results are exemplified by means of the symbolic dynamics.

  10. Experimental synchronization of chaos in a large ring of mutually coupled single-transistor oscillators: phase, amplitude, and clustering effects.

    PubMed

    Minati, Ludovico

    2014-12-01

    In this paper, experimental evidence of multiple synchronization phenomena in a large (n = 30) ring of chaotic oscillators is presented. Each node consists of an elementary circuit, generating spikes of irregular amplitude and comprising one bipolar junction transistor, one capacitor, two inductors, and one biasing resistor. The nodes are mutually coupled to their neighbours via additional variable resistors. As coupling resistance is decreased, phase synchronization followed by complete synchronization is observed, and onset of synchronization is associated with partial synchronization, i.e., emergence of communities (clusters). While component tolerances affect community structure, the general synchronization properties are maintained across three prototypes and in numerical simulations. The clusters are destroyed by adding long distance connections with distant notes, but are otherwise relatively stable with respect to structural connectivity changes. The study provides evidence that several fundamental synchronization phenomena can be reliably observed in a network of elementary single-transistor oscillators, demonstrating their generative potential and opening way to potential applications of this undemanding setup in experimental modelling of the relationship between network structure, synchronization, and dynamical properties. PMID:25554028

  11. Experimental synchronization of chaos in a large ring of mutually coupled single-transistor oscillators: Phase, amplitude, and clustering effects

    SciTech Connect

    Minati, Ludovico E-mail: ludovico.minati@unitn.it

    2014-12-01

    In this paper, experimental evidence of multiple synchronization phenomena in a large (n = 30) ring of chaotic oscillators is presented. Each node consists of an elementary circuit, generating spikes of irregular amplitude and comprising one bipolar junction transistor, one capacitor, two inductors, and one biasing resistor. The nodes are mutually coupled to their neighbours via additional variable resistors. As coupling resistance is decreased, phase synchronization followed by complete synchronization is observed, and onset of synchronization is associated with partial synchronization, i.e., emergence of communities (clusters). While component tolerances affect community structure, the general synchronization properties are maintained across three prototypes and in numerical simulations. The clusters are destroyed by adding long distance connections with distant notes, but are otherwise relatively stable with respect to structural connectivity changes. The study provides evidence that several fundamental synchronization phenomena can be reliably observed in a network of elementary single-transistor oscillators, demonstrating their generative potential and opening way to potential applications of this undemanding setup in experimental modelling of the relationship between network structure, synchronization, and dynamical properties.

  12. Controlling chaos in a fast diode resonator using extended time-delay autosynchronization: Experimental observations and theoretical analysis.

    PubMed

    Sukow, David W.; Bleich, Michael E.; Gauthier, Daniel J.; Socolar, Joshua E. S.

    1997-12-01

    We stabilize unstable periodic orbits of a fast diode resonator driven at 10.1 MHz (corresponding to a drive period under 100 ns) using extended time-delay autosynchronization. Stabilization is achieved by feedback of an error signal that is proportional to the difference between the value of a state variable and an infinite series of values of the state variable delayed in time by integral multiples of the period of the orbit. The technique is easy to implement electronically and it has an all-optical counterpart that may be useful for stabilizing the dynamics of fast chaotic lasers. We show that increasing the weights given to temporally distant states enlarges the domain of control and reduces the sensitivity of the domain of control on the propagation delays in the feedback loop. We determine the average time to obtain control as a function of the feedback gain and identify the mechanisms that destabilize the system at the boundaries of the domain of control. A theoretical stability analysis of a model of the diode resonator in the presence of time-delay feedback is in good agreement with the experimental results for the size and shape of the domain of control. (c) 1997 American Institute of Physics. PMID:12779682

  13. Teaching as Chaos

    ERIC Educational Resources Information Center

    Moseley, Bryan; Dustin, Daniel

    2008-01-01

    In this article, the authors advance a metaphor born of chaos theory that views the college classroom as a complex dynamical system. The authors reason further that "teaching as chaos" provides a more accurate representation of the teaching-learning process than the existing linear scientific metaphors on which traditional learning assessments are…

  14. "Chaos Rules" Revisited

    ERIC Educational Resources Information Center

    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…

  15. Understanding chaos via nuclei

    SciTech Connect

    Cejnar, Pavel; Stránský, Pavel

    2014-01-08

    We use two models of nuclear collective dynamics-the geometric collective model and the interacting boson model-to illustrate principles of classical and quantum chaos. We propose these models as a suitable testing ground for further elaborations of the general theory of chaos in both classical and quantum domains.

  16. Chaos and Compassion.

    ERIC Educational Resources Information Center

    Gelatt, H. B.

    1995-01-01

    Before chaos theory, Western society had no "scientific" tools to deal with disorder and unpredictability because science relied on factual evidence. With chaos theory, knowing and believing are now seen as interconnected and both are considered authentic. Counseling should reflect this authenticity with compassion, not control. (LKS)

  17. Chaos in Josephson circuits

    SciTech Connect

    Kautz, R.

    1983-05-01

    Chaotic behavior in Josephson circuits is reviewed using the rf-driven junction as an example. Topics include the effect of chaos on the I-V characteristic, the period doubling route to chaos, and power spectra for the chaotic state. Liapunov exponents and the fractal geometry of strange attractors are also discussed.

  18. 1990 SEM Spring Conference on Experimental Mechanics, Albuquerque, NM, June 4-6, 1990, Proceedings

    SciTech Connect

    Not Available

    1990-01-01

    The present conference on experimental mechanics encompasses industrial applications of photoelasticity, measurement techniques for residual stress, applications for the strain gage, digital image analysis, optical methods such as acoustoelasticity, smart structures, noncontacting sensing techniques, photoelasticity, and the fracture of engineered materials. Specific issues addressed include the energy-density approach to inelastic strain, techniques for measuring fiber response to transient moisture exposure, the application of photoelasticity to analyzing shaft splines, the yield behavior of polyethylene tubes, the calibration of composite-embedded fiber-optic strain sensors, and the design of a force transducer. Also addressed are applications of morphological filters to digital image processing, the testing of miniatures, the hardness testing of metals, stress concentrations in tube intersections, and crack propagation in a composite solid propellant.

  19. Galveston Brain Injury Conference 2010: clinical and experimental aspects of blast injury.

    PubMed

    Masel, Brent E; Bell, Randy S; Brossart, Shawn; Grill, Raymond J; Hayes, Ronald L; Levin, Harvey S; Rasband, Matthew N; Ritzel, David V; Wade, Charles E; DeWitt, Douglas S

    2012-08-10

    Blast injury is the most prevalent source of mortality and morbidity among combatants in Operations Iraqi and Enduring Freedom. Blast-induced neurotrauma (BINT) is a common cause of mortality, and even mild BINT may be associated with chronic cognitive and emotional deficits. In addition to military personnel, the increasing use of explosives by terrorists has resulted in growing numbers of blast injuries in civilian populations. Since the medical and rehabilitative communities are likely to be faced with increasing numbers of patients suffering from blast injury, the 2010 Galveston Brain Injury Conference focused on topics related to the diagnosis, treatment, and mechanisms of BINT. Although past military actions have resulted in large numbers of blast casualties, BINT is considered the signature injury of the conflicts in Iraq and Afghanistan. The attention focused on BINT has led to increased financial support for research on blast effects, contributing to the development of better experimental models of blast injury and a clearer understanding of the mechanisms of BINT. This more thorough understanding of blast injury mechanisms will result in novel and more effective therapeutic and rehabilitative strategies designed to reduce injury and facilitate recovery, thereby improving long-term outcomes in patients suffering from the devastating and often lasting effects of BINT. The following is a summary of the 2010 Galveston Brain Injury Conference, that included presentations related to the diagnosis and treatment of acute BINT, the evaluation of the long-term neuropsychological effects of BINT, summaries of current experimental models of BINT, and a debate about the relative importance of primary blast effects on the acute and long-term consequences of blast exposure.

  20. A bound on chaos

    NASA Astrophysics Data System (ADS)

    Maldacena, Juan; Shenker, Stephen H.; Stanford, Douglas

    2016-08-01

    We conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order correlation function closely related to the commutator of operators separated in time. We conjecture that the influence of chaos on this correlator can develop no faster than exponentially, with Lyapunov exponent λ L ≤ 2π k B T/ℏ. We give a precise mathematical argument, based on plausible physical assumptions, establishing this conjecture.

  1. Genome chaos: survival strategy during crisis.

    PubMed

    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. Chaos, Fractals, and Polynomials.

    ERIC Educational Resources Information Center

    Tylee, J. Louis; Tylee, Thomas B.

    1996-01-01

    Discusses chaos theory; linear algebraic equations and the numerical solution of polynomials, including the use of the Newton-Raphson technique to find polynomial roots; fractals; search region and coordinate systems; convergence; and generating color fractals on a computer. (LRW)

  3. Exploiting chaos for applications

    SciTech Connect

    Ditto, William L.; Sinha, Sudeshna

    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.

  4. Chaos and microbial systems

    SciTech Connect

    Kot, M.

    1990-07-01

    A recurrent theme of much recent research is that seemingly random fluctuations often occur as the result of simple deterministic mechanisms. Hence, much of the recent work in nonlinear dynamics has centered on new techniques for identifying order in seemingly chaotic systems. To determine the robustness of these techniques, chaos must, to some extent, be brought into the laboratory. Preliminary investigations of the forced double-Monod equations, a model for a predator and a prey in a chemostat with periodic variation in inflowing substrate concentration, suggest that simple microbial systems may provide the perfect framework for determining the efficacy and relevance of the new nonlinear dynamics in dealing with complex population dynamics. This research has two main goals, that is the mathematical analysis and computer simulation of the periodically forced double-Monod equations and of related models; and experimental (chemostat) population studies that evaluate the accuracy and generality of the models, and that judge the usefulness of various new techniques of nonlinear dynamics to the study of populations.

  5. How to Generate Chaos at Home.

    ERIC Educational Resources Information Center

    Smith, Douglas

    1992-01-01

    Describes an electronic circuit that can function as a prototype for chaotic systems. Specific applied voltages produce chaotic signals that can be viewed with an oscilloscope or be made audible with a home stereo system. Provides directions for assembly with typical costs, mathematical basis of chaos theory, and experimental extensions. (JJK)

  6. A novel chaos danger model immune algorithm

    NASA Astrophysics Data System (ADS)

    Xu, Qingyang; Wang, Song; Zhang, Li; Liang, Ying

    2013-11-01

    Making use of ergodicity and randomness of chaos, a novel chaos danger model immune algorithm (CDMIA) is presented by combining the benefits of chaos and danger model immune algorithm (DMIA). To maintain the diversity of antibodies and ensure the performances of the algorithm, two chaotic operators are proposed. Chaotic disturbance is used for updating the danger antibody to exploit local solution space, and the chaotic regeneration is referred to the safe antibody for exploring the entire solution space. In addition, the performances of the algorithm are examined based upon several benchmark problems. The experimental results indicate that the diversity of the population is improved noticeably, and the CDMIA exhibits a higher efficiency than the danger model immune algorithm and other optimization algorithms.

  7. Chaos in the Classroom: An Application of Chaos Theory.

    ERIC Educational Resources Information Center

    Trygestad, JoAnn

    A review of studies on chaos theory suggests that some elements of the theory (systems, fractals, initial effects, and bifurcations) may be applied to classroom learning. Chaos theory considers learning holistic, constructive, and dynamic. Some researchers suggest that applying chaos theory to the classroom enhances learning by reinforcing…

  8. Fractal Patterns and Chaos Games

    ERIC Educational Resources Information Center

    Devaney, Robert L.

    2004-01-01

    Teachers incorporate the chaos game and the concept of a fractal into various areas of the algebra and geometry curriculum. The chaos game approach to fractals provides teachers with an opportunity to help students comprehend the geometry of affine transformations.

  9. Order, Chaos and All That!

    ERIC Educational Resources Information Center

    Glasser, L.

    1989-01-01

    The evolution of ideas about the concept of chaos is surveyed. Discussed are chaos in deterministic, dynamic systems; order in dissipative systems; and thermodynamics and irreversibility. Included are logistic and bifurcation maps to illustrate points made in the discussion. (CW)

  10. Chaos, Topology, and Social Organization.

    ERIC Educational Resources Information Center

    Marion, Russ

    1992-01-01

    Applies chaos theory to complex social organization, beginning with a mathematical definition of chaos. Shows how a nonlinear equation might be used to describe organization. The conclusion section identifies three approaches to analyzing chaos in social organization: metaphorical analysis, mathematical modeling, and data collection. (36…

  11. Vaccination with Recombinant Microneme Proteins Confers Protection against Experimental Toxoplasmosis in Mice.

    PubMed

    Pinzan, Camila Figueiredo; Sardinha-Silva, Aline; Almeida, Fausto; Lai, Livia; Lopes, Carla Duque; Lourenço, Elaine Vicente; Panunto-Castelo, Ademilson; Matthews, Stephen; Roque-Barreira, Maria Cristina

    2015-01-01

    Toxoplasmosis, a zoonotic disease caused by Toxoplasma gondii, is an important public health problem and veterinary concern. Although there is no vaccine for human toxoplasmosis, many attempts have been made to develop one. Promising vaccine candidates utilize proteins, or their genes, from microneme organelle of T. gondii that are involved in the initial stages of host cell invasion by the parasite. In the present study, we used different recombinant microneme proteins (TgMIC1, TgMIC4, or TgMIC6) or combinations of these proteins (TgMIC1-4 and TgMIC1-4-6) to evaluate the immune response and protection against experimental toxoplasmosis in C57BL/6 mice. Vaccination with recombinant TgMIC1, TgMIC4, or TgMIC6 alone conferred partial protection, as demonstrated by reduced brain cyst burden and mortality rates after challenge. Immunization with TgMIC1-4 or TgMIC1-4-6 vaccines provided the most effective protection, since 70% and 80% of mice, respectively, survived to the acute phase of infection. In addition, these vaccinated mice, in comparison to non-vaccinated ones, showed reduced parasite burden by 59% and 68%, respectively. The protective effect was related to the cellular and humoral immune responses induced by vaccination and included the release of Th1 cytokines IFN-γ and IL-12, antigen-stimulated spleen cell proliferation, and production of antigen-specific serum antibodies. Our results demonstrate that microneme proteins are potential vaccines against T. gondii, since their inoculation prevents or decreases the deleterious effects of the infection.

  12. Harnessing quantum transport by transient chaos.

    PubMed

    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.

  13. Manifestation of resonance-related chaos in coupled Josephson junctions

    NASA Astrophysics Data System (ADS)

    Shukrinov, Yu. M.; Hamdipour, M.; Kolahchi, M. R.; Botha, A. E.; Suzuki, M.

    2012-11-01

    Manifestation of chaos in the temporal dependence of the electric charge is demonstrated through the calculation of the maximal Lyapunov exponent, phase-charge and charge-charge Lissajous diagrams and correlation functions. It is found that the number of junctions in the stack strongly influences the fine structure in the current-voltage characteristics and a strong proximity effect results from the nonperiodic boundary conditions. The observed resonance-related chaos exhibits intermittency. The criteria for a breakpoint region with no chaos are obtained. Such criteria could clarify recent experimental observations of variations in the power output from intrinsic Josephson junctions in high temperature superconductors.

  14. Organized Chaos at Europa?

    NASA Astrophysics Data System (ADS)

    Schmidt, B. E.; Blankenship, D. D.

    2010-12-01

    Historically one of the most studied and yet least constrained of Europa’s terrains, chaos regions are likely indicators of a geologically active ice shell. Chaos terrain is generally characterized by broken ice “raft” relicts of the former surface embayed by a dark, hummocky matrix rich in non-ice material. Chaos features, though they bear resemblance to broken-up terrestrial sea-ice, are generally topographically higher than the surrounding plains. Interior to these features topographic variation can also be found. From a geophysical perspective, chaos terrain may offer the possibility to test models for Europa’s ice shell thickness, its rheological properties, and its dynamics, since they occur ubiquitously across the surface. The existence of chaos terrain has, in the past, been used to suggest that either the shell is thin, and thus large-scale melt-through events have taken place to create chaos, or that the shell is actively convecting, and thus that the chaos terrain is formed by diapirism associated with rising plumes. Partial melt and the movement of warm ice have also been suggested to contribute to the formation of chaos. While these formation models are strongly tied to an ice thickness assumption, it is agreed that the break-up of ice and the subsequent motion of the blocks is suggestive of a material that has been free to flow at some point; the nature of the “fluidization” has not been discovered. In terrestrial marine ice sheets, brine infiltration is known to occur in porous layers called firn that are formed by annual accretion of snow. At the seaward edge of the sheet, or through tidally-formed basal cracks, sea water can percolate inward through the porous layer and travel kilometers from the source. In the McMurdo Ice shelf, brine extends radially through the ice to 10’s of km from the source at the shelf edge. In the Larsen ice shelf, a brine-laden layer of ice exists that does not reach the seaward edge, arguing that

  15. Quantifying chaos for ecological stoichiometry.

    PubMed

    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.

  16. In Citing Chaos.

    ERIC Educational Resources Information Center

    Paul, Danette

    2000-01-01

    Examines the role of citations both as reward and as rhetoric. Examines the reward system by tracing over time the citation patterns of 13 research articles by two groups of scientists in chaos theory. Reveals that scientists consistently used five rhetorical practices. Describes these five practices. (SG)

  17. Inverse anticipating chaos synchronization.

    PubMed

    Shahverdiev, E M; Sivaprakasam, S; Shore, K A

    2002-07-01

    We derive conditions for achieving inverse anticipating synchronization where a driven time-delay chaotic system synchronizes to the inverse future state of the driver. The significance of inverse anticipating chaos in delineating synchronization regimes in time-delay systems is elucidated. The concept is extended to cascaded time-delay systems.

  18. Experimental Investigation of 60 GHz Transmission Characteristics Between Computers on a Conference Table for WPAN Applications

    NASA Technical Reports Server (NTRS)

    Ponchak, George E.; Amadjikpe, Arnaud L.; Choudhury, Debabani; Papapolymerou, John

    2011-01-01

    In this paper, the first measurements of the received radiated power between antennas located on a conference table to simulate the environment of antennas embedded in laptop computers for 60 GHz Wireless Personal Area Network (WPAN) applications is presented. A high gain horn antenna and a medium gain microstrip patch antenna for two linear polarizations are compared. It is shown that for a typical conference table arrangement with five computers, books, pens, and coffee cups, the antennas should be placed a minimum of 5 cm above the table, but that a height of greater than 20 cm may be required to maximize the received power in all cases.

  19. Chaos Modeling: An Introduction and Research Application.

    ERIC Educational Resources Information Center

    Newman, Isadore; And Others

    1993-01-01

    Introduces the basic concepts of chaos theory and chaos modeling. Relates chaos theory to qualitative research and factor analysis. Describes some current research in education and psychology using chaos theory. Claims that the philosophical implications of chaos theory have been misapplied in practical terms. (KS)

  20. Chaos in the Belousov-Zhabotinsky reaction

    NASA Astrophysics Data System (ADS)

    Field, Richard J.

    2015-12-01

    The dynamics of reacting chemical systems is governed by typically polynomial differential equations that may contain nonlinear terms and/or embedded feedback loops. Thus the dynamics of such systems may exhibit features associated with nonlinear dynamical systems, including (among others): temporal oscillations, excitability, multistability, reaction-diffusion-driven formation of spatial patterns, and deterministic chaos. These behaviors are exhibited in the concentrations of intermediate chemical species. Bifurcations occur between particular dynamic behaviors as system parameters are varied. The governing differential equations of reacting chemical systems have as variables the concentrations of all chemical species involved, as well as controllable parameters, including temperature, the initial concentrations of all chemical species, and fixed reaction-rate constants. A discussion is presented of the kinetics of chemical reactions as well as some thermodynamic considerations important to the appearance of temporal oscillations and other nonlinear dynamic behaviors, e.g., deterministic chaos. The behavior, chemical details, and mechanism of the oscillatory Belousov-Zhabotinsky Reaction (BZR) are described. Furthermore, experimental and mathematical evidence is presented that the BZR does indeed exhibit deterministic chaos when run in a flow reactor. The origin of this chaos seems to be in toroidal dynamics in which flow-driven oscillations in the control species bromomalonic acid couple with the BZR limit cycle.

  1. Chaos in the Belousov-Zhabotinsky reaction

    NASA Astrophysics Data System (ADS)

    Field, Richard J.

    The dynamics of reacting chemical systems is governed by typically polynomial differential equations that may contain nonlinear terms and/or embedded feedback loops. Thus the dynamics of such systems may exhibit features associated with nonlinear dynamical systems, including (among others): temporal oscillations, excitability, multistability, reaction-diffusion-driven formation of spatial patterns, and deterministic chaos. These behaviors are exhibited in the concentrations of intermediate chemical species. Bifurcations occur between particular dynamic behaviors as system parameters are varied. The governing differential equations of reacting chemical systems have as variables the concentrations of all chemical species involved, as well as controllable parameters, including temperature, the initial concentrations of all chemical species, and fixed reaction-rate constants. A discussion is presented of the kinetics of chemical reactions as well as some thermodynamic considerations important to the appearance of temporal oscillations and other nonlinear dynamic behaviors, e.g., deterministic chaos. The behavior, chemical details, and mechanism of the oscillatory Belousov-Zhabotinsky Reaction (BZR) are described. Furthermore, experimental and mathematical evidence is presented that the BZR does indeed exhibit deterministic chaos when run in a flow reactor. The origin of this chaos seems to be in toroidal dynamics in which flow-driven oscillations in the control species bromomalonic acid couple with the BZR limit cycle...

  2. The 12th International Conference on Atomic Physics

    NASA Astrophysics Data System (ADS)

    Lewis, Robert R.; Rich, Arthur

    1991-02-01

    The conference began with a session devoted to the Nobel Laureates in Physics for 1989, all of whom were from the Atomic Physics community; Norman Ramsey and Hans Dehmelt spoke but Wolfgang Paul was unable to attend. Some sessions were titled as follows: Fundamental Laws and Constants; Atom and Ion Manipulation; Nonlinear Physics and Chaos; Quantum Optics and Other Laser Techniques; Photoionization Processes; Plasma Physics; Atomic Spectroscopy and Structure - Theory; Atomic Spectroscopy and Structure - Experimental; Molecular Spectroscopy and Structure, Surfaces, and Clusters; Atomic, Ionic, and Molecular Collisions; Electron and Positron Collisions; and Exotic Atomic and Special Topics.

  3. Chaos in neurons and its application: Perspective of chaos engineering

    NASA Astrophysics Data System (ADS)

    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.

  4. Chaos on the conveyor belt.

    PubMed

    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). PMID:23679502

  5. A Structure behind Primitive Chaos

    NASA Astrophysics Data System (ADS)

    Ogasawara, Yoshihito

    2015-06-01

    Recently, a new concept, primitive chaos, has been proposed as a concept closely related to the fundamental problems of physics itself such as determinism, causality, free will, predictability, and irreversibility [J. Phys. Soc. Jpn. 79, 015002 (2010)]. This paper reveals a structure hidden behind the primitive chaos; under some conditions, a new primitive chaos is constructed from the original primitive chaos, this procedure can be repeated, and the hierarchical structure of the primitive chaos is obtained. This implies such a picture that new events and causality are constructed from the old ones, with the aid of the concept of a coarse graining. As an application of this structure, interesting facts are revealed for the essential condition of the primitive chaos and for chaotic behaviors.

  6. The joy of transient chaos

    SciTech Connect

    Tél, Tamás

    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.

  7. The joy of transient chaos

    NASA Astrophysics Data System (ADS)

    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.

  8. Gullies of Gorgonus Chaos

    NASA Technical Reports Server (NTRS)

    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

  9. Chaos in quantum channels

    NASA Astrophysics Data System (ADS)

    Hosur, Pavan; Qi, Xiao-Liang; Roberts, Daniel A.; Yoshida, Beni

    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.

  10. Controlling chaos faster

    SciTech Connect

    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.

  11. Chaos in quantum channels

    DOE PAGES

    Hosur, Pavan; Qi, Xiao-Liang; Roberts, Daniel A.; Yoshida, Beni

    2016-02-01

    For this research, 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 upmore » our results with numerics in two non-integrable models and analytic results in a perfect tensor network model of chaotic time evolution. In conclusion, these results show that the butterfly effect in quantum systems implies the information-theoretic definition of scrambling.« less

  12. The Chinese chaos game

    NASA Astrophysics Data System (ADS)

    Matsushita, Raul; Gleria, Iram; Figueiredo, Annibal; Da Silva, Sergio

    2007-05-01

    The yuan-dollar returns prior to the 2005 revaluation show a Sierpinski triangle in an iterated function system clumpiness test. Yet the fractal vanishes after the revaluation. The Sierpinski commonly emerges in the chaos game, where randomness coexists with deterministic rules (M.F. Barnsley, Fractals Everywhere, Academic Press, San Diego, 1988; H.O. Peitgen, H. Jurgens, D. Saupe, Chaos and Fractals: New Frontiers of Science, Springer, New York, 1992). Here, it is explained by the yuan's pegs to the US dollar, which made more than half of the data points close to zero. Extra data from the Brazilian and Argentine experiences do confirm that the fractal emerges whenever exchange rate pegs are kept for too long.

  13. Arsinoes Chaos Landforms

    NASA Technical Reports Server (NTRS)

    2004-01-01

    23 October 2004 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows light-toned rock outcrops, possibly sedimentary rocks, in the Arsinoes Chaos region east of the Valles Marineris trough system. These rocky materials were once below the martian surface. These features are located near 7.2oS, 27.9oW. The image covers an area about 3 km (1.9 mi) wide. Sunlight illuminates the scene from the upper left.

  14. Noise tolerant spatiotemporal chaos computing

    SciTech Connect

    Kia, Behnam; Kia, Sarvenaz; Ditto, William L.; Lindner, John F.; Sinha, Sudeshna

    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.

  15. Relativistic chaos is coordinate invariant.

    PubMed

    Motter, Adilson E

    2003-12-01

    The noninvariance of Lyapunov exponents in general relativity has led to the conclusion that chaos depends on the choice of the space-time coordinates. Strikingly, we uncover the transformation laws of Lyapunov exponents under general space-time transformations and we find that chaos, as characterized by positive Lyapunov exponents, is coordinate invariant. As a result, the previous conclusion regarding the noninvariance of chaos in cosmology, a major claim about chaos in general relativity, necessarily involves the violation of hypotheses required for a proper definition of the Lyapunov exponents. PMID:14683170

  16. Polynomiography and Chaos

    NASA Astrophysics Data System (ADS)

    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.

  17. Quantum chaos in QCD and hadrons

    NASA Astrophysics Data System (ADS)

    Markum, Harald; Plessas, Willibald; Pullirsch, Rainer; Sengl, Bianka; Wagenbrunn, Robert F.

    This article starts with an introduction into quantum chaos and its relationship to classical chaos. The Bohigas-Giannoni-Schmit conjecture is formulated and evaluated within the random-matrix theory. The objective of the presentation is twofold and begins with recent results on quantum chromodynamics and the quarkgluon plasma. We conclude with recent research work on the spectroscopy of baryons. Within the framework of a relativistic constituent quark model we investigate the excitation spectra of the nucleon and the delta with regard to a possible chaotic behavior for the cases when a hyperfine interaction of either Goldstone-boson-exchange or one-gluon-exchange type is added to the confinement interaction. Agreement with the experimental hadron spectrum is established.

  18. EXPERIMENTAL CURRICULA IN CHEMISTRY, A REPORT OF THE A.C.C.C. CONFERENCE ON CURRICULUM EXPERIMENTATION (CHICAGO, OCTOBER 1963).

    ERIC Educational Resources Information Center

    HUME, DAVID N.

    FOUR PROGRAMS ARE IDENTIFIED AND DESCRIBED AS REPRESENTATIVE OF THE EXPERIMENTATION BEING CONDUCTED IN THE UNDERGRADUATE CHEMISTRY CURRICULUM IN AMERICAN HIGHER EDUCATION. (1) THE UNIVERSITY OF ILLINOIS AND THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY REQUIRE THAT A STUDENT TAKE A GROUP OF "CORE" COURSES WHICH PROVIDE, RELATIVELY EARLY IN HIS…

  19. Counseling Chaos: Techniques for Practitioners

    ERIC Educational Resources Information Center

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

    2006-01-01

    The chaos theory of careers draws together a number of themes in current theory and research. This article applies some of these themes to career counseling. The chaos theory of careers is outlined, and a conceptual framework for understanding assessment and counseling issues that focuses on convergent and emergent qualities is presented. Three…

  20. Chaos Theory and Post Modernism

    ERIC Educational Resources Information Center

    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…

  1. Chaos Criminology: A critical analysis

    NASA Astrophysics Data System (ADS)

    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.

  2. Quantum bouncer with chaos

    NASA Astrophysics Data System (ADS)

    Dembiński, S. T.; Makowski, A. J.; Pepłowski, P.

    1993-02-01

    We report for the first time quantum calculations for the so-called bouncer model, the classical analog of which is well known to manifest a chaotic behavior. Three versions of our model are fully tractable quantum mechanically and are potentially a rich source of data for establishing properties of a quantum system of which the classical mechanics can be chaotic. Among the results presented here, consequences of the varying bandwidth of infinite-dimensional transition matrices on the use of the correspondence between classical chaos and non-Poissonian quasienergy statistics are discussed.

  3. Landslide in Aureum Chaos

    NASA Technical Reports Server (NTRS)

    2004-01-01

    15 May 2004 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows the results of a small landslide off of a hillslope in the Aureum Chaos region of Mars. Mass movement occurred from right (the slope) to left (the lobate feature pointed left). Small dark dots in the landslide area are large boulders. This feature is located near 2.6oS, 24.5oW. This picture covers an area approximately 3 km (1.9 mi) across and is illuminated by sunlight from the left/upper left.

  4. Between order and chaos

    NASA Astrophysics Data System (ADS)

    Crutchfield, James P.

    2012-01-01

    What is a pattern? How do we come to recognize patterns never seen before? Quantifying the notion of pattern and formalizing the process of pattern discovery go right to the heart of physical science. Over the past few decades physics' view of nature's lack of structure--its unpredictability--underwent a major renovation with the discovery of deterministic chaos, overthrowing two centuries of Laplace's strict determinism in classical physics. Behind the veil of apparent randomness, though, many processes are highly ordered, following simple rules. Tools adapted from the theories of information and computation have brought physical science to the brink of automatically discovering hidden patterns and quantifying their structural complexity.

  5. Firefly algorithm with chaos

    NASA Astrophysics Data System (ADS)

    Gandomi, A. H.; Yang, X.-S.; Talatahari, S.; Alavi, A. H.

    2013-01-01

    A recently developed metaheuristic optimization algorithm, firefly algorithm (FA), mimics the social behavior of fireflies based on the flashing and attraction characteristics of fireflies. In the present study, we will introduce chaos into FA so as to increase its global search mobility for robust global optimization. Detailed studies are carried out on benchmark problems with different chaotic maps. Here, 12 different chaotic maps are utilized to tune the attractive movement of the fireflies in the algorithm. The results show that some chaotic FAs can clearly outperform the standard FA.

  6. Aram Chaos Rocks

    NASA Technical Reports Server (NTRS)

    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. Chaos Theory, Philosophically Old, Scientifically New.

    ERIC Educational Resources Information Center

    Butz, Michael R.

    1995-01-01

    Chaos theory has recently become a central area of scientific interest in psychology. This article explores the psychological meaning and deeper philosophical issues and cultural roots surrounding various views of chaos and provides a multicultural perspective of origins and development of the idea of chaos and its relationship to chaos theory.…

  8. Erotism and chaos.

    PubMed

    Giovacchini, P L

    1990-01-01

    There is a continuum from primitive, undifferentiated feelings that are simply the manifestations of homeostatic balance and imbalance to highly differentiated, pleasurable erotic feelings that characterize mature, intimate love relationships. Sensory reactions are elevated from simple reflex levels to highly complex, sophisticated affects that involve wide areas of the psyche. Thus, affects are associated with integration and organized psychic structure. Consequently they may function in various ways. Freud developed a continuum for anxiety as initially functioning as a conversion reaction enabling sexual feelings that cannot reach mentational levels or be consummated in erotic activity to be discharged. It reaches a final level of organization where it serves as a signal calling various defenses into play as emerging instinctual impulses threaten to upset psychodynamic equilibrium. I have focused on how affects, erotic feelings in particular, have an organizing function that binds a primitive inner agitation that occurs during what is called a prementational stage of the neonatal period. This is a stage that precedes psychological processes. Sexual feelings are generated as an attempt to bind inner chaos that stems from an amorphous, inchoate psychic state. Erotic feelings are experienced in order to smoothe inner tension. The patient tries but seldom achieves calm because the affective binding and structuralizing process, in itself, becomes painful and disruptive. I present several clinical incidents and also refer to so-called treatment relationships where the therapist absorbs the patient's chaos and then acts out sexually which leads to a total breakdown of the therapeutic setting. PMID:2354974

  9. Explorations in Chaos Physics

    NASA Astrophysics Data System (ADS)

    Maldonado, Armando; Bixler, David

    2012-03-01

    Chaos Theory is an interesting and important branch of physics. Many physical systems, such as weather or fluid flow, exhibit chaotic behavior. Experiments in simple mechanical or electrical systems, as well as simple simulations can be used as methods of studying chaos. Using a mechanical method, we connected a speaker and to a frequency modulator to bounce a table tennis ball. We recorded the ball's motion at different frequencies using a video camera. Using Tracker software we observed it's position versus it's velocity in order to analyze its chaotic behavior. For a simple simulation, we used the visual-based programming in LabView to examine chaotic behavior produced by some non-linear differential equations. Results from both the mechanical system and the simulations will be discussed. For future work, we plan to continue to explore some chaotic simulations and perform a sequence of experiments with an electrical system. Exploring these nonlinear chaotic systems can help us to better understand and model many phenomena found in nature.

  10. Chaos in brake squeal noise

    NASA Astrophysics Data System (ADS)

    Oberst, S.; Lai, J. C. S.

    2011-02-01

    Brake squeal has become an increasing concern to the automotive industry because of warranty costs and the requirement for continued interior vehicle noise reduction. Most research has been directed to either analytical and experimental studies of brake squeal mechanisms or the prediction of brake squeal propensity using finite element methods. By comparison, there is a lack of systematic analysis of brake squeal data obtained from a noise dynamometer. It is well known that brake squeal is a nonlinear transient phenomenon and a number of studies using analytical and experimental models of brake systems (e.g., pin-on-disc) indicate that it could be treated as a chaotic phenomenon. Data obtained from a full brake system on a noise dynamometer were examined with nonlinear analysis techniques. The application of recurrence plots reveals chaotic structures even in noisy data from the squealing events. By separating the time series into different regimes, lower dimensional attractors are isolated and quantified by dynamic invariants such as correlation dimension estimates or Lyapunov exponents. Further analysis of the recurrence plot of squealing events by means of recurrence quantification analysis measures reveals different regimes of laminar and random behaviour, periodicity and chaos-forming recurrent transitions. These results help to classify brake squeal mechanisms and to enhance understanding of friction-related noise phenomena.

  11. Quantum signatures of chaos in a kicked top.

    PubMed

    Chaudhury, S; Smith, A; Anderson, B E; Ghose, S; Jessen, P S

    2009-10-01

    Chaotic behaviour is ubiquitous and plays an important part in most fields of science. In classical physics, chaos is characterized by hypersensitivity of the time evolution of a system to initial conditions. Quantum mechanics does not permit a similar definition owing in part to the uncertainty principle, and in part to the Schrödinger equation, which preserves the overlap between quantum states. This fundamental disconnect poses a challenge to quantum-classical correspondence, and has motivated a long-standing search for quantum signatures of classical chaos. Here we present the experimental realization of a common paradigm for quantum chaos-the quantum kicked top- and the observation directly in quantum phase space of dynamics that have a chaotic classical counterpart. Our system is based on the combined electronic and nuclear spin of a single atom and is therefore deep in the quantum regime; nevertheless, we find good correspondence between the quantum dynamics and classical phase space structures. Because chaos is inherently a dynamical phenomenon, special significance attaches to dynamical signatures such as sensitivity to perturbation or the generation of entropy and entanglement, for which only indirect evidence has been available. We observe clear differences in the sensitivity to perturbation in chaotic versus regular, non-chaotic regimes, and present experimental evidence for dynamical entanglement as a signature of chaos. PMID:19812668

  12. Quantum chaos in nuclear physics

    NASA Astrophysics Data System (ADS)

    Bunakov, V. E.

    2016-07-01

    A definition of classical and quantum chaos on the basis of the Liouville-Arnold theorem is proposed. According to this definition, a chaotic quantum system that has N degrees of freedom should have M < N independent first integrals of motion (good quantum numbers) that are determined by the symmetry of the Hamiltonian for the system being considered. Quantitative measures of quantum chaos are established. In the classical limit, they go over to the Lyapunov exponent or the classical stability parameter. The use of quantum-chaos parameters in nuclear physics is demonstrated.

  13. [Experimental Course in Elementary Number Theory, Cambridge Conference on School Mathematics Feasibility Study No. 35.

    ERIC Educational Resources Information Center

    Hatch, Mary Jacqueline

    In the winter of 1965, an experimental course in Elementary Number Theory was presented to a 6th grade class in the Hosmer School, Watertown, Massachusetts. Prior to the introduction of the present material, students had been exposed in class to such topics from the University of Illinois Arithmetic Project as lattices, number lines, frame…

  14. A Chaos Conveyor Belt

    NASA Astrophysics Data System (ADS)

    Schmidt, Britney E.

    2013-10-01

    A critical question for the habitability of Europa remains: how does the ice shell work? The detection of shallow subsurface lenses below Europa’s chaos implies that the ice shell is recycled rapidly and that Europa may be currently active. While this is not the first time liquid water has been implicated for Europa, the location of these features combined with new perspective on their dynamics frames the question in a new way. Melt lenses are intriguing potential habitats. Moreover, their formation requires the existence of impurities within the upper ice shell that may be sources of energy for microorganisms. Geomorphic evidence also exists for hydraulic redistribution of fluids both vertically and horizontally through pores and fractures. This process, observed in terrestrial ice shelves, may preserve liquid water within the ice matrix over many kilometers from the source. Horizontal transport of material may produce interconnectivity between distinct regions of Europa, thus preserving habitable conditions within the ice over a longer duration. At a surface age of 40-90 Myr, with 25-50% covered by chaos terrain, Europa's resurfacing rate is very high and water likely plays a significant role. Because of the vigor of overturn implied by this new work, it is likely that surface and subsurface materials are well-mixed within the largest and deepest lenses, providing a mechanism for bringing oxidants and other surface contaminants to the deeper ice shell where it can reach the ocean by convective or compositional effects. The timescales over which large lenses refreeze are large compared to the timescales for vertical transport, while the timescales for smaller lenses are comparable to or shorter than convective timescales. Moreover, marine ice accretion at the bottom of the ice shell may be contributing to a compositional buoyancy engine that would change the makeup of the ice shell. From this point of view, we evaluate the habitability of Europa’s ice and

  15. Chaos and language.

    PubMed

    Mitchener, W Garrett; Nowak, Martin A

    2004-04-01

    Human language is a complex communication system with unlimited expressibility. Children spontaneously develop a native language by exposure to linguistic data from their speech community. Over historical time, languages change dramatically and unpredictably by accumulation of small changes and by interaction with other languages. We have previously developed a mathematical model for the acquisition and evolution of language in heterogeneous populations of speakers. This model is based on game dynamical equations with learning. Here, we show that simple examples of such equations can display complex limit cycles and chaos. Hence, language dynamical equations mimic complicated and unpredictable changes of languages over time. In terms of evolutionary game theory, we note that imperfect learning can induce chaotic switching among strict Nash equilibria.

  16. Eos Chaos Rocks

    NASA Technical Reports Server (NTRS)

    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

  17. Chaos-Dchroot Version 2

    SciTech Connect

    Grondona, M.

    2007-08-22

    The CHAOS dchroot utilities is a set of software used to prepare and manage "alternate root" filesystems on Linux systems. These alternate roots can be used to provide an alternate set of system software for testing and compatibility purposes.

  18. The Many Facets of Chaos

    NASA Astrophysics Data System (ADS)

    Sander, Evelyn; Yorke, James A.

    There are many ways that a person can encounter chaos, such as through a time series from a lab experiment, a basin of attraction with fractal boundaries, a map with a crossing of stable and unstable manifolds, a fractal attractor, or in a system for which uncertainty doubles after some time period. These encounters appear so diverse, but the chaos is the same in all of the underlying systems; it is just observed in different ways. We describe these different types of chaos. We then give two conjectures about the types of dynamical behavior that is observable if one randomly picks out a dynamical system without searching for a specific property. In particular, we conjecture that from picking a system at random, one observes (1) only three types of basic invariant sets: periodic orbits, quasiperiodic orbits, and chaotic sets; and (2) that all the definitions of chaos are in agreement.

  19. Controlling chaos in the brain

    NASA Astrophysics Data System (ADS)

    Schiff, Steven J.; Jerger, Kristin; Duong, Duc H.; Chang, Taeun; Spano, Mark L.; Ditto, William L.

    1994-08-01

    In a spontaneously bursting neuronal network in vitro, chaos can be demonstrated by the presence of unstable fixed-point behaviour. Chaos control techniques can increase the periodicity of such neuronal population bursting behaviour. Periodic pacing is also effective in entraining such systems, although in a qualitatively different fashion. Using a strategy of anticontrol such systems can be made less periodic. These techniques may be applicable to in vivo epileptic foci.

  20. Bose-Hubbard Hamiltonian: Quantum chaos approach

    NASA Astrophysics Data System (ADS)

    Kolovsky, Andrey R.

    2016-03-01

    We discuss applications of the theory of quantum chaos to one of the paradigm models of many-body quantum physics — the Bose-Hubbard (BH) model, which describes, in particular, interacting ultracold Bose atoms in an optical lattice. After preliminary, pure quantum analysis of the system we introduce the classical counterpart of the BH model and the governing semiclassical equations of motion. We analyze these equations for the problem of Bloch oscillations (BOs) of cold atoms where a number of experimental results are available. The paper is written for nonexperts and can be viewed as an introduction to the field.

  1. Routes to spatiotemporal chaos in Kerr optical frequency combs

    SciTech Connect

    Coillet, Aurélien; Chembo, Yanne K.

    2014-03-15

    We investigate the various routes to spatiotemporal chaos in Kerr optical frequency combs, obtained through pumping an ultra-high Q-factor whispering-gallery mode resonator with a continuous-wave laser. The Lugiato–Lefever model is used to build bifurcation diagrams with regards to the parameters that are externally controllable, namely, the frequency and the power of the pumping laser. We show that the spatiotemporal chaos emerging from Turing patterns and solitons display distinctive dynamical features. Experimental spectra of chaotic Kerr combs are also presented for both cases, in excellent agreement with theoretical spectra.

  2. Chaos reduces species extinction by amplifying local population noise.

    PubMed

    Allen, J C; Schaffer, W M; Rosko, D

    1993-07-15

    In the mid-1970s, theoretical ecologists were responsible for stimulating interest in nonlinear dynamics and chaos. Ironically, the importance of chaos in ecology itself remains controversial. Proponents of ecological chaos point to its ubiquity in mathematical models and to various empirical findings. Sceptics maintain that the models are unrealistic and that the experimental evidence is equally consistent with stochastic models. More generally, it has been argued that interdemic selection and/or enhanced rates of species extinction will eliminate populations and species that evolve into chaotic regions of parameter space. Fundamental to this opinion is the belief that violent oscillations and low minimum population densities are inevitable correlates of the chaotic state. In fact, rarity is not a necessary consequence of complex dynamical behaviour. But even when chaos is associated with frequent rarity, its consequences to survival are necessarily deleterious only in the case of species composed of a single population. Of course, the majority of real world species (for example, most insects) consist of multiple populations weakly coupled by migration, and in this circumstance chaos can actually reduce the probability of extinction. Here we show that although low densities lead to more frequent extinction at the local level, the decorrelating effect of chaotic oscillations reduces the degree of synchrony among populations and thus the likelihood that all are simultaneously extinguished.

  3. Hypomanic Experience in Young Adults Confers Vulnerability to Intrusive Imagery After Experimental Trauma

    PubMed Central

    Malik, Aiysha; Goodwin, Guy M.; Hoppitt, Laura

    2014-01-01

    Emotional mental imagery occurs across anxiety disorders, yet is neglected in bipolar disorder despite high anxiety comorbidity. Furthermore, a heightened susceptibility to developing intrusive mental images of stressful events in bipolar disorder and people vulnerable to it (with hypomanic experience) has been suggested. The current study assessed, prospectively, whether significant hypomanic experience (contrasting groups scoring high vs. low on the Mood Disorder Questionnaire, MDQ) places individuals at increased risk of visual reexperiencing after experimental stress. A total of 110 young adults watched a trauma film and recorded film-related intrusive images for 6 days. Compared to the low MDQ group, the high MDQ group experienced approximately twice as many intrusive images, substantiated by convergent measures. Findings suggest hypomanic experience is associated with developing more frequent intrusive imagery of a stressor. Because mental imagery powerfully affects emotion, such imagery may contribute to bipolar mood instability and offer a cognitive treatment target. PMID:25419498

  4. Emulating “Chaos + Chaos = Order” in Chen’s Circuit of Fractional Order by Parameter Switching

    NASA Astrophysics Data System (ADS)

    Tang, Wallace K. S.; Danca, Marius-F.

    2016-06-01

    In this paper, the effect of the parameter switching (PS) algorithm in a fractional order chaotic circuit is investigated both in simulation and experiment. The Chen system of fractional order is focused and realized in an electronic circuit. By designing a switching circuit, the PS algorithm is implemented and it is the first time, the paradoxical “Chaos + Chaos = Order” is presented in an electronic circuit. Both the simulation and experimental results confirm that the obtained attractor under switching approximates the attractor of the time-averaged model. Some important design issues for the circuitry realization of the PS scheme are pointed out. Finally, our work confirms the practical usage of PS algorithm in potential applications such as attractor synthesis and chaos control.

  5. Experimental observations of soliton explosions in ultrafast fibre lasers (Conference Presentation)

    NASA Astrophysics Data System (ADS)

    Broderick, Neil; Runge, Antoine; Erkintalo, Miro

    2016-04-01

    A soliton explosion is a dramatic effect, whereby a pulse circulating in a mode-locked laser dissipates and then remarkably reforms within a few roundtrips. Our group recently reported the first observation of such explosions in an all-fibre laser. Here, we expand on our initial work, reporting a detailed numerical and experimental study of the dynamics and characteristics of soliton explosions. Our experiment is based on a passively mode-locked Yb-doped fiber laser, where explosions occur close to the boundary between stable and noise-like operation. To capture the events, we use the dispersive Fourier transformation to record, in real time, the pulse-to-pulse spectra emitted by the laser. We explore a variety of operating conditions by systematically adjusting the laser pump power and its cavity length. We also use a realistic model based on a set of generalized nonlinear Schrodinger equations to simulate the explosion dynamics. We find that the explosion dynamics can be influenced by adjusting the operating conditions. As a general trend, the frequency of the events increases as the conditions move closer to the boundary of unstable operation. In fact, when sufficiently close to the boundary, the "explosions" can even become more frequent than ordinary pulses. Moreover, our simulations reveal that complex features in the spectral and temporal profiles of the explosion events can be explained in terms of a multi-pulsing instability. Finally we have examined how the statistics of the events depend on the laser geometry and also whether such explosions indicate the existence of a "strange attractor".

  6. Decoherence, determinism and chaos

    SciTech Connect

    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.

  7. A case for chaos theory in nursing.

    PubMed

    Lett, M

    2001-01-01

    This paper addresses the question of why nurses should understand chaos theory. A critique of the literature is used to demonstrate how chaos theory has been utilised in a number of disciplines, including nursing. Possible applications of chaos theory in nursing are proposed in order to demonstrate where it might assist nurses, in particular researchers, educators and policy makers. The appropriateness of the application of chaos theory as a framework for knowledge generation is also discussed. PMID:11878502

  8. Chaos theory for the biomedical engineer.

    PubMed

    Eberhart, R C

    1989-01-01

    A brief introduction to chaos theory is provided. Definitions of chaos and attributes of chaos and fractals are discussed. Several general examples are examined, and fractals are introduced with a brief look at the Mandelbrot and Julia sets. Biomedical examples of chaotic behaviour and fractals are presented.

  9. !CHAOS: A cloud of controls

    NASA Astrophysics Data System (ADS)

    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.

  10. High-frequency reverse-time chaos generation using an optical matched filter.

    PubMed

    Jiang, Xingxing; Liu, Deming; Cheng, Mengfan; Deng, Lei; Fu, Songnian; Zhang, Minming; Tang, Ming; Shum, Ping

    2016-03-15

    The optical reverse-time chaos is realized by modulating a binary pseudo-random bit sequence onto an optical carrier, and then driving an optical matched filter. The filter is demonstrated experimentally by using two fiber Bragg gratings and a Fourier-domain programmable optical processor. The complexity relationship between the binary input sequence and the output chaos signal is studied. This approach could be a novel way to generate a high speed repeatable and controllable optical chaos signal, which has the potential to be used in optical secure communication systems. PMID:26977658

  11. High-dimensional chaos from self-sustained collisions of solitons

    SciTech Connect

    Yildirim, O. Ozgur E-mail: oozgury@gmail.com; Ham, Donhee E-mail: oozgury@gmail.com

    2014-06-16

    We experimentally demonstrate chaos generation based on collisions of electrical solitons on a nonlinear transmission line. The nonlinear line creates solitons, and an amplifier connected to it provides gain to these solitons for their self-excitation and self-sustenance. Critically, the amplifier also provides a mechanism to enable and intensify collisions among solitons. These collisional interactions are of intrinsically nonlinear nature, modulating the phase and amplitude of solitons, thus causing chaos. This chaos generated by the exploitation of the nonlinear wave phenomena is inherently high-dimensional, which we also demonstrate.

  12. Chaos: A historical perspective

    NASA Astrophysics Data System (ADS)

    Lighthill, James

    In this introductory lecture I'd like to offer a broad historical perspective regarding the relatively recent general recognition: (a) that mechanical systems satisfying Newton's laws may be subject to the essentially unpredictable type of behavior which the word CHAOS describes—in other words, the recognition (b) that quantum effects are not required; (c) so that, notwithstanding Heisenberg, uncertainty is there on the basis of the good old classical mechanics based on Newton's Laws. But first of all I'll remind you that there are two kinds of laws in science, which we may exemplify by Kepler's Laws and Newton's Laws. Kepler in 1609 completed some very detailed observations of the motions of Mars; together with a full geometrical description of them, in the Copernican sun-centered flame of reference, as motions in a constant orbit in the shape of an ellipse with the Sun as focus. A decade later Kepler had published the Epitome Astronomiae Copernicanae (a rather more substantial work than the Dialogo which later got Galileo into some difficulties), and had there described in detail his most famous discovery: Kepler's three empirical laws concerning planetary orbits. These laws, of the elliptical shapes of orbits, of the radius covering equal areas in equal times, and of the proportionality of the square of the orbital period to the cube of the major axis, were shown from the observations to be closely satisfied by the Earth and by the five then known planets; and furthermore, by the four satellites of Jupiter which Galileo had recently discovered.

  13. Some new surprises in chaos.

    PubMed

    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. PMID:26428567

  14. Some new surprises in chaos

    NASA Astrophysics Data System (ADS)

    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 Pratchett). A brief review is presented of some recent findings in the theory of chaotic dynamics. We also prove a statement that could be naturally considered as a dual one to the Poincaré theorem on recurrences. Numerical results demonstrate that some parts of the phase space of chaotic systems are more likely to be visited earlier than other parts. A new class of chaotic focusing billiards is discussed that clearly violates the main condition considered to be necessary for chaos in focusing billiards.

  15. Chaos in laser-matter interactions

    SciTech Connect

    Ackerhalt, J.; Milonni, P.; Shih, M.L.

    1987-01-01

    This is a set of lecture notes given by the authors at the Universities of Rochester, Arkansas and Puerto Rico. This volume introduces the main ideas of chaos and its applications to a broad range of problems in quantum optics, electronics and laser physics. Contents: Introduction; Nonlinearity; The Period Doubling Route to Chaos; The Duffing Oscillator; Strange Attractors; Two-Frequency Route to Chaos; Intermittency; Dimensions of Attractors; Noise, The Lorenz Model and the Single-Mode Laser; Chaotic Lasers: Theory and Experiment; Hamiltonian Systems; The Henon-Heiles System; The Standard Mapping; Fat Fractals; Ergodicity and Mixing; Chaos and the Microwave Ionization of Hydrogen; The Kicked Pendulum: Classical Theory and Quantum Theory; Chaos and Multiple-Photon Excitation of Molecular Vibrations; Chaos and Molecular Rotations; Ideas in Quantum Chaos; Outlook.

  16. Chaos and structure of level densities

    SciTech Connect

    Moller, Peter; Aberg, Sven; Uhrenholt, Henrik; Ickhikawa, Takatoshi

    2008-01-01

    The energy region of the first few MeV above the ground state shows interesting features of the nucleus. Beyond an ordered energy region just above the ground-state the dynamics changes, and chaotic features are observed in the neutron resonance region. The statistical properties of energies and wave-functions are common to all chaotic nuclei. However, if instead a global property, like the local level-density function is studied, strong structure effects emerge. In this contribution we discuss these two different facets of warm nuclei. In section 2 the onset of chaos with increasing excitation energy is discussed, with both experimental observations and proposed theoretical mechanisms as starting points. The structure of level densities in the same excitation energy region based on the two different starting points, is treated in section 3, where we give a short presentation of a newly developed combinatorial level-density modell. Some results from the model are presented and discussed. Two coexisting facets of warm nuclei, quantum chaos and structure of the level density, are considered. A newly developed combinatorial level-density model is presented, and the role of collective enhancements discussed. An example of extreme parity enhancement is shown.

  17. Aureum Chaos: Another View

    NASA Technical Reports Server (NTRS)

    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 is located in a different part of Aureum Chaos. Compare the surface textures with yesterday's image. This image was collected during the Southern Fall season.

    Image information: VIS instrument. Latitude -4.1, Longitude 333.9 East (26.1 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

  18. The Chaos Theory of Careers.

    ERIC Educational Resources Information Center

    Pryor, Robert G. L.; Bright, Jim

    2003-01-01

    Four theoretical streams--contexualism/ecology, systems theory, realism/constructivism, and chaos theory--contributed to a theory of individuals as complex, unique, nonlinear, adaptive chaotic and open systems. Individuals use purposive action to construct careers but can make maladaptive and inappropriate choices. (Contains 42 references.) (SK)

  19. The Chaos Theory of Careers

    ERIC Educational Resources Information Center

    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…

  20. Chaos in the Solar System

    NASA Technical Reports Server (NTRS)

    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!

  1. Learning the Uses of Chaos.

    ERIC Educational Resources Information Center

    Berthoff, Ann E.

    This paper addresses the issue of learning to write and the need for defining a means of teaching the process of composing. Following a description of what kind of process writing is not, the composing process is presented as a continuum of making meaning out of a chaos of images, half-truths, remembrances, and syntactic fragments. The discovery…

  2. Optomechanics: Vibrations copying optical chaos

    NASA Astrophysics Data System (ADS)

    Sciamanna, Marc

    2016-06-01

    Mechanical oscillation in a microtoroidal optical cavity transfers chaos from a pump to a probe laser beam with a different wavelength. Through stochastic resonance, the combination of noise and internal chaotic dynamics leads to amplification of optomechanically induced light self-oscillations.

  3. Perspectives on Advertising Education: Curricula, Research--Descriptive, Research--Experimental, Industry/Educators' Cooperation, Special Interest Areas, and Instruction; Proceedings of the 1974 National Conference for University Professors of Advertising at the Univ. of Rhode Island.

    ERIC Educational Resources Information Center

    Zeigler, Sherilyn K., Ed.

    This document contains all of the presentations given at the 1974 National American Academy of Advertising Conference in Newport, Rhode Island. The theme of the conference was "Perspectives on Advertising" and the areas of focus were curricula and instruction, descriptive and experimental research, cooperation between educators and the advertising…

  4. Chaos, patterns, coherent structures, and turbulence: Reflections on nonlinear science.

    PubMed

    Ecke, Robert E

    2015-09-01

    The paradigms of nonlinear science were succinctly articulated over 25 years ago as deterministic chaos, pattern formation, coherent structures, and adaptation/evolution/learning. For chaos, the main unifying concept was universal routes to chaos in general nonlinear dynamical systems, built upon a framework of bifurcation theory. Pattern formation focused on spatially extended nonlinear systems, taking advantage of symmetry properties to develop highly quantitative amplitude equations of the Ginzburg-Landau type to describe early nonlinear phenomena in the vicinity of critical points. Solitons, mathematically precise localized nonlinear wave states, were generalized to a larger and less precise class of coherent structures such as, for example, concentrated regions of vorticity from laboratory wake flows to the Jovian Great Red Spot. The combination of these three ideas was hoped to provide the tools and concepts for the understanding and characterization of the strongly nonlinear problem of fluid turbulence. Although this early promise has been largely unfulfilled, steady progress has been made using the approaches of nonlinear science. I provide a series of examples of bifurcations and chaos, of one-dimensional and two-dimensional pattern formation, and of turbulence to illustrate both the progress and limitations of the nonlinear science approach. As experimental and computational methods continue to improve, the promise of nonlinear science to elucidate fluid turbulence continues to advance in a steady manner, indicative of the grand challenge nature of strongly nonlinear multi-scale dynamical systems. PMID:26428558

  5. Chaos, patterns, coherent structures, and turbulence: Reflections on nonlinear science

    NASA Astrophysics Data System (ADS)

    Ecke, Robert E.

    2015-09-01

    The paradigms of nonlinear science were succinctly articulated over 25 years ago as deterministic chaos, pattern formation, coherent structures, and adaptation/evolution/learning. For chaos, the main unifying concept was universal routes to chaos in general nonlinear dynamical systems, built upon a framework of bifurcation theory. Pattern formation focused on spatially extended nonlinear systems, taking advantage of symmetry properties to develop highly quantitative amplitude equations of the Ginzburg-Landau type to describe early nonlinear phenomena in the vicinity of critical points. Solitons, mathematically precise localized nonlinear wave states, were generalized to a larger and less precise class of coherent structures such as, for example, concentrated regions of vorticity from laboratory wake flows to the Jovian Great Red Spot. The combination of these three ideas was hoped to provide the tools and concepts for the understanding and characterization of the strongly nonlinear problem of fluid turbulence. Although this early promise has been largely unfulfilled, steady progress has been made using the approaches of nonlinear science. I provide a series of examples of bifurcations and chaos, of one-dimensional and two-dimensional pattern formation, and of turbulence to illustrate both the progress and limitations of the nonlinear science approach. As experimental and computational methods continue to improve, the promise of nonlinear science to elucidate fluid turbulence continues to advance in a steady manner, indicative of the grand challenge nature of strongly nonlinear multi-scale dynamical systems.

  6. Observation of Hamiltonian chaos in wave particle interaction

    NASA Astrophysics Data System (ADS)

    Doveil, Fabrice; Macor, Alessandro; Aïssi, Anass

    2008-09-01

    The motion of charged particle in longitudinal waves is a paradigm for the transition to large scale chaos in Hamiltonian systems. Recently a test cold electron beam has been used to observe its non-self-consistent interaction with externally excited wave(s) in a specially designed Traveling Wave Tube (TWT). The velocity distribution function of the electron beam is recorded with a trochoidal energy analyzer at the output of the TWT. An arbitrary waveform generator is used to launch a prescribed spectrum of waves along the slow wave structure (a 4 m long helix) of the TWT. The resonant velocity domain associated to a single wave is observed, as well as the transition to large scale chaos when the resonant domains of two waves and their secondary resonances overlap. This transition exhibits a “devil’s staircase” behavior when increasing the excitation amplitude in agreement with numerical simulation. A new strategy for control of chaos by building barriers of transport which prevent electrons to escape from a given velocity region as well as its robustness are also successfully tested. Thus generic features of Hamiltonian chaos have been experimentally observed.

  7. Complexity of chaos in three cascaded vertical-cavity surface-emitting lasers

    NASA Astrophysics Data System (ADS)

    Hong, Yanhua; Quirce, Ana; Wang, Bingjie; Panajotov, Krassimir; Spencer, Paul S.

    2016-04-01

    The complexity of chaos generated in two systems has been studied experimentally. The complexity of the chaos is quantified by calculating average normalized permutation entropy (HS(P)). In the first system, a chaotic output from a master laser (ML) is injected into a CW slave laser (SL). The results show that the complexity of chaos generated in the SL decreases with absolute value of the frequency detuning Δf1, which means the complexity of the chaos is compromised with enhancing the bandwidth, as Δf1 is increased. The second system comprises three vertical-cavity surface-emitting lasers (VCSELs); the first VCSEL (used as ML) was rendered chaotic by optical feedback, the second VCSEL is used as intermediate laser (IL), which is rendered chaotic when it is subject to optical injection from the chaotic ML and the third VCSEL is used as a SL and is a subject of optical injection from the chaotic IL, thus entering chaotic dynamics. In this three-VCSEL system, small, intermediate and wide bandwidths of the injecting chaos signals, have been used to study the effect of the bandwidth of the injecting chaos on the complexity of chaos generated in the SL. The results show that the bandwidth of the chaotic injection beam does not impact the complexity of the chaos generated in the SL for positive frequency detuning; however, for large negative frequency detuning, the complexity of the chaos in the SL has been reduced significantly for the intermediate and lower bandwidth of the chaotic injection beam.

  8. Identification of Bayesian posteriors for coefficients of chaos expansions

    SciTech Connect

    Arnst, M. Ghanem, R.; Soize, C.

    2010-05-01

    This article is concerned with the identification of probabilistic characterizations of random variables and fields from experimental data. The data used for the identification consist of measurements of several realizations of the uncertain quantities that must be characterized. The random variables and fields are approximated by a polynomial chaos expansion, and the coefficients of this expansion are viewed as unknown parameters to be identified. It is shown how the Bayesian paradigm can be applied to formulate and solve the inverse problem. The estimated polynomial chaos coefficients are hereby themselves characterized as random variables whose probability density function is the Bayesian posterior. This allows to quantify the impact of missing experimental information on the accuracy of the identified coefficients, as well as on subsequent predictions. An illustration in stochastic aeroelastic stability analysis is provided to demonstrate the proposed methodology.

  9. Contractility of glycerinated Amoeba proteus and Chaos-chaos.

    PubMed

    Rinaldi, R; Opas, M; Hrebenda, B

    1975-05-01

    Immediate contact with large volumes of cold 50% (v/v) buffered glycerol preserved typical ameboid shape of Chaos chaos and Amoeba proteus with no visible distortions. These technics allowed determination of the contraction sites in these glycerinated models upon applications of ATP-Ca-Mg-solutions. The ectoplasmic tube was the main site of contraction. Preliminary EM investigations revealed thick and thin filaments, associated with the ectoplasmic tube near the plasma-lemma, which appeared to be the basis for the contractility of the ectoplasmic tube. There was no predominant contraction of the pseudopodial tips or the endoplasm in these models. The changes of volume were as much as 50%, and in some cases were not accompanied by any change in the length of the ameba; however, lengthwise contractions of the ectoplasmic tube in some amebae occurred to as much as 25%. The data substantiate a basic requirement of the ectoplasmic tube contraction theory of ameboid locomotion.

  10. Noodle-map chaos - A simple example

    NASA Astrophysics Data System (ADS)

    Roessler, O. E.; Hudson, J. L.; Farmer, J. D.

    Chaos-generating folded two-dimensional maps can be generalized to higher dimensions in two ways: as folded-towel (or pancake) maps and as bent-walking-stick (or noddle) maps. The noodle case is of mathematical interest because the topologically one-dimensional attractors involved may, despite their thinness, be of the 'non-sink' type (that is, stand in a bijective relation to their domain of attraction). Moreover, Shtern recently showed that the well-known Kaplan-Yorke conjecture on the fractal dimensionality of chaotic attractors may fail in the case of noodle maps. We present here an explicit 3-variable noodle map with constant divergence (constant Jacobian determinant). The example is a higher analogue to the Henon diffeomorphism. A map of similar shape was recently found experimentally by Rob Shaw in a study of the irregularly dripping faucet.

  11. Wavenumber and Defect Distributions in Undulation Chaos

    NASA Astrophysics Data System (ADS)

    Daniels, Karen E.; Bodenschatz, Eberhard

    2000-11-01

    We report experimental results on thermally driven convection in a large aspect ratio inclined layer with a fluid of Prandtl number σ ≈ 1. Very close to the onset of convection for inclination angles between 20 and 70 degrees, we find the defect turbulent state of undulation chaos (Daniels, Plapp, and Bodenschatz. Phys. Rev. Lett. 84:5320). We characterize this state by determining the defect locations and the wavenumber distribution. A snapshot of the pattern, as well as its wavenumber distribution, can be well-reconstructed from a perfect underlying undulation pattern and the phase field given by the point defects. The defect density distribution shows a crossover from a Poisson to a squared Poisson distribution. By measuring the creation, annihilation, inflow, and outflow rates of defects we can quantitatively explain this behavior. This work is supported by the National Science Foundation DMR-0072077.

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

    ERIC Educational Resources Information Center

    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.

  13. A Simple Circuit for Demonstrating Regular and Synchronized Chaos.

    ERIC Educational Resources Information Center

    Carroll, Thomas L.

    1995-01-01

    Discusses the physics behind the synchronization of chaos. Describes an easy to build an electronic circuit which can be used to demonstrate chaos and the synchronization of chaos. Contains 19 references. (JRH)

  14. Stability analysis of fixed points via chaos control.

    PubMed

    Locher, M.; Johnson, G. A.; Hunt, E. R.

    1997-12-01

    This paper reviews recent advances in the application of chaos control techniques to the stability analysis of two-dimensional dynamical systems. We demonstrate how the system's response to one or multiple feedback controllers can be utilized to calculate the characteristic multipliers associated with an unstable periodic orbit. The experimental results, obtained for a single and two coupled diode resonators, agree well with the presented theory. (c) 1997 American Institute of Physics. PMID:12779684

  15. Finding Order and Direction from Chaos: A Comparison of Chaos Career Counseling and Trait Matching Counseling

    ERIC Educational Resources Information Center

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

    2005-01-01

    Chaos career counseling, based on the Chaos Theory of Careers (R. G. L. Pryor & J. E. H. Bright, 2003a, 2003b), was compared with trait matching career counseling and a wait list control. Sixty university students who attended the Careers Research and Assessment Service seeking career advice were randomly assigned to the chaos intervention, the…

  16. Optoelectronic Chaos in a Simple Light Activated Feedback Circuit

    NASA Astrophysics Data System (ADS)

    Joiner, K. L.; Palmero, F.; Carretero-González, R.

    The nonlinear dynamics of an optoelectronic negative feedback switching circuit is studied. The circuit, composed of a bulb, a photoresistor, a thyristor and a linear resistor, corresponds to a nightlight device whose light is looped back into its light sensor. Periodic bifurcations and deterministic chaos are obtained by the feedback loop created when the thyristor switches on the bulb in the absence of light being detected by the photoresistor and the bulb light is then looped back into the nightlight to switch it off. The experimental signal is analyzed using tools of delay-embedding reconstruction that yield a reconstructed attractor with fractional dimension and positive Lyapunov exponent suggesting chaotic behavior for some parameter values. We construct a simple circuit model reproducing experimental results that qualitatively matches the different dynamical regimes of the experimental apparatus. In particular, we observe an order-chaos-order transition as the strength of the feedback is varied corresponding to varying the distance between the nightlight bulb and its photo-detector. A two-dimensional parameter diagram of the model reveals that the order-chaos-order transition is generic for this system.

  17. A history of chaos theory.

    PubMed

    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

  18. A quantum correction to chaos

    NASA Astrophysics Data System (ADS)

    Fitzpatrick, A. Liam; Kaplan, Jared

    2016-05-01

    We use results on Virasoro conformal blocks to study chaotic dynamics in CFT2 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 CFT2 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.

  19. A history of chaos theory

    PubMed Central

    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

  20. Spatiotemporal chaos from bursting dynamics

    SciTech Connect

    Berenstein, Igal; De Decker, Yannick

    2015-08-14

    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.

  1. Monitoring chaos of cardiac rhythms

    SciTech Connect

    Mayer-Kress, G.

    1989-01-01

    Chaos theory provides a new paradigm in monitoring complexity changes in heart rate variability. Even in cases where the spectral analysis only shows broad band characteristics estimations of dimensional complexity parameters can show quantitative changes in the degree of chaos present in the interbeat interval dynamics. We introduce the concept of dimensional complexity as dynamical monitoring parameter and discuss its properties in connection with control data and data taken during cardiac arrest. Whereas dimensional complexity provides a quantitative indicator of overall chaotic behavior, recurrence plots allow direct visualization of recurrences in arbitrary high dimensional pattern-space. In combination these two methods from non-linear dynamics exemplify a new approach in the problem of heart rate monitoring and identification of precursors of cardiac arrest. Finally we mention a new method of chaotic control, by which selective and highly effective perturbations of nonlinear dynamical systems could be used for improved pacing patterns. 11 refs., 6 figs.

  2. Temperature chaos and quenched heterogeneities

    NASA Astrophysics Data System (ADS)

    Barucca, Paolo; Parisi, Giorgio; Rizzo, Tommaso

    2014-03-01

    We present a treatable generalization of the Sherrington-Kirkpatrick (SK) model which introduces correlations in the elements of the coupling matrix through multiplicative disorder on the single variables and investigate the consequences on the phase diagram. We define a generalized qEA parameter and test the structural stability of the SK results in this correlated case evaluating the de Almeida-Thouless line of the model. As a main result we demonstrate the increase of temperature chaos effects due to heterogeneities.

  3. Analysis of FBC deterministic chaos

    SciTech Connect

    Daw, C.S.

    1996-06-01

    It has recently been discovered that the performance of a number of fossil energy conversion devices such as fluidized beds, pulsed combustors, steady combustors, and internal combustion engines are affected by deterministic chaos. It is now recognized that understanding and controlling the chaotic elements of these devices can lead to significantly improved energy efficiency and reduced emissions. Application of these techniques to key fossil energy processes are expected to provide important competitive advantages for U.S. industry.

  4. Sedimentary Rocks of Aram Chaos

    NASA Technical Reports Server (NTRS)

    2004-01-01

    10 May 2004 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows outcroppings of light-toned, layered, sedimentary rock within Aram Chaos, an ancient, partly-filled impact crater located near 3.2oN, 19.9oW. This 1.5 meters (5 feet) per pixel picture is illuminated by sunlight from the left and covers an area about 3 km (1.9 mi) across.

  5. Ecological chaos in the wake of invasion.

    PubMed Central

    Sherratt, J A; Lewis, M A; Fowler, A C

    1995-01-01

    Irregularities in observed population densities have traditionally been attributed to discretization of the underlying dynamics. We propose an alternative explanation by demonstrating the evolution of spatiotemporal chaos in reaction-diffusion models for predator-prey interactions. The chaos is generated naturally in the wake of invasive waves of predators. We discuss in detail the mechanism by which the chaos is generated. By considering a mathematical caricature of the predator-prey models, we go on to explain the dynamical origin of the irregular behavior and to justify our assertion that the behavior we present is a genuine example of spatiotemporal chaos. Images Fig. 7 PMID:7708678

  6. Model for shock wave chaos.

    PubMed

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

    2013-03-01

    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, x<0, and the shock is located at x = 0 for any t ≥ 0. Here, u(s)(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. PMID:23521260

  7. Model for shock wave chaos.

    PubMed

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

    2013-03-01

    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, x<0, and the shock is located at x = 0 for any t ≥ 0. Here, u(s)(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.

  8. Dissipative chaos in semiconductor superlattices

    SciTech Connect

    Alekseev, K.N.; Berman, G.P. ||; Campbell, D.K.; Cannon, E.H.; Cargo, M.C.

    1996-10-01

    We consider the motion of ballistic electrons in a miniband of a semiconductor superlattice (SSL) under the influence of an external, time-periodic electric field. We use a semiclassical, balance-equation approach, which incorporates elastic and inelastic scattering (as dissipation) and the self-consistent field generated by the electron motion. The coupling of electrons in the miniband to the self-consistent field produces a cooperative nonlinear oscillatory mode which, when interacting with the oscillatory external field and the intrinsic Bloch-type oscillatory mode, can lead to complicated dynamics, including dissipative chaos. For a range of values of the dissipation parameters we determine the regions in the amplitude-frequency plane of the external field in which chaos can occur. Our results suggest that for terahertz external fields of the amplitudes achieved by present-day free-electron lasers, chaos may be observable in SSL{close_quote}s. We clarify the nature of this interesting nonlinear dynamics in the superlattice{endash}external-field system by exploring analogies to the Dicke model of an ensemble of two-level atoms coupled with a resonant cavity field, and to Josephson junctions. {copyright} {ital 1996 The American Physical Society.}

  9. Adaptation to the edge of chaos and critical scaling in self-adjusting dynamical systems

    NASA Astrophysics Data System (ADS)

    Melby, Paul Christian

    We present a mechanism for adaptation in dynamical systems. Systems which have this mechanism are called self-adjusting systems. The control parameters in a self-adjusting system are slowly varying, rather than constant. The dynamics of the control parameters are governed by a low-pass filtered feedback from the dynamical variables. We apply this model to several systems, numerically, analytically, and experimentally, and examine the behavior of the control parameters. We observe a high probability of finding the parameter at the boundary between periodicity and chaos. We therefore find that self-adjusting systems adapt to the edge of chaos. In addition, we find that noise in the system drives the parameter away from the edge of chaos on very long timescales so that chaos is suppressed in the system. We show that, with the presence of noise, the parameter can re-enter the chaotic regime. This is called a chaotic outbreak in the system and we find that the distribution of outbreaks is a power-law with the duration of the outbreak. We then study the robustness of adaptation to the edge of chaos by examining the effect of a control force being applied to the parameter. We find the behavior to be very robust, except for very large control forces. Finally, we look at systems of coupled maps and show that, adaptation to the edge of chaos occurs in systems of higher dimensions, as well.

  10. Transient spatiotemporal chaos in a diffusively and synaptically coupled Morris-Lecar neuronal network

    NASA Astrophysics Data System (ADS)

    Lafranceschina, Jacopo

    Transient spatiotemporal chaos was reported in models for chemical reactions and in experiments for turbulence in shear flow. This study shows that transient spatiotemporal chaos also exists in a diffusively coupled Morris-Lecar (ML) neuronal network, with a collapse to either a global rest state or to a state of pulse propagation. Adding synaptic coupling to this network reduces the average lifetime of spatiotemporal chaos for small to intermediate coupling strengths and almost all numbers of synapses. For large coupling strengths, close to the threshold of excitation, the average lifetime increases beyond the value for only diffusive coupling, and the collapse to the rest state dominates over the collapse to a traveling pulse state. The regime of spatiotemporal chaos is characterized by a slightly increasing Lyapunov exponent and degree of phase coherence as the number of synaptic links increases. In contrast to the diffusive network, the pulse solution must not be asymptotic in the presence of synapses. The fact that chaos could be transient in higher dimensional systems, such as the one being explored in this study, point to its presence in every day life. Transient spatiotemporal chaos in a network of coupled neurons and the associated chaotic saddle provide a possibility for switching between metastable states observed in information processing and brain function. Such transient dynamics have been observed experimentally by Mazor, when stimulating projection neurons in the locust antennal lobe with different odors.

  11. Improving the chaos bandwidth of a semiconductor laser with phase-conjugate feedback

    NASA Astrophysics Data System (ADS)

    Mercier, Émeric; Wolfersberger, Delphine; Sciamanna, Marc

    2016-04-01

    Common applications using optical chaos in a semiconductor laser include, among others, random number generation and chaos-encrypted communications. They rely on chaos of high dimension with a large bandwidth and a high entropy growth rate to achieve good results. Optical chaos from a semiconductor laser with conventional optical feedback (COF) is typically used as the primary source of chaos. Additional enhancing techniques are used to enlarge the chaos bandwidth. In this contribution, we show experimentally how using phase-conjugate feedback (PCF) can naturally produce a chaos of higher bandwidth than COF. PCF is an alternative to COF which consists of feeding the conjugate of the optical output back into the laser cavity, with a time-delay. Thanks to an oscilloscope with a fast sampling rate, and a large bandwidth, we were able to measure and observe the time-resolved frequency dynamics with a good precision. In the regime of low-frequency fluctuations (LFF), where dropouts of optical power occur randomly, we were able to compare the difference in dynamics before and after a dropout, for PCF and COF. In the range of attainable reflectivities, we measured a bandwidth increase of up to 27 % with PCF when compared to COF. Interestingly, we found that high-frequency dynamics are enabled before dropouts in PCF, where it was theoretically shown that the system jumps between destabilized self-pulsing states at harmonics of the external-cavity frequency, the so-called external-cavity modes (ECMs). This observation tends to confirm that ECMs in PCF are indeed fundamentally different than ECMs in COF, where they are simple steady-states. Finally, we believe that the enhancing techniques used with COF could also be used with PCF to obtain even wider chaotic bandwidths. These results could lead to studies about the dimension and the entropy growth rate of chaos from a laser diode with PCF.

  12. Discretization chaos - Feedback control and transition to chaos

    NASA Technical Reports Server (NTRS)

    Grantham, Walter J.; Athalye, Amit M.

    1990-01-01

    Problems in the design of feedback controllers for chaotic dynamical systems are considered theoretically, focusing on two cases where chaos arises only when a nonchaotic continuous-time system is discretized into a simpler discrete-time systems (exponential discretization and pseudo-Euler integration applied to Lotka-Volterra competition and prey-predator systems). Numerical simulation results are presented in extensive graphs and discussed in detail. It is concluded that care must be taken in applying standard dynamical-systems methods to control systems that may be discontinuous or nondifferentiable.

  13. Advising Undecided Students: Lessons from Chaos Theory.

    ERIC Educational Resources Information Center

    Beck, Amy

    1999-01-01

    Uses chaos theory as a metaphor for advising undecided college students. Applies chaos theory concepts of dependence on initial conditions, strange attractors, emergent behavior in complex systems, and fractals to the advising relationship. Suggests the paradigm reinforces the basics of advising, such as the importance of accepting the student's…

  14. "Chaos" Theory: Implications for Educational Research.

    ERIC Educational Resources Information Center

    Lindsay, Jean S.

    "Chaos" theory is a revolutionary new paradigm developed by scientists to study the behavior of natural systems. "Chaos" refers to the tendency of dynamic non-linear systems toward irregular, sometimes unpredictable, yet deterministic behavior. Major tenets of the theory are presented. The precedent for use of models developed in the natural…

  15. Life Out of Chaos

    NASA Technical Reports Server (NTRS)

    Arrhenius, Gustaf

    2002-01-01

    Doctinary overlays on the definition of life can effectively be avoided by focusing discussion on microorganisms, their vital processes, and their genetic pedigree. To reach beyond these present and highly advanced forms of life and to inquire about its origin it is necessary to consider the requirements imposed by the environment. These requirements include geophysically and geochemically acceptable conjectures for the generation of source compounds, their concentration from dilute solution, and their selective combination into functional biomolecules. For vital function these macromolecules require programming in the form of specific sequence motifs. This critical programming constitutes the scientifically least understood process in the origin of life. Once this stage has been surpassed the laws of Darwinian evolution can operate in ways that are understood and experimentally demonstrated.

  16. Scaling of chaos in strongly nonlinear lattices

    SciTech Connect

    Mulansky, Mario

    2014-06-15

    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.

  17. Quantum chaos and effective thermalization.

    PubMed

    Altland, Alexander; Haake, Fritz

    2012-02-17

    We demonstrate effective equilibration for unitary quantum dynamics under conditions of classical chaos. Focusing on the paradigmatic example of the Dicke model, we show how a constructive description of the thermalization process is facilitated by the Glauber Q or Husimi function, for which the evolution equation turns out to be of Fokker-Planck type. The equation describes a competition of classical drift and quantum diffusion in contractive and expansive directions. By this mechanism the system follows a "quantum smoothened" approach to equilibrium, which avoids the notorious singularities inherent to classical chaotic flows.

  18. Some new surprises in chaos

    SciTech Connect

    Bunimovich, Leonid A.; Vela-Arevalo, Luz V.

    2015-09-15

    A brief review is presented of some recent findings in the theory of chaotic dynamics. We also prove a statement that could be naturally considered as a dual one to the Poincaré theorem on recurrences. Numerical results demonstrate that some parts of the phase space of chaotic systems are more likely to be visited earlier than other parts. A new class of chaotic focusing billiards is discussed that clearly violates the main condition considered to be necessary for chaos in focusing billiards.

  19. Decoherence, determinism and chaos revisited

    SciTech Connect

    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.

  20. Sedimentary Rocks of Aram Chaos

    NASA Technical Reports Server (NTRS)

    2004-01-01

    4 February 2004 Aram Chaos is a large meteor impact crater that was nearly filled with sediment. Over time, this sediment was hardened to form sedimentary rock. Today, much of the eastern half of the crater has exposures of light-toned sedimentary rock, such as the outcrops shown in this Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image. The picture is located near 2.0oN, 20.3oW, and covers an area 3 km (1.9 mi) wide. Sunlight illuminates the scene from the left.

  1. Route to chaos for combustion instability in ducted laminar premixed flames

    NASA Astrophysics Data System (ADS)

    Kabiraj, Lipika; Saurabh, Aditya; Wahi, Pankaj; Sujith, R. I.

    2012-06-01

    Complex thermoacoustic oscillations are observed experimentally in a simple laboratory combustor that burns lean premixed fuel-air mixture, as a result of nonlinear interaction between the acoustic field and the combustion processes. The application of nonlinear time series analysis, particularly techniques based on phase space reconstruction from acquired pressure data, reveals rich dynamical behavior and the existence of several complex states. A route to chaos for thermoacoustic instability is established experimentally for the first time. We show that, as the location of the heat source is gradually varied, self-excited periodic thermoacoustic oscillations undergo transition to chaos via the Ruelle-Takens scenario.

  2. Heading stabilization and anti-rollover for Chaos

    NASA Astrophysics Data System (ADS)

    Berkemeier, Matthew; Poulson, Eric; King, Sidney L.

    2007-04-01

    Chaos is a 2-man-portable tele-operated vehicle designed for crossing rugged terrain. Chaos is capable of crossing large piles of cinder blocks, picnic tables, and steep hills of loose soil. These feats are accomplished through use of 4 independent track arms, each of which can be articulated at an arbitrary angle and driven at an arbitrary speed. These make the vehicle extremely capable but also demand significant skill on the part of the user. It is therefore desirable to automate the arm angles and track speeds to ease operator burden. This paper reports on preliminary efforts to implement 2 intelligent behaviors along these lines. The first involves heading stabilization: A gyroscope is used to sense yaw and yaw rate, and these are compared with the operators commands. Deviations are then used to automatically correct the heading. This is useful when Chaos is climbing stairs or other bumpy terrain, which can cause the vehicle to veer off in unwanted directions. We call the other behavior anti-rollover. In this case, the output of a gyroscope is monitored to detect if roll or pitch thresholds are exceeded. When they are, the track arms are automatically positioned to stabilize the vehicle and keep it right side up. Experimental results for both algorithms are included.

  3. Competitive coexistence in stoichiometric chaos.

    PubMed

    Deng, Bo; Loladze, Irakli

    2007-09-01

    Classical predator-prey models, such as Lotka-Volterra, track the abundance of prey, but ignore its quality. Yet, in the past decade, some new and occasionally counterintuitive effects of prey quality on food web dynamics emerged from both experiments and mathematical modeling. The underpinning of this work is the theory of ecological stoichiometry that is centered on the fact that each organism is a mixture of multiple chemical elements such as carbon (C), nitrogen (N), and phosphorus (P). The ratios of these elements can vary within and among species, providing simple ways to represent prey quality as its C:N or C:P ratios. When these ratios modeled to vary, as they frequently do in nature, seemingly paradoxical results can arise such as the extinction of a predator that has an abundant and accessible prey. Here, for the first time, we show analytically that the reduction in prey quality can give rise to chaotic oscillations. In particular, when competing predators differ in their sensitivity to prey quality then all species can coexist via chaotic fluctuations. The chaos generating mechanism is based on the existence of a junction-fold point on the nullcline surfaces of the species. Conditions on parameters are found for such a point, and the singular perturbation method and the kneading sequence analysis are used to demonstrate the existence of a period-doubling cascade to chaos as a result of the point.

  4. Chaos suppression through asymmetric coupling

    NASA Astrophysics Data System (ADS)

    Bragard, J.; Vidal, G.; Mancini, H.; Mendoza, C.; Boccaletti, S.

    2007-12-01

    We study pairs of identical coupled chaotic oscillators. In particular, we have used Roessler (in the funnel and no funnel regimes), Lorenz, and four-dimensional chaotic Lotka-Volterra models. In all four of these cases, a pair of identical oscillators is asymmetrically coupled. The main result of the numerical simulations is that in all cases, specific values of coupling strength and asymmetry exist that render the two oscillators periodic and synchronized. The values of the coupling strength for which this phenomenon occurs is well below the previously known value for complete synchronization. We have found that this behavior exists for all the chaotic oscillators that we have used in the analysis. We postulate that this behavior is presumably generic to all chaotic oscillators. In order to complete the study, we have tested the robustness of this phenomenon of chaos suppression versus the addition of some Gaussian noise. We found that chaos suppression is robust for the addition of finite noise level. Finally, we propose some extension to this research.

  5. Competitive coexistence in stoichiometric chaos.

    PubMed

    Deng, Bo; Loladze, Irakli

    2007-09-01

    Classical predator-prey models, such as Lotka-Volterra, track the abundance of prey, but ignore its quality. Yet, in the past decade, some new and occasionally counterintuitive effects of prey quality on food web dynamics emerged from both experiments and mathematical modeling. The underpinning of this work is the theory of ecological stoichiometry that is centered on the fact that each organism is a mixture of multiple chemical elements such as carbon (C), nitrogen (N), and phosphorus (P). The ratios of these elements can vary within and among species, providing simple ways to represent prey quality as its C:N or C:P ratios. When these ratios modeled to vary, as they frequently do in nature, seemingly paradoxical results can arise such as the extinction of a predator that has an abundant and accessible prey. Here, for the first time, we show analytically that the reduction in prey quality can give rise to chaotic oscillations. In particular, when competing predators differ in their sensitivity to prey quality then all species can coexist via chaotic fluctuations. The chaos generating mechanism is based on the existence of a junction-fold point on the nullcline surfaces of the species. Conditions on parameters are found for such a point, and the singular perturbation method and the kneading sequence analysis are used to demonstrate the existence of a period-doubling cascade to chaos as a result of the point. PMID:17902990

  6. Competitive coexistence in stoichiometric chaos

    NASA Astrophysics Data System (ADS)

    Deng, Bo; Loladze, Irakli

    2007-09-01

    Classical predator-prey models, such as Lotka-Volterra, track the abundance of prey, but ignore its quality. Yet, in the past decade, some new and occasionally counterintuitive effects of prey quality on food web dynamics emerged from both experiments and mathematical modeling. The underpinning of this work is the theory of ecological stoichiometry that is centered on the fact that each organism is a mixture of multiple chemical elements such as carbon (C), nitrogen (N), and phosphorus (P). The ratios of these elements can vary within and among species, providing simple ways to represent prey quality as its C:N or C:P ratios. When these ratios modeled to vary, as they frequently do in nature, seemingly paradoxical results can arise such as the extinction of a predator that has an abundant and accessible prey. Here, for the first time, we show analytically that the reduction in prey quality can give rise to chaotic oscillations. In particular, when competing predators differ in their sensitivity to prey quality then all species can coexist via chaotic fluctuations. The chaos generating mechanism is based on the existence of a junction-fold point on the nullcline surfaces of the species. Conditions on parameters are found for such a point, and the singular perturbation method and the kneading sequence analysis are used to demonstrate the existence of a period-doubling cascade to chaos as a result of the point.

  7. Recurrence-based detection of the hyperchaos-chaos transition in an electronic circuit

    NASA Astrophysics Data System (ADS)

    Ngamga, E. J.; Buscarino, A.; Frasca, M.; Sciuto, G.; Kurths, J.; Fortuna, L.

    2010-12-01

    Some complex measures based on recurrence plots give evidence about hyperchaos-chaos transitions in coupled nonlinear systems [E. G. Souza et al., "Using recurrences to characterize the hyperchaos-chaos transition," Phys. Rev. E 78, 066206 (2008)]. In this paper, these measures are combined with a significance test based on twin surrogates to identify such a transition in a fourth-order Lorenz-like system, which is able to pass from a hyperchaotic to a chaotic behavior for increasing values of a single parameter. A circuit analog of the mathematical model has been designed and implemented and the robustness of the recurrence-based method on experimental data has been tested. In both the numerical and experimental cases, the combination of the recurrence measures and the significance test allows to clearly identify the hyperchaos-chaos transition.

  8. Markov transitions and the propagation of chaos

    SciTech Connect

    Gottlieb, A.

    1998-12-01

    The propagation of chaos is a central concept of kinetic theory that serves to relate the equations of Boltzmann and Vlasov to the dynamics of many-particle systems. Propagation of chaos means that molecular chaos, i.e., the stochastic independence of two random particles in a many-particle system, persists in time, as the number of particles tends to infinity. We establish a necessary and sufficient condition for a family of general n-particle Markov processes to propagate chaos. This condition is expressed in terms of the Markov transition functions associated to the n-particle processes, and it amounts to saying that chaos of random initial states propagates if it propagates for pure initial states. Our proof of this result relies on the weak convergence approach to the study of chaos due to Sztitman and Tanaka. We assume that the space in which the particles live is homomorphic to a complete and separable metric space so that we may invoke Prohorov's theorem in our proof. We also s how that, if the particles can be in only finitely many states, then molecular chaos implies that the specific entropies in the n-particle distributions converge to the entropy of the limiting single-particle distribution.

  9. Edge of chaos and genesis of turbulence.

    PubMed

    Chian, Abraham C-L; Muñoz, Pablo R; Rempel, Erico L

    2013-11-01

    The edge of chaos is analyzed in a spatially extended system, modeled by the regularized long-wave equation, prior to the transition to permanent spatiotemporal chaos. In the presence of coexisting attractors, a chaotic saddle is born at the basin boundary due to a smooth-fractal metamorphosis. As a control parameter is varied, the chaotic transient evolves to well-developed transient turbulence via a cascade of fractal-fractal metamorphoses. The edge state responsible for the edge of chaos and the genesis of turbulence is an unstable traveling wave in the laboratory frame, corresponding to a saddle point lying at the basin boundary in the Fourier space. PMID:24329334

  10. Chaos in Magnetic Flux Ropes

    NASA Astrophysics Data System (ADS)

    Gekelman, W. N.; DeHaas, T.; Van Compernolle, B.

    2013-12-01

    Magnetic Flux Ropes Immersed in a uniform magnetoplasma are observed to twist about themselves, writhe about each other and rotate about a central axis. They are kink unstable and smash into one another as they move. Full three dimensional magnetic field and flows are measured at thousands of time steps. Each collision results in magnetic field line generation and the generation of a quasi-seperatrix layer and induced electric fields. Three dimensional magnetic field lines are computed by conditionally averaging the data using correlation techniques. The permutation entropy1 ,which is related to the Lyapunov exponent, can be calculated from the the time series of the magnetic field data (this is also done with flows) and used to calculate the positions of the data on a Jensen Shannon complexity map2. The location of data on this map indicates if the magnetic fields are stochastic, or fall into regions of minimal or maximal complexity. The complexity is a function of space and time. The complexity map, and analysis will be explained in the course of the talk. Other types of chaotic dynamical models such as the Lorentz, Gissinger and Henon process also fall on the map and can give a clue to the nature of the flux rope turbulence. The ropes fall in the region of the C-H plane where chaotic systems lie. The entropy and complexity change in space and time which reflects the change and possibly type of chaos associated with the ropes. The maps give insight as to the type of chaos (deterministic chaos, fractional diffusion , Levi flights..) and underlying dynamical process. The power spectra of much of the magnetic and flow data is exponential and Lorentzian structures in the time domain are embedded in them. Other quantities such as the Hurst exponent are evaluated for both magnetic fields and plasma flow. Work Supported by a UC-LANL Lab fund and the Basic Plasma Science Facility which is funded by DOE and NSF. 1) C. Bandt, B. Pompe, Phys. Rev. Lett., 88,174102 (2007) 2

  11. Control of collective network chaos

    NASA Astrophysics Data System (ADS)

    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.

  12. Chaos Theory and Protein Dynamics

    NASA Astrophysics Data System (ADS)

    Bui, James; Clarage, James

    2010-10-01

    Chaos theory, commonly known as the butterfly effect, states that a small change in a complex system may cause large changes in the system as time moves forward. This phenomenon was first discovered by Henri Poincare in the 1880's. The computer programs NAMD, VMD (Visual Molecular Dynamics) and Mathematica were used to calculate the movements and graphically analyze the trajectories of the protein ubiquitin. A small change was applied to a single atom's initial position in the x-coordinate to see how it would affect the future dynamics and trajectory of the protein. Our findings indicate an exponential divergence from the controlled trajectory with a Lyapunov exponent = 10.5 [1/ps]. In other words after less than a picosecond (trillionth of a second) the dynamics of a small biophysical system is no longer predictable, even though the underlying Newtonian physical laws are completely deterministic.

  13. Control of collective network chaos

    SciTech Connect

    Wagemakers, Alexandre Sanjuán, Miguel A. F.

    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.

  14. The Minerals of Aureum Chaos

    NASA Technical Reports Server (NTRS)

    2008-01-01

    [figure removed for brevity, see original site] Click on image for animation of 3-dimensional model with 5x vertical exaggeration

    This image of chaotic terrain in the Aureum Chaos region of Mars was taken by the Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) at 0858UTC (3:58 a.m. EST) on January 24, 2008, near 3.66 degrees south latitude, 26.5 degrees west longitude. The image was taken in 544 colors covering 0.36-3.92 micrometers, and shows features as small as 18 meters (60 feet) across. The image is about 10 kilometers (6.2 miles) wide at its narrowest point.

    Aureum Chaos is a 368 kilometer (229 mile) wide area of chaotic terrain in the eastern part of Valles Marineris. The chaotic terrain is thought to have formed by collapse of the surrounding Margaritifer Terra highland region. Aureum Chaos contains heavily eroded, randomly oriented mesas, plateaus, and knobs many revealing distinct layered deposits along their slopes. These deposits may be formed from remnants of the collapsed highlands, sand carried by Martian winds, dust or volcanic ash that settled out of the atmosphere, or sediments laid down on the floor of an ancient lake.

    The top panel in the montage above shows the location of the CRISM image on a mosaic taken by the Mars Odyssey spacecraft's Thermal Emission Imaging System (THEMIS). The CRISM data cover a narrow plateau near the edge of the chaotic terrain, that stretches across from the southwest to the northeast.

    The lower left image, an infrared false color image, reveals the plateau and several eroded knobs of varying sizes. The plateau's layer-cake structure is similar to that of other layered outcrops in Valles Marineris.

    The lower right image reveals the strengths of mineral spectral features overlain on a black-and-white version of the infrared image. Areas shaded in red hold more of the mineral pyroxene, a primary component of basaltic rocks that are prevalent in the highlands. Spots of green

  15. Ergodic theory, randomness, and "chaos".

    PubMed

    Ornstein, D S

    1989-01-13

    Ergodic theory is the theory of the long-term statistical behavior of dynamical systems. The baker's transformation is an object of ergodic theory that provides a paradigm for the possibility of deterministic chaos. It can now be shown that this connection is more than an analogy and that at some level of abstraction a large number of systems governed by Newton's laws are the same as the baker's transformation. Going to this level of abstraction helps to organize the possible kinds of random behavior. The theory also gives new concrete results. For example, one can show that the same process could be produced by a mechanism governed by Newton's laws or by a mechanism governed by coin tossing. It also gives a statistical analog of structural stability.

  16. Adapted polynomial chaos expansion for failure detection

    SciTech Connect

    Paffrath, M. Wever, U.

    2007-09-10

    In this paper, we consider two methods of computation of failure probabilities by adapted polynomial chaos expansions. The performance of the two methods is demonstrated by a predator-prey model and a chemical reaction problem.

  17. Detecting nonlinearity and chaos in epidemic data

    SciTech Connect

    Ellner, S.; Gallant, A.R.; Theiler, J. |

    1993-08-01

    Historical data on recurrent epidemics have been central to the debate about the prevalence of chaos in biological population dynamics. Schaffer and Kot who first recognized that the abundance and accuracy of disease incidence data opened the door to applying a range of methods for detecting chaos that had been devised in the early 1980`s. Using attractor reconstruction, estimates of dynamical invariants, and comparisons between data and simulation of SEIR models, the ``case for chaos in childhood epidemics`` was made through a series of influential papers beginning in the mid 1980`s. The proposition that the precise timing and magnitude of epidemic outbreaks are deterministic but chaotic is appealing, since it raises the hope of finding determinism and simplicity beneath the apparently stochastic and complicated surface of the data. The initial enthusiasm for methods of detecting chaos in data has been followed by critical re-evaluations of their limitations. Early hopes of a ``one size fits all`` algorithm to diagnose chaos vs. noise in any data set have given way to a recognition that a variety of methods must be used, and interpretation of results must take into account the limitations of each method and the imperfections of the data. Our goals here are to outline some newer methods for detecting nonlinearity and chaos that have a solid statistical basis and are suited to epidemic data, and to begin a re-evaluation of the claims for nonlinear dynamics and chaos in epidemics using these newer methods. We also identify features of epidemic data that create problems for the older, better known methods of detecting chaos. When we ask ``are epidemics nonlinear?``, we are not questioning the existence of global nonlinearities in epidemic dynamics, such as nonlinear transmission rates. Our question is whether the data`s deviations from an annual cyclic trend (which would reflect global nonlinearities) are described by a linear, noise-driven stochastic process.

  18. Bifurcations and chaos in a current-carrying ion sheath

    SciTech Connect

    Komori, A.; Kono, M.; Norimine, T.; Kawai, Y. )

    1992-11-01

    Cascading bifurcations to chaos are investigated experimentally and theoretically in a current-carrying stable plasma. A dc plasma current is required to produce an electron-depleted thick sheath on a grid, which obeys the Child--Langmuir law of space-charge-limited current in a diode. Bifurcation cascade and chaotic behavior are exhibited when an external periodic oscillation is applied to the grid, and are in good agreement for the first time with a theory, which describes ion dynamics in the Child--Langmuir sheath and is represented by the differential equation with three independent variables. A fractal dimension predicted by the theory is verified by the experiment.

  19. Isochronal chaos synchronization of delay-coupled optoelectronic oscillators.

    PubMed

    Illing, Lucas; Panda, Cristian D; Shareshian, Lauren

    2011-07-01

    We study experimentally chaos synchronization of nonlinear optoelectronic oscillators with time-delayed mutual coupling and self-feedback. Coupling three oscillators in a chain, we find that the outer two oscillators always synchronize. In contrast, isochronal synchronization of the mediating middle oscillator is found only when self-feedback is added to the middle oscillator. We show how the stability of the isochronal solution of any network, including the case of three coupled oscillators, can be determined by measuring the synchronization threshold of two unidirectionally coupled systems. In addition, we provide a sufficient condition that guarantees global asymptotic stability of the synchronized solution.

  20. Suppression of chaos in integrated twin DFB lasers for millimeter-wave generation.

    PubMed

    Liu, Dong; Sun, Changzheng; Xiong, Bing; Luo, Yi

    2013-01-28

    A novel and simple method for high frequency millimeter-wave signal generation with integrated twin DFB lasers is proposed and demonstrated. Both theoretical simulation and experimental results confirm that chaos induced by large-signal direct modulation of a solitary laser diode can be suppressed by introducing adequate optical coupling from another dc biased laser diode. Frequency multiplication has been demonstrated employing such chaos suppression scheme using monolithically integrated twin DFB lasers, and low phase noise millimeter wave carrier ten times the modulation frequency is generated.

  1. Barrier-induced chaos in a kicked rotor: Classical subdiffusion and quantum localization

    NASA Astrophysics Data System (ADS)

    Paul, Sanku; Pal, Harinder; Santhanam, M. S.

    2016-06-01

    The relation between classically chaotic dynamics and quantum localization is studied in a system that violates the assumptions of the Kolmogorov-Arnold-Moser (KAM) theorem, namely, the kicked rotor in a discontinuous potential barrier. We show that the discontinuous barrier induces chaos and more than two distinct subdiffusive energy growth regimes, the latter being an unusual feature for Hamiltonian chaos. We show that the dynamical localization in the quantized version of this system carries the imprint of non-KAM classical dynamics through the dependence of quantum break time on subdiffusion exponents. We briefly comment on the experimental feasibility of this system.

  2. Transition to Spatio-Temporal Chaos with Increasing Length in the Reaction-Diffusion System

    NASA Astrophysics Data System (ADS)

    Trail, Collin; Tomlin, Brett; Olsen, Thomas; Wiener, Richard J.

    2003-11-01

    Calculations based up the Reaction-Diffusion model (H. Riecke and H.-G. Paap, Europhys. Lett. 14), 1235 (1991).have proven to be suggestive for a wide variety of pattern forming systems, including Taylor-Couette flow with hourglass geometry(Richard J. Wiener et al), Phys. Rev. E 55, 5489 (1997).. Seeking insight to guide experimental investigations, we extend these calculations. Previous calculations indicated that in smaller systems, only temporal chaos, located in a small region, would be observed, while in longer systems instabilities would form over a wide region. Our simulations explore this transition from purely temporal chaos to spatio-temporal chaos as the length of the system is increased.

  3. Acute treatment with the 5-HT(1A) receptor agonist 8-OH-DPAT and chronic environmental enrichment confer neurobehavioral benefit after experimental brain trauma.

    PubMed

    Kline, Anthony E; Wagner, Amy K; Westergom, Brian P; Malena, Rebecca R; Zafonte, Ross D; Olsen, Adam S; Sozda, Christopher N; Luthra, Pallavi; Panda, Monisha; Cheng, Jeffery P; Aslam, Haris A

    2007-02-27

    Acute treatment with the 5-HT(1A) receptor agonist 8-hydroxy-2-(di-n-propylamino)tetralin (8-OH-DPAT) or chronic environmental enrichment (EE) hasten behavioral recovery after experimental traumatic brain injury (TBI). The aim of this study was to determine if combining these interventions would confer additional benefit. Anesthetized adult male rats received either a cortical impact or sham injury followed 15min later by a single intraperitoneal injection of 8-OH-DPAT (0.5mg/kg) or saline vehicle (1.0mL/kg) and then randomly assigned to either enriched or standard (STD) housing. Behavioral assessments were conducted utilizing established motor and cognitive tests on post-injury days 1-5 and 14-18, respectively. Hippocampal CA(1)/CA(3) neurons were quantified at 3 weeks. Both 8-OH-DPAT and EE attenuated CA(3) cell loss. 8-OH-DPAT enhanced spatial learning in a Morris water maze (MWM) as revealed by differences between the TBI+8-OH-DPAT+STD and TBI+VEHICLE+STD groups (P=0.0014). EE improved motor function as demonstrated by reduced time to traverse an elevated narrow beam in both the TBI+8-OH-DPAT+EE and TBI+VEHICLE+EE groups versus the TBI+VEHICLE+STD group (P=0.0007 and 0.0016, respectively). EE also facilitated MWM learning as evidenced by both the TBI+8-OH-DPAT+EE and TBI+VEHICLE+EE groups locating the escape platform quicker than the TBI+VEHICLE+STD group (P's<0.0001). MWM differences were also observed between the TBI+8-OH-DPAT+EE and TBI+8-OH-DPAT+STD groups (P=0.0004) suggesting that EE enhanced the effect of 8-OH-DPAT. However, there was no difference between the TBI+8-OH-DPAT+EE and TBI+VEHICLE+EE groups. These data replicate previous results from our laboratory showing that both a single systemic administration of 8-OH-DPAT and EE improve recovery after TBI and extend those findings by elucidating that the combination of treatments in this particular paradigm did not confer additional benefit. One explanation for the lack of an additive effect is that EE

  4. Acute treatment with the 5-HT1A receptor agonist 8-OH-DPAT and chronic environmental enrichment confer neurobehavioral benefit after experimental brain trauma

    PubMed Central

    Kline, Anthony E.; Wagner, Amy K.; Westergom, Brian P.; Malena, Rebecca R.; Zafonte, Ross D.; Olsen, Adam S.; Sozda, Christopher N.; Luthra, Pallavi; Panda, Monisha; Cheng, Jeffery P.; Aslam, Haris A.

    2007-01-01

    Acute treatment with the 5-HT1A receptor agonist 8-hydroxy-2-(di-n-propylamino)tetralin (8-OH-DPAT) or chronic environmental enrichment (EE) hasten behavioral recovery after experimental traumatic brain injury (TBI). The aim of this study was to determine if combining these interventions would confer additional benefit. Anesthetized adult male rats received either a cortical impact or sham injury followed 15 min later by a single intraperitoneal injection of 8-OH-DPAT (0.5 mg/kg) or saline vehicle (1.0 mL/kg) and then randomly assigned to either enriched or standard (STD) housing. Behavioral assessments were conducted utilizing established motor and cognitive tests on post-injury days 1-5 and 14-18, respectively. Hippocampal CA1/CA3 neurons were quantified at 3 weeks. Both 8-OH-DPAT and EE attenuated CA3 cell loss. 8-OH-DPAT enhanced spatial learning in a Morris water maze (MWM) as revealed by differences between the TBI+8-OH-DPAT+STD and TBI+VEHICLE+STD groups (P=0.0014). EE improved motor function as demonstrated by reduced time to traverse an elevated narrow beam in both the TBI+8-OH-DPAT+EE and TBI+VEHICLE+EE groups vs. the TBI+VEHICLE+STD group (P=0.0007 and P=0.0016, respectively). EE also facilitated MWM learning as evidenced by both the TBI+8-OH-DPAT+EE and TBI+VEHICLE+EE groups locating the escape platform quicker than the TBI+VEHICLE+STD group (P's<0.0001). MWM differences were also observed between the TBI+8-OH-DPAT+EE and TBI+8-OH-DPAT+STD groups (P=0.0004) suggesting that EE enhanced the effect of 8-OH-DPAT. However, there was no difference between the TBI+8-OH-DPAT+EE and TBI+VEHICLE+EE groups. These data replicate previous results from our laboratory showing that both a single systemic administration of 8-OH-DPAT and EE improve recovery after TBI and extend those findings by elucidating that the combination of treatments in this particular paradigm did not confer additional benefit. One explanation for the lack of an additive effect is that EE is a

  5. INTRODUCTION: The Physics of Chaos and Related Problems: Proceedings of the 59th Nobel Symposium

    NASA Astrophysics Data System (ADS)

    Lundqvist, Stig

    1985-01-01

    The physics of non-linear phenomena has developed in a remarkable way over the last couple of decades and has accelerated over the last few years, in particular because of the recent progress in the study of chaotic behaviour. In particular the discovery of the universal properties of the transition into chaos for certain classes of systems has stimulated much recent work in different directions both theoretically and experimentally. Chaos theory has become a real challenge to physicists in many different fields and also in many other disciplines such as astronomy, chemistry, medicine, meteorology and economics and social theory. The study of chaos-related phenomena has a truly interdisciplinary character and makes use of important concepts and methods from other disciplines. For the description of chaotic structures one needs a new, recently developed geometry called fractal geometry. For the discussion of the enormous richness of ordered structures which appear, one uses the theory of pattern recognition. In order to study even the simplest theoretical models describing chaos, a computer is essential. It should finally be mentioned that important aspects of computer science are related to the theory of order and chaos. A Nobel Symposium provides an excellent opportunity to bring together a group of prominent scientists for a stimulating exchange of new ideas and results. The Nobel Symposia are very small meetings by invitation only and the number of key participants is typically in the range 20-40. These symposia are organized through a special Nobel Symposium Committee after proposals from individuals. This symposium was sponsored by the Nobel Foundation through its Nobel Symposium Fund with grants from The Tercentenary Fund of the Bank of Sweden and The Knut Alice Wallenberg Foundation. Additional support was obtained from the Royal Academy of Sciences, The Nordic Institute for Theoretical Atomic Physics (NORDITA), Chalmers University of Technology and

  6. INTRODUCTION: The Physics of Chaos and Related Problems: Proceedings of the 59th Nobel Symposium

    NASA Astrophysics Data System (ADS)

    Lundqvist, Stig

    1985-01-01

    The physics of non-linear phenomena has developed in a remarkable way over the last couple of decades and has accelerated over the last few years, in particular because of the recent progress in the study of chaotic behaviour. In particular the discovery of the universal properties of the transition into chaos for certain classes of systems has stimulated much recent work in different directions both theoretically and experimentally. Chaos theory has become a real challenge to physicists in many different fields and also in many other disciplines such as astronomy, chemistry, medicine, meteorology and economics and social theory. The study of chaos-related phenomena has a truly interdisciplinary character and makes use of important concepts and methods from other disciplines. For the description of chaotic structures one needs a new, recently developed geometry called fractal geometry. For the discussion of the enormous richness of ordered structures which appear, one uses the theory of pattern recognition. In order to study even the simplest theoretical models describing chaos, a computer is essential. It should finally be mentioned that important aspects of computer science are related to the theory of order and chaos. A Nobel Symposium provides an excellent opportunity to bring together a group of prominent scientists for a stimulating exchange of new ideas and results. The Nobel Symposia are very small meetings by invitation only and the number of key participants is typically in the range 20-40. These symposia are organized through a special Nobel Symposium Committee after proposals from individuals. This symposium was sponsored by the Nobel Foundation through its Nobel Symposium Fund with grants from The Tercentenary Fund of the Bank of Sweden and The Knut Alice Wallenberg Foundation. Additional support was obtained from the Royal Academy of Sciences, The Nordic Institute for Theoretical Atomic Physics (NORDITA), Chalmers University of Technology and

  7. XY sex chromosome complement, compared with XX, in the CNS confers greater neurodegeneration during experimental autoimmune encephalomyelitis.

    PubMed

    Du, Sienmi; Itoh, Noriko; Askarinam, Sahar; Hill, Haley; Arnold, Arthur P; Voskuhl, Rhonda R

    2014-02-18

    Women are more susceptible to multiple sclerosis (MS) and have more robust immune responses than men. However, men with MS tend to demonstrate a more progressive disease course than women, suggesting a disconnect between the severity of an immune attack and the CNS response to a given immune attack. We have previously shown in an MS model, experimental autoimmune encephalomyelitis, that autoantigen-sensitized XX lymph node cells, compared with XY, are more encephalitogenic. These studies demonstrated an effect of sex chromosomes in the induction of immune responses, but did not address a potential role of sex chromosomes in the CNS response to immune-mediated injury. Here, we examined this possibility using XX versus XY bone marrow chimeras reconstituted with a common immune system of one sex chromosomal type. We found that experimental autoimmune encephalomyelitis mice with an XY sex chromosome complement in the CNS, compared with XX, demonstrated greater clinical disease severity with more neuropathology in the spinal cord, cerebellum, and cerebral cortex. A candidate gene on the X chromosome, toll-like receptor 7, was then examined. Toll-like receptor 7 expression in cortical neurons was higher in mice with XY compared with mice with XX CNS, consistent with the known neurodegenerative role for toll-like receptor 7 in neurons. These results suggest that sex chromosome effects on neurodegeneration in the CNS run counter to effects on immune responses, and may bear relevance to the clinical enigma of greater MS susceptibility in women but faster disability progression in men. This is a demonstration of a direct effect of sex chromosome complement on neurodegeneration in a neurological disease.

  8. Quantum chaos in nanoelectromechanical systems

    NASA Astrophysics Data System (ADS)

    Gusso, André; da Luz, M. G. E.; Rego, Luis G. C.

    2006-01-01

    We present a theoretical study of the electron-phonon coupling in suspended nanoelectromechanical systems and investigate the resulting quantum chaotic behavior. The phonons are associated with the vibrational modes of a suspended rectangular dielectric plate, with free or clamped boundary conditions, whereas the electrons are confined to a large quantum dot (QD) on the plate’s surface. The deformation potential and piezoelectric interactions are considered. By performing standard energy-level statistics we demonstrate that the spectral fluctuations exhibit the same distributions as those of the Gaussian orthogonal ensemble or the Gaussian unitary ensemble (GUE), therefore evidencing the emergence of quantum chaos. That is verified for a large range of material and geometry parameters. In particular, the GUE statistics occurs only in the case of a circular QD. It represents an anomalous phenomenon, previously reported for just a small number of systems, since the problem is time-reversal invariant. The obtained results are explained through a detailed analysis of the Hamiltonian matrix structure.

  9. Regularly timed events amid chaos

    NASA Astrophysics Data System (ADS)

    Blakely, Jonathan N.; Cooper, Roy M.; Corron, Ned J.

    2015-11-01

    We show rigorously that the solutions of a class of chaotic oscillators are characterized by regularly timed events in which the derivative of the solution is instantaneously zero. The perfect regularity of these events is in stark contrast with the well-known unpredictability of chaos. We explore some consequences of these regularly timed events through experiments using chaotic electronic circuits. First, we show that a feedback loop can be implemented to phase lock the regularly timed events to a periodic external signal. In this arrangement the external signal regulates the timing of the chaotic signal but does not strictly lock its phase. That is, phase slips of the chaotic oscillation persist without disturbing timing of the regular events. Second, we couple the regularly timed events of one chaotic oscillator to those of another. A state of synchronization is observed where the oscillators exhibit synchronized regular events while their chaotic amplitudes and phases evolve independently. Finally, we add additional coupling to synchronize the amplitudes, as well, however in the opposite direction illustrating the independence of the amplitudes from the regularly timed events.

  10. ICCK Conference Final Report

    SciTech Connect

    Green, William H.

    2013-05-28

    The 7th International Conference on Chemical Kinetics (ICCK) was held July 10-14, 2011, at Massachusetts Institute of Technology (MIT), in Cambridge, MA, hosted by Prof. William H. Green of MIT's Chemical Engineering department. This cross-disciplinary meeting highlighted the importance of fundamental understanding of elementary reactions to the full range of chemical investigations. The specific conference focus was on elementary-step kinetics in both the gas phase and in condensed phase. The meeting provided a unique opportunity to discuss how the same reactive species and reaction motifs manifest under very different reaction conditions (e.g. atmospheric, aqueous, combustion, plasma, in nonaqueous solvents, on surfaces.). The conference featured special sessions on new/improved experimental techniques, improved models and data analysis for interpreting complicated kinetics, computational kinetics (especially rate estimates for large kinetic models), and a panel discussion on how the community should document/archive kinetic data. In the past, this conference had been limited to homogeneous gas-phase and liquid-phase systems. This conference included studies of heterogeneous kinetics which provide rate constants for, or insight into, elementary reaction steps. This Grant from DOE BES covered about half of the subsidies we provided to students and postdocs who attended the conference, by charging them reduced-rate registration fees. The complete list of subsidies provided are listed in Table 1 below. This DOE funding was essential to making the conference affordable to graduate students, and indeed the attendance at this conference was higher than at previous conferences in this series. Donations made by companies provided additional subsidies, leveraging the DOE funding. The conference was very effective in educating graduate students and important in fostering scientific interactions, particularly between scientists studying gas phase and liquid phase kinetics

  11. Generic superweak chaos induced by Hall effect.

    PubMed

    Ben-Harush, Moti; Dana, Itzhack

    2016-05-01

    We introduce and study the "kicked Hall system" (KHS), i.e., charged particles periodically kicked in the presence of uniform magnetic (B) and electric (E) fields that are perpendicular to each other and to the kicking direction. We show that for resonant values of B and E and in the weak-chaos regime of sufficiently small nonintegrability parameter κ (the kicking strength), there exists a generic family of periodic kicking potentials for which the Hall effect from B and E significantly suppresses the weak chaos, replacing it by "superweak" chaos (SWC). This means that the system behaves as if the kicking strength were κ^{2} rather than κ. For E=0, SWC is known to be a classical fingerprint of quantum antiresonance, but it occurs under much less generic conditions, in particular only for very special kicking potentials. Manifestations of SWC are a decrease in the instability of periodic orbits and a narrowing of the chaotic layers, relative to the ordinary weak-chaos case. Also, for global SWC, taking place on an infinite "stochastic web" in phase space, the chaotic diffusion on the web is much slower than the weak-chaos one. Thus, the Hall effect can be relatively stabilizing for small κ. In some special cases, the effect is shown to cause ballistic motion for almost all parameter values. The generic global SWC on stochastic webs in the KHS appears to be the two-dimensional closest analog to the Arnol'd web in higher dimensional systems. PMID:27300880

  12. Generic superweak chaos induced by Hall effect

    NASA Astrophysics Data System (ADS)

    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.

  13. The Capabilities of Chaos and Complexity

    PubMed Central

    Abel, David L.

    2009-01-01

    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? PMID:19333445

  14. A relatively brief exposure to environmental enrichment after experimental traumatic brain injury confers long-term cognitive benefits.

    PubMed

    Cheng, Jeffrey P; Shaw, Kaitlyn E; Monaco, Christina M; Hoffman, Ann N; Sozda, Christopher N; Olsen, Adam S; Kline, Anthony E

    2012-11-20

    It is well established that a relatively brief exposure to environmental enrichment (EE) enhances motor and cognitive performance after experimental traumatic brain injury (TBI), but it is not known whether the benefits can be sustained after EE is discontinued. To address this important rehabilitation-relevant concern, anesthetized rats received a controlled cortical impact (CCI) or sham injury, and for phase 1 of the experiment were randomly assigned to either 3 weeks of EE or standard (STD) housing. Neurobehavioral outcome was assessed by established motor and cognitive tests on postoperative days 1-5 and 14-18, respectively. Beam-balance and spatial learning were facilitated in the TBI + EE more than the TBI + STD group (p<0.0001). In phase 2 of the experiment, half of the rats in EE were transferred to STD conditions (TBI + EE + STD and sham + EE + STD), and neurobehavior was re-assessed once per month for 6 months. The TBI + EE and TBI + EE + STD groups performed markedly better in the water maze than the TBI + STD group (p<0.0001), and did not differ from one another (p=0.53). These data replicate those of several studies from our laboratory showing that EE enhances recovery after CCI injury, and extend those findings by demonstrating that the cognitive benefits are maintained for at least 6 months post-rehabilitation. The persistent benefits shown with this paradigm provide further support for EE as a pre-clinical model of rehabilitation that can be further explored, either alone or in combination with pharmacotherapies, for optimal neurorehabilitation after TBI.

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

    ERIC Educational Resources Information Center

    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…

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

    ERIC Educational Resources Information Center

    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…

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

    ERIC Educational Resources Information Center

    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…

  18. Intermittent chaos in the forced Brusselator

    NASA Astrophysics Data System (ADS)

    Chen, S.-G.; Hao, B.-L.; Wang, G.-R.

    1984-06-01

    It is shown numerically that in the model of trimolecular reaction under external periodic force (the forced Brusselator) there exists the intermittent route to chaos. The time development of intermittent chaos and the method to distinguish intermittency from transients are studied. The large region of period 3 in the parameter space, discovered previously in the forced Brusselator, as well as smaller regions of periods 4, 5, 6, . . . etc., correspond to tangent bifurcations in one-dimensional mappings. Intermittency appears just before the start of every tangent bifurcation. Therefore, the period-doubling and the intermittent routes to chaos are 'twin' phenomena and they should be observable in many other systems described by nonlinear differential equations.

  19. Associative memory with spatiotemporal chaos control

    NASA Astrophysics Data System (ADS)

    Kushibe, Masanori; Liu, Yun; Ohtsubo, Junji

    1996-05-01

    Control of spatiotemporal chaos in a neural network with discrete time and continuous state variables is investigated. The chaos control is performed with the knowledge of only a part of the target information in the memory patterns. The success rate for the pattern associations and the dependence of the search time on the sampling number in the proposed chaos neural network are studied. By the introduction of the reinforcement factor in the learning process, the recognition rate of the network can be much enhanced. Random and regular samplings of the pattern for the control are tested and the successful results of the associations are demonstrated. The chaotic behavior and recalling ability of the system are evaluated based on the analysis of the Lyapunov spectrum of the network.

  20. Controlling chaos in wave-particle interactions.

    PubMed

    de Sousa, M C; Caldas, I L; Rizzato, F B; Pakter, R; Steffens, F M

    2012-07-01

    We analyze the behavior of a relativistic particle moving under the influence of a uniform magnetic field and a stationary electrostatic wave. We work with a set of pulsed waves that allows us to obtain an exact map for the system. We also use a method of control for near-integrable Hamiltonians that consists of the addition of a small and simple control term to the system. This control term creates invariant tori in phase space that prevent chaos from spreading to large regions, making the controlled dynamics more regular. We show numerically that the control term just slightly modifies the system but is able to drastically reduce chaos with a low additional cost of energy. Moreover, we discuss how the control of chaos and the consequent recovery of regular trajectories in phase space are useful to improve regular particle acceleration. PMID:23005517

  1. AIDS in India: constructive chaos?

    PubMed

    Chatterjee, A

    1991-08-01

    Until recently, the only sustained AIDS activity in India has been alarmist media attention complemented by occasional messages calling for comfort and dignity. Public perception of the AIDS epidemic in India has been effectively shaped by mass media. Press reports have, however, bolstered awareness of the problem among literate elements of urban populations. In the absence of sustained guidance in the campaign against AIDS, responsibility has fallen to voluntary health activists who have become catalysts for community awareness and participation. This voluntary initiative, in effect, seems to be the only immediate avenue for constructive public action, and signals the gradual development of an AIDS network in India. Proceedings from a seminar in Ahmedabad are discussed, and include plans for an information and education program targeting sex workers, health and communication programs for 150 commercial blood donors and their agents, surveillance and awareness programs for safer blood and blood products, and dialogue with the business community and trade unions. Despite the lack of coordination among volunteers and activists, every major city in India now has an AIDS group. A controversial bill on AIDS has ben circulating through government ministries and committees since mid-1989, a national AIDS committee exists with the Secretary of Health as its director, and a 3-year medium-term national plan exists for the reduction of AIDS and HIV infection and morbidity. UNICEF programs target mothers and children for AIDS awareness, and blood testing facilities are expected to be expanded. The article considers the present chaos effectively productive in forcing the Indian population to face up to previously taboo issued of sexuality, sex education, and sexually transmitted disease.

  2. An introduction to chaos theory in CFD

    NASA Technical Reports Server (NTRS)

    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.

  3. Low-dimensional chaos in turbulence

    NASA Technical Reports Server (NTRS)

    Vastano, John A.

    1989-01-01

    Direct numerical simulations are being performed on two different fluid flows in an attempt to discover the mechanism underlying the transition to turbulence in each. The first system is Taylor-Couette flow; the second, two-dimensional flow over an airfoil. Both flows exhibit a gradual transition to high-dimensional turbulence through low-dimensional chaos. The hope is that the instabilities leading to chaos will be easier to relate to physical processes in this case, and that the understanding of these mechanisms can then be applied to a wider array of turbulent systems.

  4. A geometric criterion for adiabatic chaos

    SciTech Connect

    Kaper, T.J. ); Kovacic, G. )

    1994-03-01

    Chaos in adiabatic Hamiltonian systems is a recent discovery and a pervasive phenomenon in physics. In this work, a geometric criterion is discussed based on the theory of action from classical mechanics to detect the existence of Smale horseshoe chaos in adiabatic systems. It is used to show that generic adiabatic planar Hamiltonian systems exhibit stochastic dynamics in large regions of phase space. To illustrate the method, results are obtained for three problems concerning relativistic particle dynamics, fluid mechanics, and passage through resonance, results which either could not be obtained with existing methods, or which were difficult and analytically impractical to obtain with them.

  5. Chaos in an imperfectly premixed model combustor

    SciTech Connect

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

    2015-02-15

    This article reports nonlinear bifurcations observed in a laboratory scale, turbulent combustor operating under imperfectly premixed mode with global equivalence ratio as the control parameter. The results indicate that the dynamics of thermoacoustic instability correspond to quasi-periodic bifurcation to low-dimensional, deterministic chaos, a route that is common to a variety of dissipative nonlinear systems. The results support the recent identification of bifurcation scenarios in a laminar premixed flame combustor (Kabiraj et al., Chaos: Interdiscip. J. Nonlinear Sci. 22, 023129 (2012)) and extend the observation to a practically relevant combustor configuration.

  6. The uncertainty principle and quantum chaos

    NASA Technical Reports Server (NTRS)

    Chirikov, Boris V.

    1993-01-01

    The conception of quantum chaos is described in some detail. The most striking feature of this novel phenomenon is that all the properties of classical dynamical chaos persist here but, typically, on the finite and different time scales only. The ultimate origin of such a universal quantum stability is in the fundamental uncertainty principle which makes discrete the phase space and, hence, the spectrum of bounded quantum motion. Reformulation of the ergodic theory, as a part of the general theory of dynamical systems, is briefly discussed.

  7. Subharmonic Oscillations and Chaos in Dynamic Atomic Force Microscopy

    NASA Technical Reports Server (NTRS)

    Cantrell, John H.; Cantrell, Sean A.

    2015-01-01

    The increasing use of dynamic atomic force microscopy (d-AFM) for nanoscale materials characterization calls for a deeper understanding of the cantilever dynamics influencing scan stability, predictability, and image quality. Model development is critical to such understanding. Renormalization of the equations governing d- AFM provides a simple interpretation of cantilever dynamics as a single spring and mass system with frequency dependent cantilever stiffness and damping parameters. The renormalized model is sufficiently robust to predict the experimentally observed splitting of the free-space cantilever resonance into multiple resonances upon cantilever-sample contact. Central to the model is the representation of the cantilever sample interaction force as a polynomial expansion with coefficients F(sub ij) (i,j = 0, 1, 2) that account for the effective interaction stiffness parameter, the cantilever-to-sample energy transfer, and the amplitude of cantilever oscillation. Application of the Melnikov method to the model equation is shown to predict a homoclinic bifurcation of the Smale horseshoe type leading to a cascade of period doublings with increasing drive displacement amplitude culminating in chaos and loss of image quality. The threshold value of the drive displacement amplitude necessary to initiate subharmonic generation depends on the acoustic drive frequency, the effective damping coefficient, and the nonlinearity of the cantilever-sample interaction force. For parameter values leading to displacement amplitudes below threshold for homoclinic bifurcation other bifurcation scenarios can occur, some of which lead to chaos.

  8. Iani Chaos in False Color

    NASA Technical Reports Server (NTRS)

    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 of a portion of the Iani Chaos region was collected during the Southern Fall season.

    Image information: VIS instrument. Latitude -2.6 Longitude 342.4 East (17.6 West). 36 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

  9. Controlling Chaos, Targeting, and Transport.

    NASA Astrophysics Data System (ADS)

    Bollt, Erik Matthew Arnold

    1995-01-01

    The sensitivity that defines chaotic dynamics makes accessible a wide range of behaviors using arbitrarily small control signals. "Controlling chaos" attempts to cause large changes in the dynamics using only small perturbations. In targeting, one attempts to find a fast path from an initial condition {bf a} to a target point {bf b} by exploiting the fact that transport times for a chaotic system are highly sensitive to initial conditions and parameter values. The main difficulty is finding the switching points, the times and places to apply judiciously chosen perturbations. I present a new technique to find rough orbits (epsilon chains) that rapidly achieve a desired transport. The strategy is to build the epsilon chain from segments of a long orbit. In two-dimensional maps, long orbits have recurrences in neighborhoods where faster orbits must also pass. Long orbits of higher dimensional maps are likely to have recurrences, albeit less frequently. The recurrences are used as switching points between segments. If a local hyperbolicity condition is satisfied, then a nearby shadow orbit might be constructed. In one example, I show that transport times for the standard map can typically be reduced by a factor of 10^4. In another example, I apply the technique to the restricted three-body problem from which I find a low energy Earth-Moon transfer orbit which requires 38% less characteristic velocity than a comparable Hohmann transfer orbit. In yet another example, a symbol dynamics model has a closed-form expression for the optimal transporting orbit from near {bf a} to near {bf b}. I compare the optimal orbit to the targeted orbit resulting from removing recurrences, which also takes a particularly simple form in symbol dynamics. The techniques developed here do not require a closed-form representation of the map. Using the standard map as an example, I demonstrate that predictions from a time series may be sufficient for targeting. Finally, as a contribution to the

  10. Chaos in Practice: Techniques for Career Counsellors

    ERIC Educational Resources Information Center

    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…

  11. Probability Simulations by Non-Lipschitz Chaos

    NASA Technical Reports Server (NTRS)

    Zak, Michail

    1996-01-01

    It has been demonstrated that classical probabilities, and in particular, probabilistic Turing machine, can be simulated by combining chaos and non-Lipschitz dynamics, without utilization of any man-made devices. Self-organizing properties of systems coupling simulated and calculated probabilities and their link to quantum computations are discussed.

  12. Criticality and Chaos in Systems of Communities

    NASA Astrophysics Data System (ADS)

    Ostilli, Massimo; Figueiredo, Wagner

    2016-01-01

    We consider a simple model of communities interacting via bilinear terms. After analyzing the thermal equilibrium case, which can be described by an Hamiltonian, we introduce the dynamics that, for Ising-like variables, reduces to a Glauber-like dynamics. We analyze and compare four different versions of the dynamics: flow (differential equations), map (discretetime dynamics), local-time update flow, and local-time update map. The presence of only bilinear interactions prevent the flow cases to develop any dynamical instability, the system converging always to the thermal equilibrium. The situation is different for the map when unfriendly couplings are involved, where period-two oscillations arise. In the case of the map with local-time updates, oscillations of any period and chaos can arise as a consequence of the reciprocal “tension” accumulated among the communities during their sleeping time interval. The resulting chaos can be of two kinds: true chaos characterized by positive Lyapunov exponent and bifurcation cascades, or marginal chaos characterized by zero Lyapunov exponent and critical continuous regions.

  13. Classical chaos in atom-field systems

    NASA Astrophysics Data System (ADS)

    Chávez-Carlos, J.; Bastarrachea-Magnani, M. A.; Lerma-Hernández, S.; Hirsch, J. G.

    2016-08-01

    The relation between the onset of chaos and critical phenomena, like quantum phase transitions (QPTs) and excited-state quantum phase transitions (ESQPTs), is analyzed for atom-field systems. While it has been speculated that the onset of hard chaos is associated with ESQPTs based in the resonant case, the off-resonant cases, and a close look at the vicinity of the QPTs in resonance, show clearly that both phenomena, ESQPTs and chaos, respond to different mechanisms. The results are supported in a detailed numerical study of the dynamics of the semiclassical Hamiltonian of the Dicke model. The appearance of chaos is quantified calculating the largest Lyapunov exponent for a wide sample of initial conditions in the whole available phase space for a given energy. The percentage of the available phase space with chaotic trajectories is evaluated as a function of energy and coupling between the qubit and bosonic part, allowing us to obtain maps in the space of coupling and energy, where ergodic properties are observed in the model. Different sets of Hamiltonian parameters are considered, including resonant and off-resonant cases.

  14. Neural control: Chaos control sets the pace

    NASA Astrophysics Data System (ADS)

    Schöll, Eckehard

    2010-03-01

    Even simple creatures, such as cockroaches, are capable of complex responses to changes in their environment. But robots usually require complicated dedicated control circuits to perform just a single action. Chaos control theory could allow simpler control strategies to realize more complex behaviour.

  15. Order, chaos and nuclear dynamics: An introduction

    SciTech Connect

    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. A Framework for Chaos Theory Career Counselling

    ERIC Educational Resources Information Center

    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,…

  17. Many-body chaos at weak coupling

    NASA Astrophysics Data System (ADS)

    Stanford, Douglas

    2016-10-01

    The strength of chaos in large N quantum systems can be quantified using λ L , the rate of growth of certain out-of-time-order four point functions. We calculate λ L to leading order in a weakly coupled matrix Φ4 theory by numerically diagonalizing a ladder kernel. The computation reduces to an essentially classical problem.

  18. Integrability and Chaos: The Classical Uncertainty

    ERIC Educational Resources Information Center

    Masoliver, Jaume; Ros, Ana

    2011-01-01

    In recent years there has been a considerable increase in the publishing of textbooks and monographs covering what was formerly known as random or irregular deterministic motion, now referred to as deterministic chaos. There is still substantial interest in a matter that is included in many graduate and even undergraduate courses on classical…

  19. Chaos and Change in a Suicidal Family.

    ERIC Educational Resources Information Center

    Chamberlain, Linda

    1995-01-01

    The concepts evolving from chaos theory can help clinicians identify patterns in family interactions that are critical for transformations to occur. This article explores a specific case example from such a perspective. Observation of how suicidal behavior becomes part of a pattern of family interaction offers a framework for clinicians to observe…

  20. Chaos, Collaboration, and Curriculum: A Deliberative Process.

    ERIC Educational Resources Information Center

    Goff, Katherine E.

    1998-01-01

    Presents curriculum as a complex social process. Explores chaos theory as a metaphor for understanding curriculum and a framework for viewing the curriculum-development process. Provides examples of collaborative leadership (described by David Chrislip and Carl Larson) and shows how they might answer Joseph Schwab's call for a deliberative…

  1. Classical chaos in atom-field systems.

    PubMed

    Chávez-Carlos, J; Bastarrachea-Magnani, M A; Lerma-Hernández, S; Hirsch, J G

    2016-08-01

    The relation between the onset of chaos and critical phenomena, like quantum phase transitions (QPTs) and excited-state quantum phase transitions (ESQPTs), is analyzed for atom-field systems. While it has been speculated that the onset of hard chaos is associated with ESQPTs based in the resonant case, the off-resonant cases, and a close look at the vicinity of the QPTs in resonance, show clearly that both phenomena, ESQPTs and chaos, respond to different mechanisms. The results are supported in a detailed numerical study of the dynamics of the semiclassical Hamiltonian of the Dicke model. The appearance of chaos is quantified calculating the largest Lyapunov exponent for a wide sample of initial conditions in the whole available phase space for a given energy. The percentage of the available phase space with chaotic trajectories is evaluated as a function of energy and coupling between the qubit and bosonic part, allowing us to obtain maps in the space of coupling and energy, where ergodic properties are observed in the model. Different sets of Hamiltonian parameters are considered, including resonant and off-resonant cases. PMID:27627300

  2. Gain control through divisive inhibition prevents abrupt transition to chaos in a neural mass model

    PubMed Central

    Papasavvas, Christoforos A.; Wang, Yujiang; Trevelyan, Andrew J.; Kaiser, Marcus

    2016-01-01

    Experimental results suggest that there are two distinct mechanisms of inhibition in cortical neuronal networks: subtractive and divisive inhibition. They modulate the input-output function of their target neurons either by increasing the input that is needed to reach maximum output or by reducing the gain and the value of maximum output itself, respectively. However, the role of these mechanisms on the dynamics of the network is poorly understood. We introduce a novel population model and numerically investigate the influence of divisive inhibition on network dynamics. Specifically, we focus on the transitions from a state of regular oscillations to a state of chaotic dynamics via period-doubling bifurcations. The model with divisive inhibition exhibits a universal transition rate to chaos (Feigenbaum behavior). In contrast, in an equivalent model without divisive inhibition, transition rates to chaos are not bounded by the universal constant (non-Feigenbaum behavior). This non-Feigenbaum behavior, when only subtractive inhibition is present, is linked to the interaction of bifurcation curves in the parameter space. Indeed, searching the parameter space showed that such interactions are impossible when divisive inhibition is included. Therefore, divisive inhibition prevents non-Feigenbaum behavior and, consequently, any abrupt transition to chaos. The results suggest that the divisive inhibition in neuronal networks could play a crucial role in keeping the states of order and chaos well separated and in preventing the onset of pathological neural dynamics. PMID:26465514

  3. Gain control through divisive inhibition prevents abrupt transition to chaos in a neural mass model.

    PubMed

    Papasavvas, Christoforos A; Wang, Yujiang; Trevelyan, Andrew J; Kaiser, Marcus

    2015-09-01

    Experimental results suggest that there are two distinct mechanisms of inhibition in cortical neuronal networks: subtractive and divisive inhibition. They modulate the input-output function of their target neurons either by increasing the input that is needed to reach maximum output or by reducing the gain and the value of maximum output itself, respectively. However, the role of these mechanisms on the dynamics of the network is poorly understood. We introduce a novel population model and numerically investigate the influence of divisive inhibition on network dynamics. Specifically, we focus on the transitions from a state of regular oscillations to a state of chaotic dynamics via period-doubling bifurcations. The model with divisive inhibition exhibits a universal transition rate to chaos (Feigenbaum behavior). In contrast, in an equivalent model without divisive inhibition, transition rates to chaos are not bounded by the universal constant (non-Feigenbaum behavior). This non-Feigenbaum behavior, when only subtractive inhibition is present, is linked to the interaction of bifurcation curves in the parameter space. Indeed, searching the parameter space showed that such interactions are impossible when divisive inhibition is included. Therefore, divisive inhibition prevents non-Feigenbaum behavior and, consequently, any abrupt transition to chaos. The results suggest that the divisive inhibition in neuronal networks could play a crucial role in keeping the states of order and chaos well separated and in preventing the onset of pathological neural dynamics. PMID:26465514

  4. Gain control through divisive inhibition prevents abrupt transition to chaos in a neural mass model

    NASA Astrophysics Data System (ADS)

    Papasavvas, Christoforos A.; Wang, Yujiang; Trevelyan, Andrew J.; Kaiser, Marcus

    2015-09-01

    Experimental results suggest that there are two distinct mechanisms of inhibition in cortical neuronal networks: subtractive and divisive inhibition. They modulate the input-output function of their target neurons either by increasing the input that is needed to reach maximum output or by reducing the gain and the value of maximum output itself, respectively. However, the role of these mechanisms on the dynamics of the network is poorly understood. We introduce a novel population model and numerically investigate the influence of divisive inhibition on network dynamics. Specifically, we focus on the transitions from a state of regular oscillations to a state of chaotic dynamics via period-doubling bifurcations. The model with divisive inhibition exhibits a universal transition rate to chaos (Feigenbaum behavior). In contrast, in an equivalent model without divisive inhibition, transition rates to chaos are not bounded by the universal constant (non-Feigenbaum behavior). This non-Feigenbaum behavior, when only subtractive inhibition is present, is linked to the interaction of bifurcation curves in the parameter space. Indeed, searching the parameter space showed that such interactions are impossible when divisive inhibition is included. Therefore, divisive inhibition prevents non-Feigenbaum behavior and, consequently, any abrupt transition to chaos. The results suggest that the divisive inhibition in neuronal networks could play a crucial role in keeping the states of order and chaos well separated and in preventing the onset of pathological neural dynamics.

  5. Effect of correction of aberration dynamics on chaos in human ocular accommodation.

    PubMed

    Hampson, Karen M; Cufflin, Matthew P; Mallen, Edward A H

    2013-11-15

    We used adaptive optics to determine the effect of monochromatic aberration dynamics on the level of chaos in the accommodation control system. Four participants viewed a stationary target while the dynamics of their aberrations were either left uncorrected, defocus was corrected, or all aberrations except defocus were corrected. Chaos theory analysis was used to discern changes in the accommodative microfluctuations. We found a statistically significant reduction in the chaotic nature of the accommodation microfluctuations during correction of defocus, but not when all aberrations except defocus were corrected. The Lyapunov exponent decreased from 0.71 ± 0.07 D/s (baseline) to 0.55 ± 0.03 D/s (correction of defocus fluctuations). As the reduction of chaos in physiological signals is indicative of stress to the system, the results indicate that for the participants included in this study, fluctuations in defocus have a more profound effect than those of the other aberrations. There were no changes in the power spectrum between experimental conditions. Hence chaos theory analysis is a more subtle marker of changes in the accommodation control system and will be of value in the study of myopia onset and progression. PMID:24322122

  6. THEORY OF SECULAR CHAOS AND MERCURY'S ORBIT

    SciTech Connect

    Lithwick, Yoram; Wu Yanqin

    2011-09-20

    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 {approx}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.

  7. Conference Resolution

    NASA Astrophysics Data System (ADS)

    2009-04-01

    Since the first IUPAP International Conference on Women in Physics (Paris, March 2002) and the Second Conference (Rio de Janeiro, May 2005), progress has continued in most countries and world regions to attract girls to physics and advance women into leadership roles, and many working groups have formed. The Third Conference (Seoul, October 2008), with 283 attendees from 57 countries, was dedicated to celebrating the physics achievements of women throughout the world, networking toward new international collaborations, building each participant's capacity for career success, and aiding the formation of active regional working groups to advance women in physics. Despite the progress, women remain a small minority of the physics community in most countries.

  8. Brownian motion properties of optoelectronic random bit generators based on laser chaos.

    PubMed

    Li, Pu; Yi, Xiaogang; Liu, Xianglian; Wang, Yuncai; Wang, Yongge

    2016-07-11

    The nondeterministic property of the optoelectronic random bit generator (RBG) based on laser chaos are experimentally analyzed from two aspects of the central limit theorem and law of iterated logarithm. The random bits are extracted from an optical feedback chaotic laser diode using a multi-bit extraction technique in the electrical domain. Our experimental results demonstrate that the generated random bits have no statistical distance from the Brownian motion, besides that they can pass the state-of-the-art industry-benchmark statistical test suite (NIST SP800-22). All of them give a mathematically provable evidence that the ultrafast random bit generator based on laser chaos can be used as a nondeterministic random bit source. PMID:27410852

  9. Brownian motion properties of optoelectronic random bit generators based on laser chaos.

    PubMed

    Li, Pu; Yi, Xiaogang; Liu, Xianglian; Wang, Yuncai; Wang, Yongge

    2016-07-11

    The nondeterministic property of the optoelectronic random bit generator (RBG) based on laser chaos are experimentally analyzed from two aspects of the central limit theorem and law of iterated logarithm. The random bits are extracted from an optical feedback chaotic laser diode using a multi-bit extraction technique in the electrical domain. Our experimental results demonstrate that the generated random bits have no statistical distance from the Brownian motion, besides that they can pass the state-of-the-art industry-benchmark statistical test suite (NIST SP800-22). All of them give a mathematically provable evidence that the ultrafast random bit generator based on laser chaos can be used as a nondeterministic random bit source.

  10. Biomedical Conferences

    NASA Technical Reports Server (NTRS)

    1976-01-01

    As a result of Biomedical Conferences, Vivo Metric Systems Co. has produced cardiac electrodes based on NASA technology. Frequently in science, one highly specialized discipline is unaware of relevant advances made in other areas. In an attempt to familiarize researchers in a variety of disciplines with medical problems and needs, NASA has sponsored conferences that bring together university scientists, practicing physicians and manufacturers of medical instruments.

  11. A robust DCT domain watermarking algorithm based on chaos system

    NASA Astrophysics Data System (ADS)

    Xiao, Mingsong; Wan, Xiaoxia; Gan, Chaohua; Du, Bo

    2009-10-01

    Digital watermarking is a kind of technique that can be used for protecting and enforcing the intellectual property (IP) rights of the digital media like the digital images containting in the transaction copyright. There are many kinds of digital watermarking algorithms. However, existing digital watermarking algorithms are not robust enough against geometric attacks and signal processing operations. In this paper, a robust watermarking algorithm based on chaos array in DCT (discrete cosine transform)-domain for gray images is proposed. The algorithm provides an one-to-one method to extract the watermark.Experimental results have proved that this new method has high accuracy and is highly robust against geometric attacks, signal processing operations and geometric transformations. Furthermore, the one who have on idea of the key can't find the position of the watermark embedded in. As a result, the watermark not easy to be modified, so this scheme is secure and robust.

  12. Drift waves and chaos in a LAPTAG plasma physics experiment

    NASA Astrophysics Data System (ADS)

    Gekelman, Walter; Pribyl, Patrick; Birge-Lee, Henry; Wise, Joe; Katz, Cami; Wolman, Ben; Baker, Bob; Marmie, Ken; Patankar, Vedang; Bridges, Gabriel; Buckley-Bonanno, Samuel; Buckley, Susan; Ge, Andrew; Thomas, Sam

    2016-02-01

    In a project involving an alliance between universities and high schools, a magnetized plasma column with a steep pressure gradient was established in an experimental device. A two-dimensional probe measured fluctuations in the plasma column in a plane transverse to the background magnetic field. Correlation techniques determined that the fluctuations were that of electrostatic drift waves. The time series data were used to generate the Bandt-Pompe entropy and Jensen-Shannon complexity for the data. These quantities, when plotted against one another, revealed that a combination of drift waves and other background fluctuations were a deterministically chaotic system. Our analysis can be used to tell the difference between deterministic chaos and random noise, making it a potentially useful technique in nonlinear dynamics.

  13. Chaos in coherence modulation: bifurcations of an oscillator generating optical delay fluctuations

    SciTech Connect

    Larger, Laurent; Lee, Min Won; Goedgebuer, Jean-Pierre; Elflein, Wilhelm; Erneux, Thomas

    2001-08-01

    A new chaos generator is described that produces chaotic fluctuations of the optical-path difference in a coherence modulator driven electrically by a nonlinear delayed-feedback loop. Numerical simulations and experimental results are reported. A closed branch of periodic solutions bounded by a forward and a reverse Hopf bifurcation is observed for the first time, to our knowledge, for this type of nonlinear dynamical system. {copyright} 2001 Optical Society of America

  14. Optomechanically induced stochastic resonance and chaos transfer between optical fields

    NASA Astrophysics Data System (ADS)

    Monifi, Faraz; Zhang, Jing; Özdemir, Şahin Kaya; Peng, Bo; Liu, Yu-Xi; Bo, Fang; Nori, Franco; Yang, Lan

    2016-06-01

    Chaotic dynamics has been reported in many physical systems and has affected almost every field of science. Chaos involves hypersensitivity to the initial conditions of a system and introduces unpredictability into its output. Thus, it is often unwanted. Interestingly, the very same features make chaos a powerful tool to suppress decoherence, achieve secure communication and replace background noise in stochastic resonance—a counterintuitive concept that a system's ability to transfer information can be coherently amplified by adding noise. Here, we report the first demonstration of chaos-induced stochastic resonance in an optomechanical system, as well as the optomechanically mediated chaos transfer between two optical fields such that they follow the same route to chaos. These results will contribute to the understanding of nonlinear phenomena and chaos in optomechanical systems, and may find applications in the chaotic transfer of information and for improving the detection of otherwise undetectable signals in optomechanical systems.

  15. [Chaos and fractals and their applications in electrocardial signal research].

    PubMed

    Jiao, Qing; Guo, Yongxin; Zhang, Zhengguo

    2009-06-01

    Chaos and fractals are ubiquitous phenomena of nature. A system with fractal structure usually behaves chaos. As a complicated nonlinear dynamics system, heart has fractals structure and behaves as chaos. The deeper inherent mechanism of heart can be opened out when the chaos and fractals theory is utilized in the research of the electrical activity of heart. Generally a time series of a system was used for describing the status of the strange attractor of the system. The indices include Poincare plot, fractals dimension, Lyapunov exponent, entropy, scaling exponent, Hurst index and so on. In this article, the basic concepts and the methods of chaos and fractals were introduced firstly. Then the applications of chaos and fractals theories in the study of electrocardial signal were expounded with example of how they are used for ventricular fibrillation.

  16. Stochastic Representation of Chaos Using Terminal Attractors

    NASA Technical Reports Server (NTRS)

    Zak, Michail

    2006-01-01

    A nonlinear version of the Liouville equation based on terminal attractors is part of a mathematical formalism for describing postinstability motions of dynamical systems characterized by exponential divergences of trajectories leading to chaos (including turbulence as a form of chaos). The formalism can be applied to both conservative systems (e.g., multibody systems in celestial mechanics) and dissipative systems (e.g., viscous fluids). The development of the present formalism was undertaken in an effort to remove positive Lyapunov exponents. The means chosen to accomplish this is coupling of the governing dynamical equations with the corresponding Liouville equation that describes the evolution of the flow of error probability. The underlying idea is to suppress the divergences of different trajectories that correspond to different initial conditions, without affecting a target trajectory, which is one that starts with prescribed initial conditions.

  17. Chaos theory perspective for industry clusters development

    NASA Astrophysics Data System (ADS)

    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.

  18. Noise suppressions in synchronized chaos lidars.

    PubMed

    Wu, Wen-Ting; Liao, Yi-Huan; Lin, Fan-Yi

    2010-12-01

    The noise suppressions in the chaos lidar (CLIDAR) and the synchronized chaos lidar (S-CLIDAR) systems with the optoelectronic feedback (OEF) and optical feedback (OF) schemes are studied numerically. Compared with the CLIDAR system, the S-CLIDAR system with the OEF scheme has better correlation coefficients in the large noise regime for SNR < 15 dB. For the S-CLIDAR system with the OF scheme, better detections are also achieved in wide ranges depending on the levels of the phase noise presented in the channel. To have the best synchronization and detection quality, the optimized conditions for the coupling and feedback strengths in the S-CLIDAR system are also discussed.

  19. Chaos: Understanding and Controlling Laser Instability

    NASA Technical Reports Server (NTRS)

    Blass, William E.

    1997-01-01

    In order to characterize the behavior of tunable diode lasers (TDL), the first step in the project involved the redesign of the TDL system here at the University of Tennessee Molecular Systems Laboratory (UTMSL). Having made these changes it was next necessary to optimize the new optical system. This involved the fine adjustments to the optical components, particularly in the monochromator, to minimize the aberrations of coma and astigmatism and to assure that the energy from the beam is focused properly on the detector element. The next step involved the taking of preliminary data. We were then ready for the analysis of the preliminary data. This required the development of computer programs that use mathematical techniques to look for signatures of chaos. Commercial programs were also employed. We discovered some indication of high dimensional chaos, but were hampered by the low sample rate of 200 KSPS (kilosamples/sec) and even more by our sample size of 1024 (1K) data points. These limitations were expected and we added a high speed data acquisition board. We incorporated into the system a computer with a 40 MSPS (million samples/sec) data acquisition board. This board can also capture 64K of data points so that were then able to perform the more accurate tests for chaos. The results were dramatic and compelling, we had demonstrated that the lead salt diode laser had a chaotic frequency output. Having identified the chaotic character in our TDL data, we proceeded to stage two as outlined in our original proposal. This required the use of an Occasional Proportional Feedback (OPF) controller to facilitate the control and stabilization of the TDL system output. The controller was designed and fabricated at GSFC and debugged in our laboratories. After some trial and error efforts, we achieved chaos control of the frequency emissions of the laser. The two publications appended to this introduction detail the entire project and its results.

  20. Chaos control of parametric driven Duffing oscillators

    SciTech Connect

    Jin, Leisheng; Mei, Jie; Li, Lijie

    2014-03-31

    Duffing resonators are typical dynamic systems, which can exhibit chaotic oscillations, subject to certain driving conditions. Chaotic oscillations of resonating systems with negative and positive spring constants are identified to investigate in this paper. Parametric driver imposed on these two systems affects nonlinear behaviours, which has been theoretically analyzed with regard to variation of driving parameters (frequency, amplitude). Systematic calculations have been performed for these two systems driven by parametric pumps to unveil the controllability of chaos.

  1. Solitons in the midst of chaos

    SciTech Connect

    Seghete, Vlad; Menyuk, Curtis R.; Marks, Brian S.

    2007-10-15

    A system of coupled nonlinear Schroedinger equations describes pulse propagation in weakly birefringent optical fibers. Soliton solutions of this system are found numerically through the shooting method. We employ Poincare surface of section plots - a standard dynamical systems approach - to analyze the phase space behavior of these solutions and neighboring trajectories. Chaotic behavior around the solitons is apparent and suggests dynamical instability. A Lyapunov stability analysis confirms this result. Thus, solitons exist in the midst of chaos.

  2. Reducing or enhancing chaos using periodic orbits.

    PubMed

    Bachelard, R; Chandre, C; Leoncini, X

    2006-06-01

    A method to reduce or enhance chaos in Hamiltonian flows with two degrees of freedom is discussed. This method is based on finding a suitable perturbation of the system such that the stability of a set of periodic orbits changes (local bifurcations). Depending on the values of the residues, reflecting their linear stability properties, a set of invariant tori is destroyed or created in the neighborhood of the chosen periodic orbits. An application on a paradigmatic system, a forced pendulum, illustrates the method.

  3. Detecting chaos in irregularly sampled time series

    NASA Astrophysics Data System (ADS)

    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.

  4. Detecting chaos in irregularly sampled time series.

    PubMed

    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. PMID:24089946

  5. Nonadiabatic quantum chaos in atom optics

    NASA Astrophysics Data System (ADS)

    Prants, S. V.

    2012-07-01

    Coherent dynamics of atomic matter waves in a standing-wave laser field is studied. In the dressed-state picture, wave packets of ballistic two-level atoms propagate simultaneously in two optical potentials. The probability to make a transition from one potential to another one is maximal when centroids of wave packets cross the field nodes and is given by a simple formula with the single exponent, the Landau-Zener parameter κ. If κ ≫ 1, the motion is essentially adiabatic. If κ ≪ 1, it is (almost) resonant and periodic. If κ ≃ 1, atom makes nonadiabatic transitions with a splitting of its wave packet at each node and strong complexification of the wave function as compared to the two other cases. This effect is referred as nonadiabatic quantum chaos. Proliferation of wave packets at κ ≃ 1 is shown to be connected closely with chaotic center-of-mass motion in the semiclassical theory of point-like atoms with positive values of the maximal Lyapunov exponent. The quantum-classical correspondence established is justified by the fact that the Landau-Zener parameter κ specifies the regime of the semiclassical dynamical chaos in the map simulating chaotic center-of-mass motion. Manifestations of nonadiabatic quantum chaos are found in the behavior of the momentum and position probabilities.

  6. Detecting chaos in irregularly sampled time series.

    PubMed

    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.

  7. Flavors of Chaos in the Asteroid Belt

    NASA Astrophysics Data System (ADS)

    Tsiganis, Kleomenis

    2016-10-01

    The asteroid belt is a natural laboratory for studying chaos, as a large fraction of asteroids actually reside on chaotic orbits. Numerous studies over the past 25 years have unveiled a multitude of dynamical chaos-generating mechanisms, operating on different time-scales and dominating over different regions of the belt. In fact, the distribution of chaotic asteroids in orbital space can be largely understood as the outcome of the combined action of resonant gravitational perturbations and the Yarkovsky effect – two topics on which Paolo Farinella has made an outstanding contribution! – notwithstanding the fact that the different "flavors" of chaos can give rise to a wide range of outcomes, from fast escape (e.g. to NEA space) to slow (~100s My) macroscopic diffusion (e.g. spreading of families) and strange, stable-looking, chaotic orbits (ultra-slow diffusion). In this talk I am going to present an overview of these mechanisms, presenting both analytical and numerical results, and their role in understanding the long-term evolution and stability of individual bodies, asteroid groups and families.

  8. Exploring Chaos: A Case Study.

    ERIC Educational Resources Information Center

    Nemirovsky, Ricardo; Tinker, Robert

    1993-01-01

    Describes software, hardware, and devices that were designed to provide students with an environment to experiment with basic ideas of mechanics, including nonlinear dynamics. Examines the behavior of a Lorenzian water wheel by comparing experimental data with theoretical results obtained from computer-based sensors. (MDH)

  9. Two-field description of chaos synchronization in diode lasers with incoherent optical feedback and injection

    SciTech Connect

    Sukow, David W.; Baracco, Michael J.; Parmenter, Zachary A.; Blackburn, Karen L.; Gavrielides, Athanasios

    2005-10-15

    Synchronized chaotic dynamics are investigated theoretically and experimentally in a system of unidirectionally-coupled semiconductor lasers subject to delayed, polarization-rotated optical feedback and injection. Experimental data in the time and frequency domains demonstrate chaos synchronization with a lag between transmitter and receiver equal to the injection time, also known as driving synchronization. The natural polarization mode of the transmitter is shown to synchronize most efficiently to the orthogonal state of the receiver which is being injected. A full two-polarization model is used for both lasers, and is in good agreement with polarization-resolved experimental measurements.

  10. Experimental Research in TV Instruction. Proceedings of an International Conference (2nd, St. John's, Newfoundland, Canada, June 21-23, 1979). [Volume 2.

    ERIC Educational Resources Information Center

    Baggaley, Jon, Ed.; Sharpe, Joan, Ed.

    A foreword by Arthur M. Sullivan and an introduction by Jon P. Baggaley introduce the 12 conference papers included in this collection. The papers are as follows: (1) "Research on 'Sesame Street': Designing the Educational Context" (Rodney Dennis); (2) "'Sesame Street' in Labrador" (Graham Skanes and Lorne Taylor); (3) "Videotapes for…

  11. Experimental Research in TV Instruction. Proceedings of an International Conference (4th, St. John's, Newfoundland, Canada, September 28-30, 1981). Volume 4.

    ERIC Educational Resources Information Center

    Baggaley, Jon, Ed.; Janega, Patti, Ed.

    An introduction by Jon Baggaley provides background information on this international conference and its participants, and introduces 10 papers which were presented. The papers are as follows: (1) "Teaching Production Research and Design: The Interface of Theory and Practice" (James M. Linton); (2) "The Impact of Television on Adolescents in South…

  12. Experimental Research in TV Instruction. Proceedings of an International Conference (5th, St. John's, Newfoundland, June 28-30, 1982). Volume 5.

    ERIC Educational Resources Information Center

    Baggaley, Jon, Ed.; Janega, Patti, Ed.

    An introduction briefly summarizes the four previous conferences in this series, identifies trends in topics addressed, and introduces the 16 presented papers in this collection. The papers are as follows: (1) "Formative Evaluation and the New Technologies" (Marjorie Cambre); (2) "Formative Evaluation of Sesame Street Using Eye Movement…

  13. Proceedings of the Third International Conference on Experimental Research in Televised Instruction. Memorial University of Newfoundland (Newfoundland, Canada, August 25-27, 1980).

    ERIC Educational Resources Information Center

    Baggaley, Jon, Ed.

    The 11 papers in this collection focus on research in instructional television, the theme of a conference attended by media producers, researchers, and policy makers from Australia, Britain, Canada, France, West Germany, the Netherlands, South Africa, and the United States. The opening paper by Deane Hutton discusses two parallel but contrasting…

  14. Current Self-Oscillations and Chaos in Semiconductor Superlattices

    NASA Astrophysics Data System (ADS)

    Grahn, H. T.

    spectra under application of an external ac voltage shows the well-known route to chaos via alternating windows of frequency locking and quasi-periodicity. Real-time current traces have been used to construct Poincaré sections, which support this interpretation. However, for other dc voltages, the route to chaos can become much more complex. Recently, the multi-fractal dimension of the chaotic attractors has been determined as a function of the dc voltage using the experimentally derived Poincaré sections.

  15. Observation of Temperature Chaos in Mesoscopic Spin Glasses

    NASA Astrophysics Data System (ADS)

    Guchhait, Samaresh

    Temperature Chaos (TC) results from a change in temperature for spin glasses (SG), polymers, and other glassy materials. When the temperature is changed, TC means that the new state has no memory of the preparation of the initial state. TC was predicted long ago [PRL 48, 767 (1982)]. However, ``An experimental measurement of TC is still missing'' [EPL 103, 67003 (2013)]. One reason for this is the question of length scale. In the thermodynamic limit, even an infinitesimal temperature change, ΔT , will create a chaotic condition. However, by working at the mesoscale, one can establish a length scale sufficiently small to exhibit reversible behavior before crossing over to chaotic behavior as the temperature change increases. Observation of TC is possible because, on reasonable laboratory time scales, the SG correlation length can grow to the size of the thickness of the film, L. The lower critical dimension for a SG is ~ 2 . 5 , so that the thin film SG crosses over to a glass temperature Tg = 0 . However, there remains quasi-equilibrium SG states with length scales < L . After crossover, a small ΔT will generate a TC coherence length which, if greater than L, will leave the system in a reversible state. However, when ΔT is sufficiently large, such that the TC coherence length is less than L, and chaos will ensue. I will discuss our recent results of temperature cycling on 15.5 nm SG films of amorphous Ge:Mn. By use of end of aging and temperature cycling, both the reversible region and the chaotic region are observed. Remarkably, the transition from a reversible to chaotic behavior is abrupt, and not smooth as a function of ΔT . This is in contrast to previous work using polycrystalline materials where the distribution of length scales smoothed out the transition to chaos. Using the calculated TC critical exponent, the range of ΔT for reversible behavior is calculated and is in very good agreement with the measured range. This work was supported by the U

  16. Application of Chaos Theory to Psychological Models

    NASA Astrophysics Data System (ADS)

    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

  17. Adaptive sparse polynomial chaos expansion based on least angle regression

    NASA Astrophysics Data System (ADS)

    Blatman, Géraud; Sudret, Bruno

    2011-03-01

    Polynomial chaos (PC) expansions are used in stochastic finite element analysis to represent the random model response by a set of coefficients in a suitable (so-called polynomial chaos) basis. The number of terms to be computed grows dramatically with the size of the input random vector, which makes the computational cost of classical solution schemes (may it be intrusive (i.e. of Galerkin type) or non intrusive) unaffordable when the deterministic finite element model is expensive to evaluate. To address such problems, the paper describes a non intrusive method that builds a sparse PC expansion. First, an original strategy for truncating the PC expansions, based on hyperbolic index sets, is proposed. Then an adaptive algorithm based on least angle regression (LAR) is devised for automatically detecting the significant coefficients of the PC expansion. Beside the sparsity of the basis, the experimental design used at each step of the algorithm is systematically complemented in order to avoid the overfitting phenomenon. The accuracy of the PC metamodel is checked using an estimate inspired by statistical learning theory, namely the corrected leave-one-out error. As a consequence, a rather small number of PC terms are eventually retained ( sparse representation), which may be obtained at a reduced computational cost compared to the classical "full" PC approximation. The convergence of the algorithm is shown on an analytical function. Then the method is illustrated on three stochastic finite element problems. The first model features 10 input random variables, whereas the two others involve an input random field, which is discretized into 38 and 30 - 500 random variables, respectively.

  18. Subharmonic generation, chaos, and subharmonic resurrection in an acoustically driven fluid-filled cavity.

    PubMed

    Cantrell, John H; Adler, Laszlo; Yost, William T

    2015-02-01

    Traveling wave solutions of the nonlinear acoustic wave equation are obtained for the fundamental and second harmonic resonances of a fluid-filled cavity. The solutions lead to the development of a non-autonomous toy model for cavity oscillations. Application of the Melnikov method to the model equation predicts homoclinic bifurcation of the Smale horseshoe type leading to a cascade of period doublings with increasing drive displacement amplitude culminating in chaos. The threshold value of the drive displacement amplitude at tangency is obtained in terms of the acoustic drive frequency and fluid attenuation coefficient. The model prediction of subharmonic generation leading to chaos is validated from acousto-optic diffraction measurements in a water-filled cavity using a 5 MHz acoustic drive frequency and from the measured frequency spectrum in the bifurcation cascade regime. The calculated resonant threshold amplitude of 0.2 nm for tangency is consistent with values estimated for the experimental set-up. Experimental evidence for the appearance of a stable subharmonic beyond chaos is reported. PMID:25725651

  19. Subharmonic generation, chaos, and subharmonic resurrection in an acoustically driven fluid-filled cavity

    SciTech Connect

    Cantrell, John H. Yost, William T.; Adler, Laszlo

    2015-02-15

    Traveling wave solutions of the nonlinear acoustic wave equation are obtained for the fundamental and second harmonic resonances of a fluid-filled cavity. The solutions lead to the development of a non-autonomous toy model for cavity oscillations. Application of the Melnikov method to the model equation predicts homoclinic bifurcation of the Smale horseshoe type leading to a cascade of period doublings with increasing drive displacement amplitude culminating in chaos. The threshold value of the drive displacement amplitude at tangency is obtained in terms of the acoustic drive frequency and fluid attenuation coefficient. The model prediction of subharmonic generation leading to chaos is validated from acousto-optic diffraction measurements in a water-filled cavity using a 5 MHz acoustic drive frequency and from the measured frequency spectrum in the bifurcation cascade regime. The calculated resonant threshold amplitude of 0.2 nm for tangency is consistent with values estimated for the experimental set-up. Experimental evidence for the appearance of a stable subharmonic beyond chaos is reported.

  20. Chaos synchronization and communication of mutual coupling laser ring based on incoherent injection

    NASA Astrophysics Data System (ADS)

    Hu, Juju; Ma, Junshan; Lin, Jinzhong

    2009-11-01

    A chaos secure communication system of mutual coupling lasers ring based on incoherent optical injection is proposed, in which fine tuning of optical frequency is not required compared with other schemes based on coherent optical injection. Therefore the secure communication scheme is attractive for experimental investigation. The dynamics of semiconductor lasers in the coupling ring are examined. Numerical investigations indicate that zero lag synchronization can be achieved under equal coupling time and strength of mutual coupling. Furthermore, by chaos shift keying (CSK), secure communication is simulated with a random bit stream of 1.0Gbit/s. The results confirm the possibility of applying incoherent schemes of mutual coupling lasers ring to realize chaotic secure communication.

  1. [A Method of Synthesizing Tinnitus Rehabilitation Sound Based on Pentatonic Scale and Chaos].

    PubMed

    Chen, Jiemei; He, Peiyu; Pan, Fan

    2015-12-01

    Tinnitus is a common clinical symptom and its occurrence rate is high. It seriously affects life quality of the patients. Scientific researches show that listening some similar and none-repetitive music can relieve tinnitus to some extent. The overall music accorded with self-similarity character by the direct mapping method based on chaos. However, there were often the same tones continuous repeating a few times and tone mutations. To solve the problem, this paper proposes a new method for tinnitus rehabilitation sound synthesis based on pentatonic scale, chaos and musical instrument digital interface (MIDI). Experimental results showed that the tinnitus rehabilitation sounds were not only self-similar and incompletely reduplicate, but also no sudden changes. Thus, it has a referential significance for tinnitus treatment. PMID:27079109

  2. Chaos, bifurcation and intermittent phenomena in DC-DC converters under resonant parametric perturbation

    NASA Astrophysics Data System (ADS)

    Deivasundari, P.; Geetha, R.; Uma, G.; Murali, K.

    2013-07-01

    DC-DC converters act as a black box to study various bifurcations. In the present study, the influence of external periodic interference signal in the input of DC-DC voltage-mode controlled buck converter has been considered. It is found that the presence of sinusoidal or saw-tooth interference signal whose frequency is comparable with the switching frequency of the converter or its rational multiples manifests as remerging chaotic band attractors (or Feigenbaum trees) and intermittent chaos. However, the presence of sinusoidal interference signal having irrational frequency ratios with the switching frequency of the converter leads to quasi-periodic route to chaos. The study was carried out both theoretically and experimentally.

  3. Parameter Space of Fixed Points of the Damped Driven Pendulum Susceptible to Control of Chaos Algorithms

    NASA Astrophysics Data System (ADS)

    Dittmore, Andrew; Trail, Collin; Olsen, Thomas; Wiener, Richard J.

    2003-11-01

    We have previously demonstrated the experimental control of chaos in a Modified Taylor-Couette system with hourglass geometry( Richard J. Wiener et al), Phys. Rev. Lett. 83, 2340 (1999).. Identifying fixed points susceptible to algorithms for the control of chaos is key. We seek to learn about this process in the accessible numerical model of the damped, driven pendulum. Following Baker(Gregory L. Baker, Am. J. Phys. 63), 832 (1995)., we seek points susceptible to the OGY(E. Ott, C. Grebogi, and J. A. Yorke, Phys. Rev. Lett. 64), 1196 (1990). algorithm. We automate the search for fixed points that are candidates for control. We present comparisons of the space of candidate fixed points with the bifurcation diagrams and Poincare sections of the system. We demonstrate control at fixed points which do not appear on the attractor. We also show that the control algorithm may be employed to shift the system between non-communicating branches of the attractor.

  4. A unit on oscillations, determinism and chaos for introductory physics students

    NASA Astrophysics Data System (ADS)

    Laws, Priscilla W.

    2004-04-01

    This article describes a unit on oscillations, determinism and chaos developed for calculus-based introductory physics students as part of the laboratory-centered Workshop Physics curriculum. Students begin by observing the motion of a simple pendulum with a paper clip bob with and without magnets in its vicinity. This observation provides an introduction to the contrasting concepts of Laplacian determinism and chaos. The rest of the unit involves a step-by-step study of a pendulum system that becomes increasingly complex until it is driven into chaotic motion. The time series graphs and phase plots of various configurations of the pendulum are created using a computer data acquisition system with a rotary motion sensor. These experimental results are compared to iterative spreadsheet models developed by students based on the nature of the torques the system experiences. The suitability of the unit for introductory physics students in traditional laboratory settings is discussed.

  5. Chaos in a chemical system

    NASA Astrophysics Data System (ADS)

    Srivastava, R.; Srivastava, P. K.; Chattopadhyay, J.

    2013-07-01

    Chaotic oscillations have been observed experimentally in dual-frequency oscillator OAP - Ce+4-BrO- 3-H2SO4 in CSTR. The system shows variation of oscillating potential and frequencies when it moves from low frequency to high frequency region and vice-versa. It was observed that system bifurcate from low frequency to chaotic regime through periode-2 and period-3 on the other hand system bifurcate from chaotic regime to high frequency oscillation through period-2. It was established that the observed oscillations are chaotic in nature on the basis of next amplitude map and bifurcation sequences.

  6. Conference Summary

    NASA Technical Reports Server (NTRS)

    Harrington, James L., Jr.

    2000-01-01

    Celebrations and special events were in order this year as the Minority University-Space Interdisciplinary Network (MU-SPIN) Program and NASA's Minority University Research and Education Division (MURED) both reached their 10th anniversaries. In honor of this occasion, the 2000 Annual Users' Conference held at Morris Brown College (MBC) in Atlanta, Georgia, September 11-15, 2000, was the first to be jointly hosted by MU-SPIN and MURED. It was particularly fitting that this anniversary should fall in the year 2000. The start of the new millennium propelled us to push bold new ideas and renew our commitment to minority university participation in all areas of NASA. With the theme 'Celebrating Our Tenth Year With Our Eyes on the Prize,' the conference provided a national forum for showcasing successful MU-SPIN and MURED Program (MUREP) experiences to enhance faculty/student development in areas of scientific and technical research and education. Our NASA-relevant conference agenda resulted in a record-breaking 220 registered attendees. Using feedback from past participants, we designed a track of student activities closely tailored to their interests. The resulting showcase of technical assistance and best practices set a new standard for our conferences in the years to come. This year's poster session was our largest ever, with over 50 presentations from students, faculty, and teachers. Posters covered a broad range of NASA activities from 'A Study of the Spiral Galaxy M101' to 'Network Cabling Characteristics.'

  7. Analysis of Discovery of Chaos: Social and Cognitive Aspects.

    ERIC Educational Resources Information Center

    Kim, J. B.

    The purpose of this study was to examine Edward Lorenz's psychological processes and other environmental aspects in the discovery of chaos at that time. The general concept of chaos is discussed based on relations with previous scientific theories such as Newtonian physics and quantum mechanics. The constraints of discovery in terms of available…

  8. Applying Chaos Theory to Lesson Planning and Delivery

    ERIC Educational Resources Information Center

    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…

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

    ERIC Educational Resources Information Center

    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…

  10. Master Teachers: Making a Difference on the Edge of Chaos

    ERIC Educational Resources Information Center

    Chapin, Dexter

    2008-01-01

    The No Child Left Behind legislation, by legitimizing a stark, one-size-fits-all, industrial model of education, has denied the inherent complexity and richness of what teachers do. Discussing teaching in terms of Chaos Theory, Chapin explains that while excellent teaching may occur at the edge of chaos, it is not chaotic. There are patterns…

  11. Chaos Theory: No Strange Attractor in Teacher Education.

    ERIC Educational Resources Information Center

    Benson, Garth D.; Hunter, William J.

    1993-01-01

    It is inappropriate to apply chaos theory to teaching and teacher education, primarily because of the inherent difficulties of applying methods and criteria developed for the physical sciences to nonphysical phenomena such as human behaviors. Nor is it clear that chaos theorists intended that theory to encompass teaching, learning, and the process…

  12. Chaos Theory as a Lens for Advancing Quality Schooling.

    ERIC Educational Resources Information Center

    Snyder, Karolyn J.; Acker-Hocevar, Michele; Wolf, Kristen M.

    Chaos theory provides a useful mental model for guiding change as leaders garner the energy from unpredictable events for realizing transformation goals. The paper considers chaos theory as a framework for managing school change toward Total Quality Management work cultures. Change is possible to manage when plans are made and then followed by a…

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

    ERIC Educational Resources Information Center

    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…

  14. Chaos Theory: Implications for Nonlinear Dynamics in Counseling.

    ERIC Educational Resources Information Center

    Stickel, Sue A.

    The purpose of this paper is to explore the implications of chaos theory for counseling. The scientific notion of chaos refers to the tendency of dynamical, nonlinear systems toward irregular, sometimes unpredictable, yet deterministic behavior. Therapists, especially those working from a brief approach, have noted the importance of the client's…

  15. The "Chaos" Pattern in Piaget's Theory of Cognitive Development.

    ERIC Educational Resources Information Center

    Lindsay, Jean S.

    Piaget's theory of the cognitive development of the child is related to the recently developed non-linear "chaos" model. The term "chaos" refers to the tendency of dynamical, non-linear systems toward irregular, sometimes unpredictable, deterministic behavior. Piaget identified this same pattern in his model of cognitive development in children.…

  16. Chaos: A Topic for Interdisciplinary Education in Physics

    ERIC Educational Resources Information Center

    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…

  17. Transition to Chaos in Random Neuronal Networks

    NASA Astrophysics Data System (ADS)

    Kadmon, Jonathan; Sompolinsky, Haim

    2015-10-01

    Firing patterns in the central nervous system often exhibit strong temporal irregularity and considerable heterogeneity in time-averaged response properties. Previous studies suggested that these properties are the outcome of the intrinsic chaotic dynamics of the neural circuits. Indeed, simplified rate-based neuronal networks with synaptic connections drawn from Gaussian distribution and sigmoidal nonlinearity are known to exhibit chaotic dynamics when the synaptic gain (i.e., connection variance) is sufficiently large. In the limit of an infinitely large network, there is a sharp transition from a fixed point to chaos, as the synaptic gain reaches a critical value. Near the onset, chaotic fluctuations are slow, analogous to the ubiquitous, slow irregular fluctuations observed in the firing rates of many cortical circuits. However, the existence of a transition from a fixed point to chaos in neuronal circuit models with more realistic architectures and firing dynamics has not been established. In this work, we investigate rate-based dynamics of neuronal circuits composed of several subpopulations with randomly diluted connections. Nonzero connections are either positive for excitatory neurons or negative for inhibitory ones, while single neuron output is strictly positive with output rates rising as a power law above threshold, in line with known constraints in many biological systems. Using dynamic mean field theory, we find the phase diagram depicting the regimes of stable fixed-point, unstable-dynamic, and chaotic-rate fluctuations. We focus on the latter and characterize the properties of systems near this transition. We show that dilute excitatory-inhibitory architectures exhibit the same onset to chaos as the single population with Gaussian connectivity. In these architectures, the large mean excitatory and inhibitory inputs dynamically balance each other, amplifying the effect of the residual fluctuations. Importantly, the existence of a transition to chaos

  18. Classical chaos in nonseparable wave propagation problems

    NASA Astrophysics Data System (ADS)

    Palmer, David R.; Brown, Michael G.; Tappert, Frederick D.; Bezdek, Hugo F.

    1988-06-01

    Numerical calculations show that acoustic ray paths in a weakly range-dependent deterministic ocean model exhibit chaotic behavior, that is, have an exponentially sensitive dependence on initial conditions. Since the ray equations define a nonautonomous Hamiltonian system with one degree of freedom, these results may be understood in terms of recent advances in classical chaos. The Hamiltonian structure of ray equations in general suggests that chaotic ray trajectories will be present in all types of linear wave motion in geophysics when variables do not separate, as in laterally inhomogeneous media.

  19. Decoherence, chaos, and the second law

    SciTech Connect

    Zurek, W.H.; Paz, J.P. )

    1994-04-18

    Quantum wave function of a chaotic system spreads rapidly over distances on which the potential is significantly nonlinear. As a result, the effective force is no longer just a gradient of the potential, and predictions of classical and quantum dynamics begin to differ. We show how the interaction with the environment limits distances over which quantum coherence can persist, and therefore reconciles quantum dynamics with classical Hamiltonian chaos. The entropy production rate for such open chaotic systems exhibits a sharp transition between reversible and dissipative regimes, where it is set by the chaotic dynamics.

  20. Chaos in a Fractional Order Chua System

    NASA Technical Reports Server (NTRS)

    Lorenzo, Carl F.; Hartley, Tom T.; Qammar, Helen Killory

    1996-01-01

    This report studies the effects of fractional dynamics in chaotic systems. In particular, Chua's system is modified to include fractional order elements. Varying the total system order incrementally from 2.6 to 3.7 demonstrates that systems of 'order' less than three can exhibit chaos as well as other nonlinear behavior. This effectively forces a clarification of the definition of order which can no longer be considered only by the total number of differentiations or by the highest power of the Laplace variable.

  1. Quasiperiodic graphs at the onset of chaos.

    PubMed

    Luque, B; Cordero-Gracia, M; Gómez, M; Robledo, A

    2013-12-01

    We examine the connectivity fluctuations across networks obtained when the horizontal visibility (HV) algorithm is used on trajectories generated by nonlinear circle maps at the quasiperiodic transition to chaos. The resultant HV graph is highly anomalous as the degrees fluctuate at all scales with amplitude that increases with the size of the network. We determine families of Pesin-like identities between entropy growth rates and generalized graph-theoretical Lyapunov exponents. An irrational winding number with pure periodic continued fraction characterizes each family. We illustrate our results for the so-called golden, silver, and bronze numbers.

  2. The CHAOS-4 Geomagnetic Field Model

    NASA Astrophysics Data System (ADS)

    Olsen, N.; Finlay, C. C.; Luhr, H.; Sabaka, T. J.; Michaelis, I.; Rauberg, J.; Tøffner-clausen, L.

    2013-12-01

    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 resolution (allowing for investigations of sub-annual core field changes). More than 14 years of data from the satellites Ørsted (March 1999 to June 2013), CHAMP (July 2000 to September 2010) and SAC-C (2000 to 2004), augmented with ground observatory revised monthly mean values (1997 to 2013) have been used for this model. Maximum spherical harmonic degree of the static (crustal) field is n=100. The core field time changes are expressed by spherical harmonic expansion coefficients up to n=20, described by order 6 splines (with 6-month knot spacing) spanning the time interval 1997.0 to 2013.5. The third time derivative of the squared magnetic field intensity is regularized at the core-mantle boundary. No spatial regularization is applied for the core field, but the high-degree crustal field is regularized for n>85. As part of the modeling effort we co-estimate a model of the large-scale magnetospheric field (with expansions in the GSM and SM coordinate system up to degree n = 2 and parameterization of the time dependence using the decomposition of Dst into external (Est) and induced (Ist) parts) and perform an in-flight alignment of the vector data (co-estimation of the Euler describing the rotation 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 of course including newer satellite observations), while its high-degree crustal field part is solely determined from low-altitude CHAMP satellite observations between January 2009 and

  3. Beyond Benford's Law: Distinguishing Noise from Chaos

    PubMed Central

    Li, Qinglei; Fu, Zuntao; Yuan, Naiming

    2015-01-01

    Determinism and randomness are two inherent aspects of all physical processes. Time series from chaotic systems share several features identical with those generated from stochastic processes, which makes them almost undistinguishable. In this paper, a new method based on Benford's law is designed in order to distinguish noise from chaos by only information from the first digit of considered series. By applying this method to discrete data, we confirm that chaotic data indeed can be distinguished from noise data, quantitatively and clearly. PMID:26030809

  4. Mode-locking and the transition to chaos in dissipative systems

    SciTech Connect

    Bak, P.; Bohr, T.; Jensen, M.H.

    1984-01-01

    Dissipative systems with two competing frequencies exhibit transitions to chaos. We have investigated the transition through a study of discrete maps of the circle onto itself, and by constructing and analyzing return maps of differential equations representing some physical systems. The transition is caused by interaction and overlap of mode-locked resonances and takes place at a critical line where the map losses invertibility. At this line the mode-locked intervals trace up a complete Devil's Staircase whose complementary set is a Cantor set with universal fractal dimension D approx. 0.87. Below criticality there is room for quasiperiodic orbits, whose measure is given by an exponent ..beta.. approx. 0.34 which can be related to D through a scaling relation, just as for second order phase transitions. The Lebesgue measure serves as an order parameter for the transition to chaos. The resistively shunted Josephson junction, and charge density waves (CDWs) in rf electric fields are usually described by the differential equation of the damped driven pendulum. The 2d return map for this equation collapses to ld circle map at and below the transition to chaos. The theoretical results on universal behavior, derived here and elsewhere, can thus readily be checked experimentally by studying real physical systems. Recent experiments on Josephson junctions and CDWs indicating the predicted fractal scaling of mode-locking at criticality are reviewed.

  5. Chaos in hydrodynamic BL Herculis models

    NASA Astrophysics Data System (ADS)

    Smolec, R.; Moskalik, P.

    2014-06-01

    We present non-linear, convective, BL Her-type hydrodynamic models that show complex variability characteristic for deterministic chaos. The bifurcation diagram reveals a rich structure, with many phenomena detected for the first time in hydrodynamic models of pulsating stars. The phenomena include not only period doubling cascades en route to chaos (detected in earlier studies) but also periodic windows within chaotic band, type-I and type-III intermittent behaviour, interior crisis bifurcation and others. Such phenomena are known in many textbook chaotic systems, from the simplest discrete logistic map, to more complex systems like Lorenz equations. We discuss the physical relevance of our models. Although except of period doubling such phenomena were not detected in any BL Her star, chaotic variability was claimed in several higher luminosity siblings of BL Her stars - RV Tau variables, and also in longer-period, luminous irregular pulsators. Our models may help to understand these poorly studied stars. Particularly interesting are periodic windows which are intrinsic property of chaotic systems and are not necessarily caused by resonances between pulsation modes, as sometimes claimed in the literature.

  6. Equilibrium behavior of coarse-grained chaos

    NASA Astrophysics Data System (ADS)

    Egolf, David A.; Ballard, Christopher C.; Esty, C. Clark

    2015-03-01

    A wide variety of systems exhibiting spatiotemporal chaos have been shown to be extensive, in that their fractal dimensions grow linearly with volume. Ruelle argued that this extensivity is evidence that these systems can be viewed as a gas of weakly-interacting regions. We have tested this idea by performing large-scale computational studies of spatiotemporal chaos in the 1D complex Ginzburg-Landau equation, and we have found that aspects of the coarse-grained system are well-described not only as a gas, but as an equilibrium gas -- in particular, a Tonks gas (and variants) in the grand canonical ensemble. Furthermore, for small system sizes, the average number of particles in the corresponding Tonks gas exhibits oscillatory, decaying deviations from extensivity in agreement with deviations in the fractal dimension found by Fishman and Egolf. This result not only supports Ruelle's picture but also suggests that the coarse-grained behavior of this far-from-equilibrium system might be understood using equilibrium statistical mechanics.

  7. RAPID DYNAMICAL CHAOS IN AN EXOPLANETARY SYSTEM

    SciTech Connect

    Deck, Katherine M.; Winn, Joshua N.; Holman, Matthew J.; Carter, Joshua A.; Ragozzine, Darin; Agol, Eric; Lissauer, Jack J.

    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.

  8. A chaos model of meandering rivers

    SciTech Connect

    Stoelum, H.H.

    1991-03-01

    A meandering river is a nonlinear dynamic system, and fractal geometry describes well the meander bends of such rivers. Based on a qualitative, sedimentological model of the process of meandering, a chaos model is proposed, describing meandering as the outcome of two processes: the feedback interaction between river curvature and a high-velocity thalweg channel within the river; and the interaction between meander bends causing abandonment and straightening of the river course. The system, when initiated from a nearly straight river course, moves toward a dynamic equilibrium in which the meander bends are fractal. This development is a case of self-organized criticality. The equilibrium represents a state of optimal energy dissipation in a situation where two counteracting processes are balancing each other. Sedimentology may be seen as the science that describes how nonlinear dynamic processes interact to create a depositional system. As indicated by the example of meandering rivers, the use of chaos and fractal models may give sedimentology a new turn toward understanding sedimentary processes and the 3-D architecture of sediment bodies.

  9. Chaos induced by coupling between Josephson junctions

    NASA Astrophysics Data System (ADS)

    Shukrinov, Yu. M.; Azemtsa-Donfack, H.; Botha, A. E.

    2015-02-01

    It is found that, in a stack of intrinsic Josephson junctions in layered high temperature superconductors under external electromagnetic radiation, the chaotic features are triggered by interjunction coupling, i.e., the coupling between different junctions in the stack. While the radiation is well known to produce chaotic effects in the single junction, the effect of interjunction coupling is fundamentally different and it can lead to the onset of chaos via a different route to that of the single junction. A precise numerical study of the phase dynamics of intrinsic Josephson junctions, as described by the CCJJ+DC model, is performed. We demonstrate the charging of superconducting layers, in a bias current interval corresponding to a Shapiro step subharmonic, due to the creation of a longitudinal plasma wave along the stack of junctions. With increase in radiation amplitude chaotic behavior sets in. The chaotic features of the coupled Josephson junctions are analyzed by calculations of the Lyapunov exponents. We compare results for a stack of junctions to the case of a single junction and prove that the observed chaos is induced by the coupling between the junctions. The use of Shapiro step subharmonics may allow longitudinal plasma waves to be excited at low radiation power.

  10. New mechanism of chaos in triangular billiards

    NASA Astrophysics Data System (ADS)

    Naydenov, S. V.; Naplekov, D. M.; Yanovsky, V. V.

    2013-12-01

    A new mechanism of weak chaos in triangular billiards has been proposed owing to the effect of cutting of beams of rays. A similar mechanism is also implemented in other polygonal billiards. Cutting of beams results in the separation of initially close rays at a finite angle by jumps in the process of reflections of beams at the vertices of a billiard. The opposite effect of joining of beams of rays occurs in any triangular billiard along with cutting. It has been shown that the cutting of beams has an absolute character and is independent of the form of a triangular billiard or the parameters of a beam. On the contrary, joining has a relative character and depends on the commensurability of the angles of the triangle with π. Joining always suppresses cutting in triangular billiards whose angles are commensurable with π. For this reason, their dynamics cannot be chaotic. In triangular billiards whose angles are rationally incommensurable with π, cutting always dominates, leading to weak chaos. The revealed properties are confirmed by numerical experiments on the phase portraits of typical triangular billiards.

  11. Decrease of cardiac chaos in congestive heart failure

    NASA Astrophysics Data System (ADS)

    Poon, Chi-Sang; Merrill, Christopher K.

    1997-10-01

    The electrical properties of the mammalian heart undergo many complex transitions in normal and diseased states. It has been proposed that the normal heartbeat may display complex nonlinear dynamics, including deterministic chaos,, and that such cardiac chaos may be a useful physiological marker for the diagnosis and management, of certain heart trouble. However, it is not clear whether the heartbeat series of healthy and diseased hearts are chaotic or stochastic, or whether cardiac chaos represents normal or abnormal behaviour. Here we have used a highly sensitive technique, which is robust to random noise, to detect chaos. We analysed the electrocardiograms from a group of healthy subjects and those with severe congestive heart failure (CHF), a clinical condition associated with a high risk of sudden death. The short-term variations of beat-to-beat interval exhibited strongly and consistently chaotic behaviour in all healthy subjects, but were frequently interrupted by periods of seemingly non-chaotic fluctuations in patients with CHF. Chaotic dynamics in the CHF data, even when discernible, exhibited a high degree of random variability over time, suggesting a weaker form of chaos. These findings suggest that cardiac chaos is prevalent in healthy heart, and a decrease in such chaos may be indicative of CHF.

  12. Metabolic Engineering VII Conference

    SciTech Connect

    Kevin Korpics

    2012-12-04

    The aims of this Metabolic Engineering conference are to provide a forum for academic and industrial researchers in the field; to bring together the different scientific disciplines that contribute to the design, analysis and optimization of metabolic pathways; and to explore the role of Metabolic Engineering in the areas of health and sustainability. Presentations, both written and oral, panel discussions, and workshops will focus on both applications and techniques used for pathway engineering. Various applications including bioenergy, industrial chemicals and materials, drug targets, health, agriculture, and nutrition will be discussed. Workshops focused on technology development for mathematical and experimental techniques important for metabolic engineering applications will be held for more in depth discussion. This 2008 meeting will celebrate our conference tradition of high quality and relevance to both industrial and academic participants, with topics ranging from the frontiers of fundamental science to the practical aspects of metabolic engineering.

  13. Theory of the nucleus as applied to quantum chaos

    SciTech Connect

    Bunakov, V. E.

    2014-12-15

    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. It is proposed to specify a regular versus a chaotic behavior on the basis of symmetries of the system being considered and global integrals of motion that are associated with these symmetries in accordance with the Liouville-Arnold theorem rather than on the basis of the concept of Lyapunov’s instability of trajectories. Numerical criteria of quantum chaos that follow from the proposed concept are analyzed.

  14. The role of chaos in poverty and children's socioemotional adjustment.

    PubMed

    Evans, Gary W; Gonnella, Carrie; Marcynyszyn, Lyscha A; Gentile, Lauren; Salpekar, Nicholas

    2005-07-01

    There are growing levels of chaos in the lives of American children, youth, and families. Increasingly, children grow up in households lacking in structure and routine, inundated by background stimulation from noise and crowding, and forced to contend with the frenetic pace of modern life. Although widespread, chaos does not occur randomly in the population. We document that low-income adolescents face higher levels of chaos than their more affluent counterparts and provide longitudinal evidence that some of the adverse effects of poverty on socioemotional adjustment are mediated by exposure to chaotic living conditions. PMID:16008790

  15. Contributions of plasma physics to chaos and nonlinear dynamics

    NASA Astrophysics Data System (ADS)

    Escande, D. F.

    2016-11-01

    This topical review focusses on the contributions of plasma physics to chaos and nonlinear dynamics bringing new methods which are or can be used in other scientific domains. It starts with the development of the theory of Hamiltonian chaos, and then deals with order or quasi order, for instance adiabatic and soliton theories. It ends with a shorter account of dissipative and high dimensional Hamiltonian dynamics, and of quantum chaos. Most of these contributions are a spin-off of the research on thermonuclear fusion by magnetic confinement, which started in the fifties. Their presentation is both exhaustive and compact. [15 April 2016

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

    PubMed

    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.

  17. Comment on: ``Chaos in the Showalter-Noyes-Bar-Eli model of the Belousov-Zhabotinskii reaction''

    NASA Astrophysics Data System (ADS)

    Györgyi, László; Field, Richard J.

    1990-08-01

    The recent numerical work of Lindberg et al. convincingly demonstrates that chemical chaos in a continuous flow, stirred tank reactor (CSTR) can be reproduced by a spatially homogeneous, accurate model of the kinetics of the Belousov-Zhabotinskii(BZ) reaction. However, some problems remain. The chaos in this model and two others, one using an accurate model of the chemical kinetics in conjunction with spatial inhomogeneity resulting from the finite CSTR mixing time and the other using a flawed model of the BZ chemical kinetics, results from coupling of two cycles coexisting within the complex dynamic model. The second cycle in the case of the homogeneous models involves a product of the main chemical limit cycle which is present at a high average concentration. In the Lindberg et al. model this product is assumed to be HOBr. It is clear, however, that a large [HOBr] does not accumulate in the real system because of its rapid reaction with Br-. We suggest that while the Lindberg et al. results are clearly important, this process still needs to be accounted for. Furthermore, the rate parameter values used by Lindberg et al. are not those currently thought to be correct, and the chaos disappears if the accurate rate constant values are used. We discuss why this is so. It is further argued that the Lindberg et al. results do not eliminate the possibility that at least part of the experimentally observed CSTR chaos results from effects related to incomplete mixing.

  18. Next conference

    NASA Astrophysics Data System (ADS)

    Hexemer, Alexander; Toney, Michael F.

    2010-11-01

    After the successful conference on Synchrotron Radiation in Polymer Science (SRPS) in Rolduc Abbey (the Netherlands), we are now looking forward to the next meeting in this topical series started in 1995 by H G Zachmann, one of the pioneers of the use of synchrotron radiation techniques in polymer science. Earlier meetings were held in Hamburg (1995), Sheffield (2002), Kyoto (2006), and Rolduc (2009). In September of 2012 the Synchrotron Radiation and Polymer Science V conferences will be organized in a joint effort by the SLAC National Accelerator Laboratory and Lawrence Berkeley National Laboratory. Stanford Linear Accelerator Laboratory Stanford Linear Accelerator Laboratory Advanced Light Source at LBL Advanced Light Source at LBL The conference will be organised in the heart of beautiful San Francisco. The program will consist of invited and contributed lectures divided in sessions on the use of synchrotron SAXS/WAXD, imaging and tomography, soft x-rays, x-ray spectroscopy, GISAXS and reflectivity, micro-beams and hyphenated techniques in polymer science. Poster contributions are more than welcome and will be highlighted during the poster sessions. Visits to both SLAC as well as LBL will be organised. San Francisco can easily be reached. It is served by two major international airports San Francisco International Airport and Oakland International Airport. Both are being served by most major airlines with easy connections to Europe and Asia as well as national destinations. Both also boast excellent connections to San Francisco city centre. We are looking forward to seeing you in the vibrant city by the Bay in September 2012. Golden gate bridge Alexander Hexemer Lawrence Berkeley National Laboratory, Advanced Light Source, Berkeley, CA 94720, USA Michael F Toney Stanford Synchrotron Radiation Lightsource, Menlo Pk, CA 94025, USA E-mail: ahexemer@lbl.gov, mftoney@slac.stanford.edu

  19. Conference Summary

    NASA Astrophysics Data System (ADS)

    Ellis, R. S.

    2008-10-01

    This first Subaru international conference has highlighted the remarkably diverse and significant contributions made using the 8.2m Subaru telescope by both Japanese astronomers and the international community. As such, it serves as a satisfying tribute to the pioneering efforts of Professors Keiichi Kodaira and Sadanori Okamura whose insight and dedication is richly rewarded. Here I try to summarize the recent impact of wide field science in extragalactic astronomy and cosmology and take a look forward to the key questions we will address in the near future.

  20. Conferences revisited

    NASA Astrophysics Data System (ADS)

    Radcliffe, Jonathan

    2008-08-01

    Way back in the mid-1990s, as a young PhD student, I wrote a Lateral Thoughts article about my first experience of an academic conference (Physics World 1994 October p80). It was a peach of a trip - most of the lab decamped to Grenoble for a week of great weather, beautiful scenery and, of course, the physics. A whole new community was there for me to see in action, and the internationality of it all helped us to forget about England's non-appearance in the 1994 World Cup finals.

  1. Computational Biology Support: RECOMB Conference Series (Conference Support)

    SciTech Connect

    Michael Waterman

    2006-06-15

    collection of nine keynotes awarded to researchers of highest international esteem who are asked to inform the community about landmark advances in computational and experimental research and inject new directions into the field of computational molecular biology. This includes the following conference events: Next we present a list of the names of the students and postdocs supported. Those supported either presented a paper (10 in 2001, 6 in 2002, 7 in 2003, 14 in 2004, and 20 in 2006) or were they presenter of a poster. This support was vital to the quality and success of the Conference. At the conclusion we give the publication details of the relevant Recomb proceedings.

  2. PREFACE: Quark Matter 2006 Conference

    NASA Astrophysics Data System (ADS)

    Ma, Yu-Gang; Wang, En-Ke; Cai, Xu; Huang, Huan-Zhong; Wang, Xin-Nian; Zhu, Zhi-Yuan

    2007-07-01

    scientific program of the conference began with an overview of high energy nuclear physics in China by Professor Wenqing Shen, vice president of the National Natural Science Foundation of China. Professor Shen highlighted many contributions made by the Chinese scientists in both theory and experiment. Dr Nick Samios, former director of Brookhaven National Laboratory (BNL), gave a vivid account of the early years of RHIC and recent accomplishments. Highlights of the conference include new results from RHIC at BNL and SPS (Super Proton Synchrotron) at CERN (European Organization for Nuclear Research). Many experimental results reported at the conference support the notion that the quark-gluon matter at RHIC behaves like a perfect liquid with minimum viscosity to entropy ratio. There were 15 plenary sessions which covered 54 plenary talks, 12 parallel sessions and 1 poster session. A total of 320 abstracts were submitted to the conference out of which 124 were selected for oral presentation and the rest were assigned to the poster session. Talks and posters in the conference covered a broad range of experimental and theoretical progress in ultra-relativistic heavy-ion collisions, which includes new evidence of sQGP, jet quenching and heavy quark energy loss, heavy-ion collision phenomenology, quantum field theory at finite temperature and/or density, and relevant areas of astrophysics and plasma physics. The Quark Matter 2006 conference coincided with the 80th birthday of Professor T D Lee. A special reception was held in the banquet hall of the Shanghai Grand Theatre to celebrate Professor Lee's birthday and to honor his great contributions to physics, in particular, to the development of high energy nuclear physics research in China. We would like to thank the members of the International Advisory Committee for providing valuable advice on a variety of matters, from the general structure of the conference to the selection of the plenary speakers and selection of abstracts for

  3. Chaos computing in terms of periodic orbits.

    PubMed

    Kia, Behnam; Spano, Mark L; Ditto, William L

    2011-09-01

    The complex dynamics of chaotic systems can perform computations. The parameters and/or the initial conditions of a dynamical system are the data inputs and the resulting system state is the output of the computation. By controlling how inputs are mapped to outputs, a specific function can be performed. Previously no clear connection has been drawn between the structure of the dynamics and the computation. In this paper we demonstrate how chaos computation can be explained, modeled, and even predicted in terms of the dynamics of the underlying chaotic system, specifically the periodic orbit structure of the system. Knowing the dynamical equations of the system, we compute the system's periodic orbits as well as its stability in terms of its eigenvalues, thereby demonstrating how, how well, and what the chaotic system can compute.

  4. Chaos, fractals, and our concept of disease.

    PubMed

    Varela, Manuel; Ruiz-Esteban, Raul; Mestre de Juan, Maria Jose

    2010-01-01

    The classic anatomo-clinic paradigm based on clinical syndromes is fraught with problems. Nevertheless, for multiple reasons, clinicians are reluctant to embrace a more pathophysiological approach, even though this is the prevalent paradigm under "which basic sciences work. In recent decades, nonlinear dynamics ("chaos theory") and fractal geometry have provided powerful new tools to analyze physiological systems. However, these tools are embedded in the pathophysiological perspective and are not easily translated to our classic syndromes. This article comments on the problems raised by the conventional anatomo-clinic paradigm and reviews three areas in which the influence of nonlinear dynamics and fractal geometry can be especially prominent: disease as a loss of complexity, the idea of homeostasis, and fractals in pathology.

  5. Adaptive functional systems: Learning with chaos

    NASA Astrophysics Data System (ADS)

    Komarov, M. A.; Osipov, G. V.; Burtsev, M. S.

    2010-12-01

    We propose a new model of adaptive behavior that combines a winnerless competition principle and chaos to learn new functional systems. The model consists of a complex network of nonlinear dynamical elements producing sequences of goal-directed actions. Each element describes dynamics and activity of the functional system which is supposed to be a distributed set of interacting physiological elements such as nerve or muscle that cooperates to obtain certain goal at the level of the whole organism. During "normal" behavior, the dynamics of the system follows heteroclinic channels, but in the novel situation chaotic search is activated and a new channel leading to the target state is gradually created simulating the process of learning. The model was tested in single and multigoal environments and had demonstrated a good potential for generation of new adaptations.

  6. Control of neural chaos by synaptic noise.

    PubMed

    Cortes, J M; Torres, J J; Marro, J

    2007-02-01

    We study neural automata - or neurobiologically inspired cellular automata - which exhibits chaotic itinerancy among the different stored patterns or memories. This is a consequence of activity-dependent synaptic fluctuations, which continuously destabilize the attractor and induce irregular hopping to other possible attractors. The nature of these irregularities depends on the dynamic details, namely, on the intensity of the synaptic noise and the number of sites of the network, which are synchronously updated at each time step. Varying these factors, different regimes occur, ranging from regular to chaotic dynamics. As a result, and in absence of external agents, the chaotic behavior may turn regular after tuning the noise intensity. It is argued that a similar mechanism might be on the basis of self-controlling chaos in natural systems.

  7. A simple guide to chaos and complexity

    PubMed Central

    Rickles, Dean; Hawe, Penelope; Shiell, Alan

    2007-01-01

    The concepts of complexity and chaos are being invoked with increasing frequency in the health sciences literature. However, the concepts underpinning these concepts are foreign to many health scientists and there is some looseness in how they have been translated from their origins in mathematics and physics, which is leading to confusion and error in their application. Nonetheless, used carefully, “complexity science” has the potential to invigorate many areas of health science and may lead to important practical outcomes; but if it is to do so, we need the discipline that comes from a proper and responsible usage of its concepts. Hopefully, this glossary will go some way towards achieving that objective. PMID:17933949

  8. Detecting recursive and nonrecursive filters using chaos.

    PubMed

    Carroll, T L

    2010-03-01

    Filtering a chaotic signal through a recursive [or infinite impulse response (IIR)] filter has been shown to increase the dimension of chaos under certain conditions. Filtering with a nonrecursive [or finite impulse response (FIR)] filter should not increase dimension, but it has been shown that if the FIR filter has a long tail, measurements of actual signals may appear to show a dimension increase. I simulate IIR and FIR filters that correspond to naturally occurring resonant objects, and I show that using dimension measurements, I can distinguish the filter type. These measurements could be used to detect resonances using radar, sonar, or laser signals, or to determine if a resonance is due to an IIR or an FIR filter.

  9. Semiclassical Foundation of Universality in Quantum Chaos

    NASA Astrophysics Data System (ADS)

    Müller, Sebastian; Heusler, Stefan; Braun, Petr; Haake, Fritz; Altland, Alexander

    2004-07-01

    We sketch the semiclassical core of a proof of the so-called Bohigas-Giannoni-Schmit conjecture: A dynamical system with full classical chaos has a quantum energy spectrum with universal fluctuations on the scale of the mean level spacing. We show how in the semiclassical limit all system specific properties fade away, leaving only ergodicity, hyperbolicity, and combinatorics as agents determining the contributions of pairs of classical periodic orbits to the quantum spectral form factor. The small-time form factor is thus reproduced semiclassically. Bridges between classical orbits and (the nonlinear sigma model of) quantum field theory are built by revealing the contributing orbit pairs as topologically equivalent to Feynman diagrams.

  10. Rocks Exposed on Slope in Aram Chaos

    NASA Technical Reports Server (NTRS)

    2003-01-01

    MGS MOC Release No. MOC2-550, 20 November 2003

    This spectacular vista of sedimentary rocks outcropping on a slope in Aram Chaos was acquired by the Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) on 14 November 2003. Dark piles of coarse talus have come down the slopes as these materials continue to erode over time. Note that there are no small meteor impact craters in this image, indicating that erosion of these outcrops has been recent, if not on-going. This area is located near 2.8oS, 20.5oW. The 200 meter scale bar is about 656 feet across. Sunlight illuminates the scene from the lower right.

  11. Low-temperature physics: Chaos in the cold

    NASA Astrophysics Data System (ADS)

    Julienne, Paul S.

    2014-03-01

    A marriage between theory and experiment has shown that ultracold erbium atoms trapped with laser light and subjected to a magnetic field undergo collisions that are characterized by quantum chaos. See Letter p.475

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

    SciTech Connect

    Akhmet, Marat Fen, Mehmet Onur; Rafatov, Ismail

    2014-12-15

    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).].

  13. Filtering with Marked Point Process Observations via Poisson Chaos Expansion

    SciTech Connect

    Sun Wei; Zeng Yong; Zhang Shu

    2013-06-15

    We study a general filtering problem with marked point process observations. The motivation comes from modeling financial ultra-high frequency data. First, we rigorously derive the unnormalized filtering equation with marked point process observations under mild assumptions, especially relaxing the bounded condition of stochastic intensity. Then, we derive the Poisson chaos expansion for the unnormalized filter. Based on the chaos expansion, we establish the uniqueness of solutions of the unnormalized filtering equation. Moreover, we derive the Poisson chaos expansion for the unnormalized filter density under additional conditions. To explore the computational advantage, we further construct a new consistent recursive numerical scheme based on the truncation of the chaos density expansion for a simple case. The new algorithm divides the computations into those containing solely system coefficients and those including the observations, and assign the former off-line.

  14. Chaos and the Marketing of Computing Services on Campus.

    ERIC Educational Resources Information Center

    May, James H.

    1989-01-01

    In an age of chaos and uncertainty in computing services delivery, the best marketing strategy that can be adopted is concern for user constituencies and the long range solutions to their problems. (MLW)

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

    PubMed

    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).].

  16. Chaotic operation and chaos control of travelling wave ultrasonic motor.

    PubMed

    Shi, Jingzhuo; Zhao, Fujie; Shen, Xiaoxi; Wang, Xiaojie

    2013-08-01

    The travelling wave ultrasonic motor, which is a nonlinear dynamic system, has complex chaotic phenomenon with some certain choices of system parameters and external inputs, and its chaotic characteristics have not been studied until now. In this paper, the preliminary study of the chaos phenomenon in ultrasonic motor driving system has been done. The experiment of speed closed-loop control is designed to obtain several groups of time sampling data sequence of the amplitude of driving voltage, and phase-space reconstruction is used to analyze the chaos characteristics of these time sequences. The largest Lyapunov index is calculated and the result is positive, which shows that the travelling wave ultrasonic motor has chaotic characteristics in a certain working condition Then, the nonlinear characteristics of travelling wave ultrasonic motor are analyzed which includes Lyapunov exponent map, the bifurcation diagram and the locus of voltage relative to speed based on the nonlinear chaos model of a travelling wave ultrasonic motor. After that, two kinds of adaptive delay feedback controllers are designed in this paper to control and suppress chaos in USM speed control system. Simulation results show that the method can control unstable periodic orbits, suppress chaos in USM control system. Proportion-delayed feedback controller was designed following and arithmetic of fuzzy logic was used to adaptively adjust the delay time online. Simulation results show that this method could fast and effectively change the chaos movement into periodic or fixed-point movement and make the system enter into stable state from chaos state. Finally the chaos behavior was controlled.

  17. Chaos in axially symmetric potentials with octupole deformation

    SciTech Connect

    Heiss, W.D.; Nazmitdinov, R.G.; Radu, S. Departamento de Fisica Teorica C-XI, Universidad Autonoma de Madrid, E-28049, Madrid )

    1994-04-11

    Classical and quantum mechanical results are reported for the single particle motion in a harmonic oscillator potential which is characterized by a quadrupole deformation and an additional octupole deformation. The chaotic character of the motion is strongly dependent on the quadrupole deformation in that for a prolate deformation virtually no chaos is discernible while for the oblate case the motion shows strong chaos when the octupole term is turned on.

  18. Different routes from a matter wavepacket to spatiotemporal chaos

    SciTech Connect

    Rong Shiguang; Hai Wenhua; Xie Qiongtao; Zhong Honghua

    2012-09-15

    We investigate the dynamics of a quasi-one-dimensional Bose-Einstein condensate confined in a double-well potential with spatiotemporally modulated interaction. A variety of phenomena is identified in different frequency regimes, including the self-compression, splitting, breathing-like, and near-fidelity of the matter wavepacket, which are associated with different routes for the onset of spatiotemporal chaos. The results also reveal that chaos can retain space-inversion symmetry of the system.

  19. Chaos suppression in a spin-torque nano-oscillator

    NASA Astrophysics Data System (ADS)

    Xu, H. Z.; Chen, X.; Liu, J.-M.

    2008-11-01

    We propose a novel practicable self-control scheme to suppress chaos in a spin-torque nano-oscillator in the presence of spin-polarized dc and ac. The magnetization dynamics is investigated by performing micromagnetic simulation. A complete chaos control diagram is obtained, indicating that employment of this proper self-control scheme over a broad frequency range of the ac can greatly reduce the degree of chaoticity in the oscillator.

  20. Philosophical perspectives on quantum chaos: Models and interpretations

    NASA Astrophysics Data System (ADS)

    Bokulich, Alisa Nicole

    2001-09-01

    The problem of quantum chaos is a special case of the larger problem of understanding how the classical world emerges from quantum mechanics. While we have learned that chaos is pervasive in classical systems, it appears to be almost entirely absent in quantum systems. The aim of this dissertation is to determine what implications the interpretation of quantum mechanics has for attempts to explain the emergence of classical chaos. There are three interpretations of quantum mechanics that have set out programs for solving the problem of quantum chaos: the standard interpretation, the statistical interpretation, and the deBroglie-Bohm causal interpretation. One of the main conclusions of this dissertation is that an interpretation alone is insufficient for solving the problem of quantum chaos and that the phenomenon of decoherence must be taken into account. Although a completely satisfactory solution of the problem of quantum chaos is still outstanding, I argue that the deBroglie-Bohm interpretation with the help of decoherence outlines the most promising research program to pursue. In addition to making a contribution to the debate in the philosophy of physics concerning the interpretation of quantum mechanics, this dissertation reveals two important methodological lessons for the philosophy of science. First, issues of reductionism and intertheoretic relations cannot be divorced from questions concerning the interpretation of the theories involved. Not only is the exploration of intertheoretic relations a central part of the articulation and interpretation of an individual theory, but the very terms used to discuss intertheoretic relations, such as `state' and `classical limit', are themselves defined by particular interpretations of the theory. The second lesson that emerges is that, when it comes to characterizing the relationship between classical chaos and quantum mechanics, the traditional approaches to intertheoretic relations, namely reductionism and

  1. Chaos and microbial systems. Progress report, July 1989--July 1990

    SciTech Connect

    Kot, M.

    1990-07-01

    A recurrent theme of much recent research is that seemingly random fluctuations often occur as the result of simple deterministic mechanisms. Hence, much of the recent work in nonlinear dynamics has centered on new techniques for identifying order in seemingly chaotic systems. To determine the robustness of these techniques, chaos must, to some extent, be brought into the laboratory. Preliminary investigations of the forced double-Monod equations, a model for a predator and a prey in a chemostat with periodic variation in inflowing substrate concentration, suggest that simple microbial systems may provide the perfect framework for determining the efficacy and relevance of the new nonlinear dynamics in dealing with complex population dynamics. This research has two main goals, that is the mathematical analysis and computer simulation of the periodically forced double-Monod equations and of related models; and experimental (chemostat) population studies that evaluate the accuracy and generality of the models, and that judge the usefulness of various new techniques of nonlinear dynamics to the study of populations.

  2. Curl force dynamics: symmetries, chaos and constants of motion

    NASA Astrophysics Data System (ADS)

    Berry, M. V.; Shukla, Pragya

    2016-06-01

    This is a theoretical study of Newtonian trajectories governed by curl forces, i.e. position-dependent but not derivable from a potential, investigating in particular the possible existence of conserved quantities. Although nonconservative and nonhamiltonian, curl forces are not dissipative because volume in the position-velocity state space is preserved. A physical example is the effective forces exerted on small particles by light. When the force has rotational symmetry, for example when generated by an isolated optical vortex, particles spiral outwards and escape, even with an attractive gradient force, however strong. Without rotational symmetry, and for dynamics in the plane, the state space is four-dimensional, and to search for possible constants of motion we introduce the Volume of section: a numerical procedure, in which orbits are plotted as dots in a three-dimensional subspace. For some curl forces, e.g. optical fields with two opposite-strength vortices, the dots lie on a surface, indicating a hidden constant of motion. For other curl forces, e.g. those from four vortices, the dots explore clouds, in an unfamiliar kind of chaos, suggesting that no constant of motion exists. The curl force dynamics generated by optical vortices could be studied experimentally.

  3. Chaos Time Series Prediction Based on Membrane Optimization Algorithms

    PubMed Central

    Li, Meng; Yi, Liangzhong; Pei, Zheng; Gao, Zhisheng

    2015-01-01

    This paper puts forward a prediction model based on membrane computing optimization algorithm for chaos time series; the model optimizes simultaneously the parameters of phase space reconstruction (τ, m) and least squares support vector machine (LS-SVM) (γ, σ) by using membrane computing optimization algorithm. It is an important basis for spectrum management to predict accurately the change trend of parameters in the electromagnetic environment, which can help decision makers to adopt an optimal action. Then, the model presented in this paper is used to forecast band occupancy rate of frequency modulation (FM) broadcasting band and interphone band. To show the applicability and superiority of the proposed model, this paper will compare the forecast model presented in it with conventional similar models. The experimental results show that whether single-step prediction or multistep prediction, the proposed model performs best based on three error measures, namely, normalized mean square error (NMSE), root mean square error (RMSE), and mean absolute percentage error (MAPE). PMID:25874249

  4. Curl force dynamics: symmetries, chaos and constants of motion

    NASA Astrophysics Data System (ADS)

    Berry, M. V.; Shukla, Pragya

    2016-06-01

    This is a theoretical study of Newtonian trajectories governed by curl forces, i.e. position-dependent but not derivable from a potential, investigating in particular the possible existence of conserved quantities. Although nonconservative and nonhamiltonian, curl forces are not dissipative because volume in the position–velocity state space is preserved. A physical example is the effective forces exerted on small particles by light. When the force has rotational symmetry, for example when generated by an isolated optical vortex, particles spiral outwards and escape, even with an attractive gradient force, however strong. Without rotational symmetry, and for dynamics in the plane, the state space is four-dimensional, and to search for possible constants of motion we introduce the Volume of section: a numerical procedure, in which orbits are plotted as dots in a three-dimensional subspace. For some curl forces, e.g. optical fields with two opposite-strength vortices, the dots lie on a surface, indicating a hidden constant of motion. For other curl forces, e.g. those from four vortices, the dots explore clouds, in an unfamiliar kind of chaos, suggesting that no constant of motion exists. The curl force dynamics generated by optical vortices could be studied experimentally.

  5. Memristor, Hodgkin-Huxley, and edge of chaos.

    PubMed

    Chua, Leon

    2013-09-27

    From a pedagogical point of view, the memristor is defined in this tutorial as any 2-terminal device obeying a state-dependent Ohm's law. This tutorial also shows that from an experimental point of view, the memristor can be defined as any 2-terminal device that exhibits the fingerprints of 'pinched' hysteresis loops in the v-i plane. It also shows that memristors endowed with a continuum of equilibrium states can be used as non-volatile analog memories. This tutorial shows that memristors span a much broader vista of complex phenomena and potential applications in many fields, including neurobiology. In particular, this tutorial presents toy memristors that can mimic the classic habituation and LTP learning phenomena. It also shows that sodium and potassium ion-channel memristors are the key to generating the action potential in the Hodgkin-Huxley equations, and that they are the key to resolving several unresolved anomalies associated with the Hodgkin-Huxley equations. This tutorial ends with an amazing new result derived from the new principle of local activity, which uncovers a minuscule life-enabling 'Goldilocks zone', dubbed the edge of chaos, where complex phenomena, including creativity and intelligence, may emerge. From an information processing perspective, this tutorial shows that synapses are locally-passive memristors, and that neurons are made of locally-active memristors.

  6. Memristor, Hodgkin-Huxley, and edge of chaos.

    PubMed

    Chua, Leon

    2013-09-27

    From a pedagogical point of view, the memristor is defined in this tutorial as any 2-terminal device obeying a state-dependent Ohm's law. This tutorial also shows that from an experimental point of view, the memristor can be defined as any 2-terminal device that exhibits the fingerprints of 'pinched' hysteresis loops in the v-i plane. It also shows that memristors endowed with a continuum of equilibrium states can be used as non-volatile analog memories. This tutorial shows that memristors span a much broader vista of complex phenomena and potential applications in many fields, including neurobiology. In particular, this tutorial presents toy memristors that can mimic the classic habituation and LTP learning phenomena. It also shows that sodium and potassium ion-channel memristors are the key to generating the action potential in the Hodgkin-Huxley equations, and that they are the key to resolving several unresolved anomalies associated with the Hodgkin-Huxley equations. This tutorial ends with an amazing new result derived from the new principle of local activity, which uncovers a minuscule life-enabling 'Goldilocks zone', dubbed the edge of chaos, where complex phenomena, including creativity and intelligence, may emerge. From an information processing perspective, this tutorial shows that synapses are locally-passive memristors, and that neurons are made of locally-active memristors. PMID:23999613

  7. Memristor, Hodgkin-Huxley, and Edge of Chaos

    NASA Astrophysics Data System (ADS)

    Chua, Leon

    2013-09-01

    From a pedagogical point of view, the memristor is defined in this tutorial as any 2-terminal device obeying a state-dependent Ohm’s law. This tutorial also shows that from an experimental point of view, the memristor can be defined as any 2-terminal device that exhibits the fingerprints of ‘pinched’ hysteresis loops in the v-i plane. It also shows that memristors endowed with a continuum of equilibrium states can be used as non-volatile analog memories. This tutorial shows that memristors span a much broader vista of complex phenomena and potential applications in many fields, including neurobiology. In particular, this tutorial presents toy memristors that can mimic the classic habituation and LTP learning phenomena. It also shows that sodium and potassium ion-channel memristors are the key to generating the action potential in the Hodgkin-Huxley equations, and that they are the key to resolving several unresolved anomalies associated with the Hodgkin-Huxley equations. This tutorial ends with an amazing new result derived from the new principle of local activity, which uncovers a minuscule life-enabling ‘Goldilocks zone’, dubbed the edge of chaos, where complex phenomena, including creativity and intelligence, may emerge. From an information processing perspective, this tutorial shows that synapses are locally-passive memristors, and that neurons are made of locally-active memristors.

  8. Bluetooth Based Chaos Synchronization Using Particle Swarm Optimization and Its Applications to Image Encryption

    PubMed Central

    Yau, Her-Terng; Hung, Tzu-Hsiang; Hsieh, Chia-Chun

    2012-01-01

    This study used the complex dynamic characteristics of chaotic systems and Bluetooth to explore the topic of wireless chaotic communication secrecy and develop a communication security system. The PID controller for chaos synchronization control was applied, and the optimum parameters of this PID controller were obtained using a Particle Swarm Optimization (PSO) algorithm. Bluetooth was used to realize wireless transmissions, and a chaotic wireless communication security system was developed in the design concept of a chaotic communication security system. The experimental results show that this scheme can be used successfully in image encryption. PMID:22969355

  9. Chaos in a quantum well in tilted fields: A scaling system

    NASA Astrophysics Data System (ADS)

    Monteiro, T. S.; Dando, P. A.

    1996-04-01

    Recent experiments have shown that the resonant tunneling diode in a tilted magnetic field is a new and promising probe of quantum chaos. We show that by using a scaling transformation a quantum spectrum is obtained that corresponds to a single classical regime and may be reliably analyzed in terms of periodic orbits. We show that for parameters close to experimental values (with an injection energy of about 25% of that due to the voltage drop), with increasing tilt angle, the disappearance of one set of fluctuations in the tunneling current is associated with a confluence where two periodic orbits are absorbed, persisting briefly in the spectrum as a ``ghost.''

  10. Bluetooth based chaos synchronization using particle swarm optimization and its applications to image encryption.

    PubMed

    Yau, Her-Terng; Hung, Tzu-Hsiang; Hsieh, Chia-Chun

    2012-01-01

    This study used the complex dynamic characteristics of chaotic systems and Bluetooth to explore the topic of wireless chaotic communication secrecy and develop a communication security system. The PID controller for chaos synchronization control was applied, and the optimum parameters of this PID controller were obtained using a Particle Swarm Optimization (PSO) algorithm. Bluetooth was used to realize wireless transmissions, and a chaotic wireless communication security system was developed in the design concept of a chaotic communication security system. The experimental results show that this scheme can be used successfully in image encryption.

  11. Chaos and order in models of black hole pairs

    SciTech Connect

    Levin, Janna

    2006-12-15

    Chaos in the orbits of black hole pairs has by now been confirmed by several independent groups. While the chaotic behavior of binary black hole orbits is no longer argued, it remains difficult to quantify the importance of chaos to the evolutionary dynamics of a pair of comparable mass black holes. None of our existing approximations are robust enough to offer convincing quantitative conclusions in the most highly nonlinear regime. It is intriguing to note that, in three different approximations to a black hole pair built of a spinning black hole and a nonspinning companion, two approximations exhibit chaos and one approximation does not. The fully relativistic scenario of a spinning test mass around a Schwarzschild black hole shows chaos, as does the post-Newtonian Lagrangian approximation. However, the approximately equivalent post-Newtonian Hamiltonian approximation does not show chaos when only one body spins. It is well known in dynamical systems theory that one system can be regular while an approximately related system is chaotic, so there is no formal conflict. However, the physical question remains: Is there chaos for comparable mass binaries when only one object spins? We are unable to answer this question given the poor convergence of the post-Newtonian approximation to the fully relativistic system. A resolution awaits better approximations that can be trusted in the highly nonlinear regime.

  12. Phase-modulated dual-path feedback for time delay signature suppression from intensity and phase chaos in semiconductor laser

    NASA Astrophysics Data System (ADS)

    Xiang, Shuiying; Pan, Wei; Zhang, Liyue; Wen, Aijun; Shang, Lei; Zhang, Huixing; Lin, Lin

    Phase-modulated dual-path feedback (PM-DPF) is proposed to conceal time delay (TD) signatures from both intensity chaos and phase chaos in semiconductor lasers (SLs). The TD signatures are evaluated via both auto-correlation function and permutation entropy function. For the purpose of comparison, we also consider three other feedback configurations: SL with single-path feedback (SPF), SL with phase-modulated single-path feedback (PM-SPF), and SL with dual-path feedback (DPF). It is found that, for four feedback configurations, under the condition of strong feedback, successful TD concealment from both intensity and phase chaos can only be realized in SL with PM-DPF, due to the joint contribution of dual path feedback structure and phase modulation. Furthermore, to check the key factor contributing to TD concealment in SL with PM-DPF, the effects of feedback strength, feedback delay, modulation depth and modulation frequency are examined carefully. It is shown that, to obtain successful TD concealment from both intensity and phase chaos under the condition of strong feedback, the modulation frequency close to or greater than the relaxation oscillation frequency is suggested, while the modulation depth is the most important factor contributing to TD concealment, and higher modulation depth is desired. Besides, similar feedback strengths for two feedback paths are suggested. The TD signatures of intensity chaos for SLs with different feedback configurations are also verified experimentally. The SL with PM-DPF is an excellent chaotic source for security-enhanced chaotic communication systems as well as random number of generators based on chaotic SLs.

  13. PREFACE: The International Conference on Science of Friction

    NASA Astrophysics Data System (ADS)

    Miura, Kouji; Matsukawa, Hiroshi

    2007-07-01

    The first international conference on the science of friction in Japan was held at Irago, Aichi on 9-13 September 2007. The conference focused on the elementary process of friction phenomena from the atomic and molecular scale view. Topics covered in the conference are shown below.:

  14. Superlubricity and friction
  15. Electronic and phononic contributions to friction
  16. Friction on the atomic and molecular scales
  17. van der Waals friction and Casimir force
  18. Molecular motor and friction
  19. Friction and adhesion in soft matter systems
  20. Wear and crack on the nanoscale
  21. Theoretical studies on the atomic scale friction and energy dissipation
  22. Friction and chaos
  23. Mechanical properties of nanoscale contacts
  24. Friction of powder
  25. The number of participants in the conference was approximately 100, registered from 11 countries. 48 oral and 29 poster talks were presented at the conference. This volume of Journal of Physics: Conference Series includes 23 papers devoted to the above topics of friction. The successful organization of the conference was made possible by the contribution of the members of the Organizing Committee and International Advisory Committee. The conference was made possible thanks to the financial support from Aichi University of Education and the Taihokogyo Tribology Research Foundation (TTRF), and moreover thanks to the approval societies of The Physical Society of Japan, The Surface Science Society of Japan, The Japanese Society of Tribologists and Toyota Physical and Chemical Research Institute. The details of the conference are available at http://www.science-of-friction.com . Finally we want to thank the speakers for the high quality of their talks and all participants for coming to Irago, Japan and actively contributing to the conference. Kouji Miura and Hiroshi Matsukawa Editors

  26. PREFACE: Quark Matter 2006 Conference

    NASA Astrophysics Data System (ADS)

    Ma, Yu-Gang; Wang, En-Ke; Cai, Xu; Huang, Huan-Zhong; Wang, Xin-Nian; Zhu, Zhi-Yuan

    2007-07-01

    scientific program of the conference began with an overview of high energy nuclear physics in China by Professor Wenqing Shen, vice president of the National Natural Science Foundation of China. Professor Shen highlighted many contributions made by the Chinese scientists in both theory and experiment. Dr Nick Samios, former director of Brookhaven National Laboratory (BNL), gave a vivid account of the early years of RHIC and recent accomplishments. Highlights of the conference include new results from RHIC at BNL and SPS (Super Proton Synchrotron) at CERN (European Organization for Nuclear Research). Many experimental results reported at the conference support the notion that the quark-gluon matter at RHIC behaves like a perfect liquid with minimum viscosity to entropy ratio. There were 15 plenary sessions which covered 54 plenary talks, 12 parallel sessions and 1 poster session. A total of 320 abstracts were submitted to the conference out of which 124 were selected for oral presentation and the rest were assigned to the poster session. Talks and posters in the conference covered a broad range of experimental and theoretical progress in ultra-relativistic heavy-ion collisions, which includes new evidence of sQGP, jet quenching and heavy quark energy loss, heavy-ion collision phenomenology, quantum field theory at finite temperature and/or density, and relevant areas of astrophysics and plasma physics. The Quark Matter 2006 conference coincided with the 80th birthday of Professor T D Lee. A special reception was held in the banquet hall of the Shanghai Grand Theatre to celebrate Professor Lee's birthday and to honor his great contributions to physics, in particular, to the development of high energy nuclear physics research in China. We would like to thank the members of the International Advisory Committee for providing valuable advice on a variety of matters, from the general structure of the conference to the selection of the plenary speakers and selection of abstracts for

  27. PREFACE: XXI Fluid Mechanics Conference

    NASA Astrophysics Data System (ADS)

    Szmyd, Janusz S.; Fornalik-Wajs, Elzbieta; Jaszczur, Marek

    2014-08-01

    This Conference Volume contains the papers presented at the 21st Fluid Mechanics Conference (XXI FMC) held at AGH - University of Science and Technology in Krakow, Poland, 15-18 June 2014, and accepted for Proceedings published in the Journal of Physics: Conference Series. The Fluid Mechanics Conferences have been taking place every two years since 1974, a total of forty years. The 21st Fluid Mechanics Conference (XXI FMC) is being organized under the auspices of the Polish Academy of Sciences, Committee of Mechanics. The goal of this conference is to provide a forum for the exposure and exchange of ideas, methods and results in fluid mechanics. Conference topics include, but are not limited to Aerodynamics, Atmospheric Science, Bio-Fluids, Combustion and Reacting Flows, Computational Fluid Dynamics, Experimental Fluid Mechanics, Flow Machinery, General Fluid Dynamics, Hydromechanics, Heat and Fluid Flow, Measurement Techniques, Micro- and Nano- Flow, Multi-Phase Flow, Non-Newtonian Fluids, Rotating and Stratified Flows, Turbulence. Within the general subjects of this conference, the Professor Janusz W. Elsner Competition for the best fluid mechanics paper presented during the Conference is organized. Authors holding a M.Sc. or a Ph.D. degree and who are not older than 35 years of age may enter the Competition. Authors with a Ph.D. degree must present individual papers; authors with a M.Sc. degree may present papers with their supervisor as coauthor, including original results of experimental, numerical or analytic research. Six state-of-the-art keynote papers were delivered by world leading experts. All contributed papers were peer reviewed. Recommendations were received from the International Scientific Committee, reviewers and the advisory board. Accordingly, of the 163 eligible extended abstracts submitted, after a review process by the International Scientific Committee, 137 papers were selected for presentation at the 21st Fluid Mechanics Conference, 68

  28. Conference summary

    NASA Astrophysics Data System (ADS)

    Rebolo, R.

    ``Brown dwarfs come of age" was a stimulating conference attended by a large number of very active researchers, including many young students and post-docs who were largely responsible for the lively atmosphere that we enjoyed during the full meeting. Major theoretical and observational challenges currently faced in the study of brown dwarfs were reviewed. Key spectroscopic work is being conducted to determine atmospheric temperatures, surface gravities and metallicities, essential to understand the evolution of substellar objects. Research on ultracool atmospheres is extended down to temperatures typical of the atmosphere of the Earth. Characterisation of brown dwarfs at all wavelengths from X-ray to radio is ongoing and investigation of time domain phenomena reveal interesting new processes in cool atmospheres. In addition to talks on these topics, a large number of presentations addressed the formation and evolution of brown dwarfs, the lower end of the Initial Mass Function, the properties of substellar binaries, the angular momentum and disk evolution in very low-mass systems, results of large scale surveys aimed to find the lowest luminosity and coolest brown dwarfs, searches in star clusters delineating the evolution with age of the properties of brown dwarfs, binary searches and subsequent follow-up work enabling dynamical mass determinations. The excellent level of the review talks, oral and poster presentations and the work of the enthusiastic researchers that attended the meeting ensure a brilliant future for substellar research 18 years after the discovery of the first brown dwarfs.

  29. The Application of Chaos Theory to the Career-Plateaued Worker.

    ERIC Educational Resources Information Center

    Duffy, Jean Ann

    2000-01-01

    Applies some of the principles of chaos theory to career-plateaued workers on the basis of a case study. Concludes that chaos theory provides career practitioners a useful application for working with this type of client. (Author/JDM)

  30. Chaos in the Showalter-Noyes-Bar-Eli model of the Belousov-Zhabotinskii reaction

    NASA Astrophysics Data System (ADS)

    Lindberg, David; Turner, Jack S.; Barkley, Dwight

    1990-03-01

    The observation of robust, large-scale chaos in the Showalter-Noyes-Bar-Eli model of the Belousov-Zhabotinskii reaction is reported. The chaos observed is comparable to that found in CSTR experiments at low flow rates.

  31. Comparison Between Terrestrial Explosion Crater Morphology in Floating Ice and Europan Chaos

    NASA Technical Reports Server (NTRS)

    Billings, S. E.; Kattenhorn, S. A.

    2003-01-01

    Craters created by explosives have been found to serve as valuable analogs to impact craters, within limits. Explosion craters have been created in floating terrestrial ice in experiments related to clearing ice from waterways. Features called chaos occur on the surface of Europa s floating ice shell. Chaos is defined as a region in which the background plains have been disrupted. Common features of chaos include rafted blocks of pre-existing terrain suspended in a matrix of smooth or hummocky material; low surface albedo; and structural control on chaos outline shape by pre-existing lineaments. All published models of chaos formation call on endogenic processes whereby chaos forms through thermal processes. Nonetheless, we note morphological similarities between terrestrial explosion craters and Europan chaos at a range of scales and consider whether some chaos may have formed by impact. We explore these similarities through geologic and morphologic mapping.

  32. Superfluidity and Chaos in low dimensional circuits.

    PubMed

    Arwas, Geva; Vardi, Amichay; Cohen, Doron

    2015-01-01

    The hallmark of superfluidity is the appearance of "vortex states" carrying a quantized metastable circulating current. Considering a unidirectional flow of particles in a ring, at first it appears that any amount of scattering will randomize the velocity, as in the Drude model, and eventually the ergodic steady state will be characterized by a vanishingly small fluctuating current. However, Landau and followers have shown that this is not always the case. If elementary excitations (e.g. phonons) have higher velocity than that of the flow, simple kinematic considerations imply metastability of the vortex state: the energy of the motion cannot dissipate into phonons. On the other hand if this Landau criterion is violated the circulating current can decay. Below we show that the standard Landau and Bogoliubov superfluidity criteria fail in low-dimensional circuits. Proper determination of the superfluidity regime-diagram must account for the crucial role of chaos, an ingredient missing from the conventional stability analysis. Accordingly, we find novel types of superfluidity, associated with irregular or chaotic or breathing vortex states. PMID:26315272

  1. Asynchronous Rate Chaos in Spiking Neuronal Circuits.

    PubMed

    Harish, Omri; Hansel, David

    2015-07-01

    The brain exhibits temporally complex patterns of activity with features similar to those of chaotic systems. Theoretical studies over the last twenty years have described various computational advantages for such regimes in neuronal systems. Nevertheless, it still remains unclear whether chaos requires specific cellular properties or network architectures, or whether it is a generic property of neuronal circuits. We investigate the dynamics of networks of excitatory-inhibitory (EI) spiking neurons with random sparse connectivity operating in the regime of balance of excitation and inhibition. Combining Dynamical Mean-Field Theory with numerical simulations, we show that chaotic, asynchronous firing rate fluctuations emerge generically for sufficiently strong synapses. Two different mechanisms can lead to these chaotic fluctuations. One mechanism relies on slow I-I inhibition which gives rise to slow subthreshold voltage and rate fluctuations. The decorrelation time of these fluctuations is proportional to the time constant of the inhibition. The second mechanism relies on the recurrent E-I-E feedback loop. It requires slow excitation but the inhibition can be fast. In the corresponding dynamical regime all neurons exhibit rate fluctuations on the time scale of the excitation. Another feature of this regime is that the population-averaged firing rate is substantially smaller in the excitatory population than in the inhibitory population. This is not necessarily the case in the I-I mechanism. Finally, we discuss the neurophysiological and computational significance of our results. PMID:26230679

  2. Chaos Synchronization in Navier-Stokes Turbulence

    NASA Astrophysics Data System (ADS)

    Lalescu, Cristian; Meneveau, Charles; Eyink, Gregory

    2013-03-01

    Chaos synchronization (CS) has been studied for some time now (Pecora & Carroll 1990), for systems with only a few degrees of freedom as well as for systems described by partial differential equations (Boccaletti et al 2002). CS in general is said to be present in coupled dynamical systems when a specific property of each system has the same time evolution for all, even though the evolution itself is chaotic. The Navier-Stokes (NS) equations describe the velocity for a wide range of fluids, and their solutions are usually called turbulent if fluctuation amplitudes decrease as a power of their wavenumber. There have been some studies of CS for continuous systems (Kocarev et al 1997), but CS for NS turbulence seems not to have been investigated so far. We focus on the synchronization of the small scales of a turbulent flow for which the time history of large scales is prescribed. Our DNS results show that high-wavenumbers in turbulence are fully slaved to modes with wavenumbers up to a critical fraction of the Kolmogorov dissipation wavenumber. The motivation for our work is to study deeply sub-Kolmogorov scales in fully developed turbulence (Schumacher 2007), which we found to be recoverable even at very high Reynolds number from simulations with moderate resolutions. This work is supported by the National Science Foundation's CDI-II program, project CMMI-0941530

  3. Chaos Synchronization in Navier-Stokes Turbulence

    NASA Astrophysics Data System (ADS)

    Lalescu, Cristian C.; Meneveau, Charles; Eyink, Gregory L.

    2012-11-01

    Chaos synchronization (CS) has been studied for some time now (Pecora & Carroll 1990), for systems with only a few degrees of freedom as well as for systems described by partial differential equations (Boccaletti et al. 2002). CS in general is said to be present in a pair of coupled dynamical systems when a specific property of each system has the same time evolution for both, even though the evolution itself is chaotic. There have been some studies of CS for systems with an infinite number of degrees of freedom (Kocarev et al. 1997), but CS for Navier-Stokes (NS) turbulence seems not to have been investigated so far. We focus on the synchronization of the small scales of a turbulent flow for which the time history of large scales is prescribed. We present DNS results which show that high-wavenumbers in turbulence are fully slaved to modes with wavenumbers up to a critical fraction of the Kolmogorov dissipation wavenumber. We compare our results with related ideas of ``approximate inertial manifolds.'' The motivation for our work is to study deeply sub-Kolmogorov scales in fully developed turbulence (Schumacher 2007), which we show are recoverable even at very high Reynolds number from simulations that only resolve down to about the Kolmogorov scale. This work is supported by the National Science Foundation's CDI-II program, project CMMI-0941530.

  4. Interactive Workshop Discusses Nonlinear Waves and Chaos

    NASA Astrophysics Data System (ADS)

    Tsurutani, Bruce; Morales, George; Passot, Thierry

    2010-07-01

    Eighth International Nonlinear Wave Workshop; La Jolla, California, 1-5 March 2010; Nonlinear waves and chaos were the focus of a weeklong series of informal and interactive discussions at the Eighth International Nonlinear Wave Workshop (NWW8), held in California. The workshop gathered nonlinear plasma and water wave experts from the United States, France, Czech Republic, Germany, Greece, Holland, India, and Japan. Attendees were from the fields of space, laboratory, and fusion plasma physics, astrophysics, and applied mathematics. Special focus was placed on nonlinear waves and turbulence in the terrestrial environment as well as in the interstellar medium from observational, laboratory, and theoretical perspectives. Discussions covered temperature anisotropies and related instabilities, the properties and origin of the so-called dissipation range, and various coherent structures of electromagnetic as well as electrostatic nature. Reconnection and shocks were also topics of discussion, as were properties of magnetospheric whistler and chorus waves. Examples and analysis techniques for superdiffusion and subdiffusion were identified. On this last topic, a good exchange of ideas and results occurred between a water wave expert and a plasma expert, with the rest of the audience listening intently.

  5. Asynchronous Rate Chaos in Spiking Neuronal Circuits

    PubMed Central

    Harish, Omri; Hansel, David

    2015-01-01

    The brain exhibits temporally complex patterns of activity with features similar to those of chaotic systems. Theoretical studies over the last twenty years have described various computational advantages for such regimes in neuronal systems. Nevertheless, it still remains unclear whether chaos requires specific cellular properties or network architectures, or whether it is a generic property of neuronal circuits. We investigate the dynamics of networks of excitatory-inhibitory (EI) spiking neurons with random sparse connectivity operating in the regime of balance of excitation and inhibition. Combining Dynamical Mean-Field Theory with numerical simulations, we show that chaotic, asynchronous firing rate fluctuations emerge generically for sufficiently strong synapses. Two different mechanisms can lead to these chaotic fluctuations. One mechanism relies on slow I-I inhibition which gives rise to slow subthreshold voltage and rate fluctuations. The decorrelation time of these fluctuations is proportional to the time constant of the inhibition. The second mechanism relies on the recurrent E-I-E feedback loop. It requires slow excitation but the inhibition can be fast. In the corresponding dynamical regime all neurons exhibit rate fluctuations on the time scale of the excitation. Another feature of this regime is that the population-averaged firing rate is substantially smaller in the excitatory population than in the inhibitory population. This is not necessarily the case in the I-I mechanism. Finally, we discuss the neurophysiological and computational significance of our results. PMID:26230679

  6. Kinematic dynamo, supersymmetry breaking, and chaos

    NASA Astrophysics Data System (ADS)

    Ovchinnikov, Igor V.; Enßlin, Torsten A.

    2016-04-01

    The kinematic dynamo (KD) describes the growth of magnetic fields generated by the flow of a conducting medium in the limit of vanishing backaction of the fields onto the flow. The KD is therefore an important model system for understanding astrophysical magnetism. Here, the mathematical correspondence between the KD and a specific stochastic differential equation (SDE) viewed from the perspective of the supersymmetric theory of stochastics (STS) is discussed. The STS is a novel, approximation-free framework to investigate SDEs. The correspondence reported here permits insights from the STS to be applied to the theory of KD and vice versa. It was previously known that the fast KD in the idealistic limit of no magnetic diffusion requires chaotic flows. The KD-STS correspondence shows that this is also true for the diffusive KD. From the STS perspective, the KD possesses a topological supersymmetry, and the dynamo effect can be viewed as its spontaneous breakdown. This supersymmetry breaking can be regarded as the stochastic generalization of the concept of dynamical chaos. As this supersymmetry breaking happens in both the diffusive and the nondiffusive cases, the necessity of the underlying SDE being chaotic is given in either case. The observed exponentially growing and oscillating KD modes prove physically that dynamical spectra of the STS evolution operator that break the topological supersymmetry exist with both real and complex ground state eigenvalues. Finally, we comment on the nonexistence of dynamos for scalar quantities.

  7. Genotoxicity of drinking water from Chao Lake

    SciTech Connect

    Liu, Q.; Jiao, Q.C.; Huang, X.M.; Jiang, J.P.; Cui, S.Q.; Yao, G.H.; Jiang, Z.R.; Zhao, H.K.; Wang, N.Y.

    1999-02-01

    Genotoxic activity appears to originate primarily from reactions of chlorine with humic substances in the source waters. Comparisons of extracts of settled versus chlorinated water have confirmed that chlorinating during water treatment produces mutagenic activity in the mutagenicity tests. Present work on XAD-2 extracts of raw, chlorinated (treated), and settled water from the Chao Lake region of China has involved a battery of mutagenicity assays for various genetic endpoints: the Salmonella test, the sister-chromatid exchange (SCE) induction in Chinese hamster lung (CHL) cells, and the micronucleus (MN) induction in the peripheral blood erythrocytes of silver carp. Extracts of raw and treated water but not the settled water are mutagenic in the Salmonella assay. On the other hand, extracts of three water samples show activity in the SCE and MN assays, especially the raw and treated water. These data show that contamination and chlorinating contribute mutagens to drinking water and suggest that the mammalian assays may be more sensitive for detecting mutagenicity in aquatic environment than the Salmonella test.

  8. Streamflow Prediction based on Chaos Theory

    NASA Astrophysics Data System (ADS)

    Li, X.; Wang, X.; Babovic, V. M.

    2015-12-01

    Chaos theory is a popular method in hydrologic time series prediction. Local model (LM) based on this theory utilizes time-delay embedding to reconstruct the phase-space diagram. For this method, its efficacy is dependent on the embedding parameters, i.e. embedding dimension, time lag, and nearest neighbor number. The optimal estimation of these parameters is thus critical to the application of Local model. However, these embedding parameters are conventionally estimated using Average Mutual Information (AMI) and False Nearest Neighbors (FNN) separately. This may leads to local optimization and thus has limitation to its prediction accuracy. Considering about these limitation, this paper applies a local model combined with simulated annealing (SA) to find the global optimization of embedding parameters. It is also compared with another global optimization approach of Genetic Algorithm (GA). These proposed hybrid methods are applied in daily and monthly streamflow time series for examination. The results show that global optimization can contribute to the local model to provide more accurate prediction results compared with local optimization. The LM combined with SA shows more advantages in terms of its computational efficiency. The proposed scheme here can also be applied to other fields such as prediction of hydro-climatic time series, error correction, etc.

  9. Chaos in Quantum Many-Body Systems

    NASA Astrophysics Data System (ADS)

    Mitchell, G. E.

    1997-11-01

    Recent developments have led to a new appreciation of the significance of Random Matrix Theory (RMT). The Bohigas conjecture(O. Bohigas, M. J. Giannoni, and C. Schmit, Phys. Rev. Lett. 52), 1 (1984). assumes a generic connection between RMT and the spectral fluctuations of quantum analogs of classically chaotic systems. Level statistics are now used as a signature of chaos. RMT has been applied to a large number and variety of physical systems.(T. Guhr, A. Müller, and H. A. Weidenmüller, Phys. Reports (to be published).) The theory was originally developed by Wigner and Dyson to describe the fluctuation properties of nuclear resonances. It is impressive that a theory developed for the nucleus has been applied to complex atoms and molecules. The successful description of the properties of disordered solids is more surprising. The successful description of the elastomechanical eigenfrequencies of irregularly shaped quartz crystals and of the eigenmodes of microwaves in two-dimensional superconducting cavities suggests a near universality of RMT.

  10. Linear vs nonlinear and infinite vs finite: An interpretation of chaos

    SciTech Connect

    Protopopescu, V.

    1990-10-01

    An example of a linear infinite-dimensional system is presented that exhibits deterministic chaos and thus challenges the presumably unquestionable connection between chaos and nonlinearity. Via this example, the roles of, and relationships between, linearity, nonlinearity, infinity and finiteness in the occurrence of chaos are investigated. The analysis of these complementary but related aspects leads to: a new interpretation of chaos as the manifestation of incompressible and thus incompressible information and a conjecture about the nonexistence of operationally accessible linear systems.

  11. Behavior modeling through CHAOS for simulation of dismounted soldier operations

    NASA Astrophysics Data System (ADS)

    Ubink, Emiel; Aldershoff, Frank; Lotens, Wouter; Woering, Arend

    2008-04-01

    One of the major challenges in human behavior modeling for military applications is dealing with all factors that can influence behavior and performance. In a military context, behavior and performance are influenced by the task at hand, the internal (cognitive and physiological) and external (climate, terrain, threat, equipment, etc.) state. Modeling the behavioral effects of all these factors in a centralized manner would lead to a complex rule-base that is difficult to maintain or expand. To better cope with this complexity we have developed the Capability-based Human-performance Architecture for Operational Simulation (CHAOS). CHAOS is a multi-agent system for human behavior modeling that is based on pandemonium theory. Every agent in CHAOS represents a specific part of behavior, such as 'reaction to threat' or 'performing a patrol task'. These agents are competing over a limited set of resources that represent human capabilities. By combining the element of competition with multiple limited resources, CHAOS allows us to model stress, strain and multi-tasking in an intuitive manner. The CHAOS architecture is currently used in firefighter and dismounted soldier simulations and has shown itself to be suitable for human behavior and performance modeling.

  12. Chaos based encryption system for encrypting electroencephalogram signals.

    PubMed

    Lin, Chin-Feng; Shih, Shun-Han; Zhu, Jin-De

    2014-05-01

    In the paper, we use the Microsoft Visual Studio Development Kit and C# programming language to implement a chaos-based electroencephalogram (EEG) encryption system involving three encryption levels. A chaos logic map, initial value, and bifurcation parameter for the map were used to generate Level I chaos-based EEG encryption bit streams. Two encryption-level parameters were added to these elements to generate Level II chaos-based EEG encryption bit streams. An additional chaotic map and chaotic address index assignment process was used to implement the Level III chaos-based EEG encryption system. Eight 16-channel EEG Vue signals were tested using the encryption system. The encryption was the most rapid and robust in the Level III system. The test yielded superior encryption results, and when the correct deciphering parameter was applied, the EEG signals were completely recovered. However, an input parameter error (e.g., a 0.00001 % initial point error) causes chaotic encryption bit streams, preventing the recovery of 16-channel EEG Vue signals.

  13. Developments in experimental techniques in heat transfer and combustion; Proceedings of the Twenty-fourth National Heat Transfer Conference and Exhibition, Pittsburgh, PA, Aug. 9-12, 1987

    NASA Astrophysics Data System (ADS)

    Warrington, R. O., Jr.; Chen, M. M.; Felske, J. D.; Grosshandler, W. L.

    1987-08-01

    This volume includes articles related to the developments in experimental techniques in heat transfer and in combustion. Papers are presented on high-resolution heat-transfer-coefficient maps applicable to compound-curve surfaces using liquid crystals in a transient wind tunnel, an instrument for the measurement of the heat flux distribution along a contour of a surface at uniform temperature, an advanced viscometric thermometer for steady and unsteady states temperature measurement in electric or magnetic fields, the development of a thermopile-based deposition sensor, and the measurement of surface heat flux, using the Peltier effect. Consideration is also given to a new method of experimentally determining heat transfer coefficients in direct-contact bubble evaporation, temperature measurements by light scattering methods, the design calibration and error analysis of instrumentation for heat transfer in internal combustion, the application of an electrodynamic balance to study mass transfer from a single particle, single droplet studies in a hot high-pressure environment, and the measurement of flame propagation through a moving mixture.

  14. Chaos in the Composition Classroom: Why Do Some Classes Fail To Function?

    ERIC Educational Resources Information Center

    Salmon, Vickie

    1999-01-01

    The author asserts that through chaos theory, she began to view the failures and successes of one particular semester in a different light. Describes chaos theory in layman's terms and provides recommendations for teaching in this new paradigm. Asserts that understanding chaos theory will allow instructors to celebrate diversity, disorder, and…

  15. Chaos Theory and Its Application to Education: Mehmet Akif Ersoy University Case

    ERIC Educational Resources Information Center

    Akmansoy, Vesile; Kartal, Sadik

    2014-01-01

    Discussions have arisen regarding the application of the new paradigms of chaos theory to social sciences as compared to physical sciences. This study examines what role chaos theory has within the education process and what effect it has by describing the views of university faculty regarding chaos and education. The participants in this study…

  16. Chaos and Christianity: A Response to Butz and a Biblical Alternative.

    ERIC Educational Resources Information Center

    Watts, Richard E.; Trusty, Jerry

    1997-01-01

    M.R. Butz's position regarding chaos theory and Christianity is reviewed. The compatibility of biblical theology and the sciences is discussed. Parallels between chaos theory and the philosophical perspective of Soren Kierkegaard are explored. A biblical model is offered for counselors in assisting Christian clients in embracing chaos. (Author/EMK)

  17. Planning in Higher Education and Chaos Theory: A Model, a Method.

    ERIC Educational Resources Information Center

    Cutright, Marc

    This paper proposes a model, based on chaos theory, that explores strategic planning in higher education. It notes that chaos theory was first developed in the physical sciences to explain how apparently random activity was, in fact, complexity patterned. The paper goes on to describe how chaos theory has subsequently been applied to the social…

  18. Nonlinear system vibration---The appearance of chaos

    SciTech Connect

    Hunter, N.F. Jr.

    1990-01-01

    This paper begins with an examination of the differential equation for a single degree of freedom force excited oscillator and considers the state space behavior of linear, nonlinear, and chaotic single degree of freedom systems. The fundamental characteristics of classical chaos are reviewed: sensitivity to initial conditions, positive Lyapunov exponents, complex Poincare maps, fractal properties of motion in the state space, and broadening of the power spectrum of the system response. Illustrated examples of chaotic behavior include motion in a two well potential -- the chaos beam described in Moon and a hardening base excited Duffing system. Chaos-like phenomenon which occur with nonperiodic forcing are examined in the context of the two well potential and hardening Duffing systems. The paper concludes with some suggestions for detecting and modelling nonlinear or chaotic behavior. 19 refs., 19 figs.

  19. Dynamical topology and statistical properties of spatiotemporal chaos.

    PubMed

    Zhuang, Quntao; Gao, Xun; Ouyang, Qi; Wang, Hongli

    2012-12-01

    For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a large extent, the location and movement of these topologically special points determine the qualitative structure of the disordered states. We analyze numerically statistical properties of the topologically special points in one-dimensional spatiotemporal chaos. The probability distribution functions for the number of point, the lifespan, and the distance covered during their lifetime are obtained from numerical simulations. Mathematically, we establish a probabilistic model to describe the dynamics of these topologically special points. In spite of the different definitions in different spatiotemporal chaos, the dynamics of these special points can be described in a uniform approach.

  20. Multistability, chaos, and random signal generation in semiconductor superlattices.

    PubMed

    Ying, Lei; Huang, Danhong; Lai, Ying-Cheng

    2016-06-01

    Historically, semiconductor superlattices, artificial periodic structures of different semiconductor materials, were invented with the purpose of engineering or manipulating the electronic properties of semiconductor devices. A key application lies in generating radiation sources, amplifiers, and detectors in the "unusual" spectral range of subterahertz and terahertz (0.1-10 THz), which cannot be readily realized using conventional radiation sources, the so-called THz gap. Efforts in the past three decades have demonstrated various nonlinear dynamical behaviors including chaos, suggesting the potential to exploit chaos in semiconductor superlattices as random signal sources (e.g., random number generators) in the THz frequency range. We consider a realistic model of hot electrons in semiconductor superlattice, taking into account the induced space charge field. Through a systematic exploration of the phase space we find that, when the system is subject to an external electrical driving of a single frequency, chaos is typically associated with the occurrence of multistability. That is, for a given parameter setting, while there are initial conditions that lead to chaotic trajectories, simultaneously there are other initial conditions that lead to regular motions. Transition to multistability, i.e., the emergence of multistability with chaos as a system parameter passes through a critical point, is found and argued to be abrupt. Multistability thus presents an obstacle to utilizing the superlattice system as a reliable and robust random signal source. However, we demonstrate that, when an additional driving field of incommensurate frequency is applied, multistability can be eliminated, with chaos representing the only possible asymptotic behavior of the system. In such a case, a random initial condition will lead to a trajectory landing in a chaotic attractor with probability 1, making quasiperiodically driven semiconductor superlattices potentially as a reliable

  1. ONSET OF CHAOS IN A MODEL OF QUANTUM COMPUTATION

    SciTech Connect

    G. BERMAN; ET AL

    2001-02-01

    Recently, the question of a relevance of the so-called quantum chaos has been raised in applications to quantum computation [2,3]. Indeed, according to the general approach to closed systems of finite number of interacting Fermi-particles (see, e.g. [4,5]), with an increase of an interaction between qubits a kind of chaos is expected to emerge in the energy spectra and structure of many-body states. Specifically, the fluctuations of energy levels and components of the eigenstates turn out to be very strong and described by the Random Matrix Theory. Clearly, if this happens in a quantum computer, it may lead to a destruction of the coherence of quantum computations due to internal decoherence inside many-body states. It is important to stress that quantum chaos occurs not only in the systems with random interaction, but also for purely dynamical interaction. In the latter case, the mechanism of chaos is due to a complex (non-linear) form of a two-body interaction represented in the basis of non-interacting particles. Numerical analysis [2] of a simplest model of quantum computer (2D model of 1/2-spins with a random interqubit interaction J) shows that with an increase of the number L of qubits, the chaos threshold J{sub cr} decreases as J{sub cr} {infinity} 1/L. On this ground, it was claimed that the onset of quantum chaos could be dangerous for quantum computers, since their effectiveness requires L >> 1. On the other hand, in [3] it was argued that in order to treat this problem properly, one needs to distinguish between chaotic properties of stationary states, and the dynamical process of quantum computation.

  2. Multistability, chaos, and random signal generation in semiconductor superlattices.

    PubMed

    Ying, Lei; Huang, Danhong; Lai, Ying-Cheng

    2016-06-01

    Historically, semiconductor superlattices, artificial periodic structures of different semiconductor materials, were invented with the purpose of engineering or manipulating the electronic properties of semiconductor devices. A key application lies in generating radiation sources, amplifiers, and detectors in the "unusual" spectral range of subterahertz and terahertz (0.1-10 THz), which cannot be readily realized using conventional radiation sources, the so-called THz gap. Efforts in the past three decades have demonstrated various nonlinear dynamical behaviors including chaos, suggesting the potential to exploit chaos in semiconductor superlattices as random signal sources (e.g., random number generators) in the THz frequency range. We consider a realistic model of hot electrons in semiconductor superlattice, taking into account the induced space charge field. Through a systematic exploration of the phase space we find that, when the system is subject to an external electrical driving of a single frequency, chaos is typically associated with the occurrence of multistability. That is, for a given parameter setting, while there are initial conditions that lead to chaotic trajectories, simultaneously there are other initial conditions that lead to regular motions. Transition to multistability, i.e., the emergence of multistability with chaos as a system parameter passes through a critical point, is found and argued to be abrupt. Multistability thus presents an obstacle to utilizing the superlattice system as a reliable and robust random signal source. However, we demonstrate that, when an additional driving field of incommensurate frequency is applied, multistability can be eliminated, with chaos representing the only possible asymptotic behavior of the system. In such a case, a random initial condition will lead to a trajectory landing in a chaotic attractor with probability 1, making quasiperiodically driven semiconductor superlattices potentially as a reliable

  3. Multistability, chaos, and random signal generation in semiconductor superlattices

    NASA Astrophysics Data System (ADS)

    Ying, Lei; Huang, Danhong; Lai, Ying-Cheng

    2016-06-01

    Historically, semiconductor superlattices, artificial periodic structures of different semiconductor materials, were invented with the purpose of engineering or manipulating the electronic properties of semiconductor devices. A key application lies in generating radiation sources, amplifiers, and detectors in the "unusual" spectral range of subterahertz and terahertz (0.1-10 THz), which cannot be readily realized using conventional radiation sources, the so-called THz gap. Efforts in the past three decades have demonstrated various nonlinear dynamical behaviors including chaos, suggesting the potential to exploit chaos in semiconductor superlattices as random signal sources (e.g., random number generators) in the THz frequency range. We consider a realistic model of hot electrons in semiconductor superlattice, taking into account the induced space charge field. Through a systematic exploration of the phase space we find that, when the system is subject to an external electrical driving of a single frequency, chaos is typically associated with the occurrence of multistability. That is, for a given parameter setting, while there are initial conditions that lead to chaotic trajectories, simultaneously there are other initial conditions that lead to regular motions. Transition to multistability, i.e., the emergence of multistability with chaos as a system parameter passes through a critical point, is found and argued to be abrupt. Multistability thus presents an obstacle to utilizing the superlattice system as a reliable and robust random signal source. However, we demonstrate that, when an additional driving field of incommensurate frequency is applied, multistability can be eliminated, with chaos representing the only possible asymptotic behavior of the system. In such a case, a random initial condition will lead to a trajectory landing in a chaotic attractor with probability 1, making quasiperiodically driven semiconductor superlattices potentially as a reliable

  4. A "chaos" of Phanerozoic eustatic curves

    NASA Astrophysics Data System (ADS)

    Ruban, Dmitry A.

    2016-04-01

    The knowledge of eustasy has changed during the past two decades. Although there is not any single global sea-level curve for the entire Phanerozoic, new curves have been proposed for all periods. For some geological time intervals, there are two and more alternative reconstructions, from which it is difficult to choose. A significant problem is the available eustatic curves are justified along different geological time scales (sometimes without proper explanations), which permits to correlate eustatic events with the possible error of 1-3 Ma. This degree of error permits to judge about only substage- or stage-order global sea-level changes. Close attention to two geological time slices, namely the late Cambrian (Epoch 3‒Furongian) and the Late Cretaceous, implies that only a few eustatic events (6 events in the case of the late Cambrian and 9 events in the case of the Late Cretaceous) appear on all available alternative curves for these periods, and different (even opposite) trends of eustatic fluctuations are shown on these curves. This reveals significant uncertainty in our knowledge of eustasy that restricts our ability to decipher factors responsible for regional transgressions and regressions and relative sea-level changes. A big problem is also inadequate awareness of the geological research community of the new eustatic developments. Generally, the situation with the development and the use of the Phanerozoic eustatic reconstructions seems to be "chaotic". The example of the shoreline shifts in Northern Africa during the Late Cretaceous demonstrates the far-going consequences of this situation. The practical recommendations to avoid this "chaos" are proposed. Particularly, these claim for good awareness of all eustatic developments, their critical discussion, and clear explanation of the employed geological time scale.

  5. ASTEROIDS: Living in the Kingdom of Chaos

    NASA Astrophysics Data System (ADS)

    Morbidelli, A.

    2000-10-01

    The existence of chaotic regions in the main asteroid belt, related with the lowest-order mean-motion and secular resonances, has long been known. However, only in the last decade have semi-analytic theories allowed a proper understanding of the chaotic behavior observed in numerical simulations which accurately incorporate the entire planetary system. The most spectacular result has been the discovery that the asteroids in some of these resonance may collide with the Sun on typical time scales of a few million year, their eccentricities being pumped to unity during their chaotic evolution. But the asteroid belt is not simply divided into violent chaotic zones and regular regions. It has been shown that the belt is criss-crossed by a large number of high-order mean-motion resonances with Jupiter or Mars, as well as by `three-body resonances' with Jupiter and Saturn. All these weak resonances cause the slow chaotic drift of the `proper' eccentricities and inclinations. The traces left by this evolution are visible, for example, in the structure of the Eos and Themis asteroid families. Weak chaos may also explain the anomalous dispersion of the eccentricities and inclinations observed in the Flora ``clan." Moreover, due to slow increases in their eccentricities, many asteroids start to cross the orbit of Mars, over a wide range of semimajor axes. The improved knowledge of the asteroid belt's chaotic structure provides, for the first time, an opportunity to build detailed quantitative models of the origin and the orbital distribution of Near-Earth Asteroids and meteorites. In turn, these models seem to imply that the semimajor axes of main-belt asteroids must also slowly evolve with time. For asteroids larger than about 20 km this is due mainly to encounters with Ceres, Pallas, and Vesta, while for smaller bodies the so-called Yarkovsky effect should dominate. Everything moves chaotically in the asteroid belt.

  6. Saturn's F Ring Core: Calm Amidst Chaos

    NASA Astrophysics Data System (ADS)

    Whizin, A.; Cuzzi, J.; Hogan, R.; Dobrovolskis, A.; Colwell, J. E.; Scargle, J.; Dones, L.; Showalter, M.

    2012-12-01

    Near the edge of Saturn's Roche Zone the F ring is straddled on either side by two small satellites Prometheus and Pandora and as such undergoes perturbations that result in orbital chaos (Scargle et al 1993 DPS 25, #26.04, Winter et al 2007 MNRAS 380, L54; 2010 A&A 523, A67). Even in such an unstable environment the F ring appears to be relatively stable. Thus we postulate there are quiescent stable zones arising from mutual resonant interactions from the two ring moons. It is in one of these zones we believe the F ring has found a stable foothold despite the chaotic orbits in the region. At locations we call "anti-resonances" ring particles have much smaller changes over time in their semi-major axes and eccentricities than particles outside of these anti-resonance zones. We devise an impulse-based perturbation model that explains the orbital outcomes from successive perturbations from two satellites. In addition we compute the orbital evolution of thousands of mass-less test particles with a Bulirsch-Stoer N-body integrator over a narrow radial range covering the F ring core region at high spatial resolution. We find that the variance of the semi-major axes of particles in anti-resonances can be less than ~1km over a period of 32 years, while just a few kilometers away in either radial direction the variance can be tens of kilometers. More importantly, particles outside of these stable zones can migrate into a stable zone due to chaotic orbits, but once they enter an anti-resonance zone they remain there. The anti-resonances act as long-lived sinks for ring particles and explain the location of the F ring core despite its location not being in overall torque balance with ring moons.

  7. The Small Saturnian Satellites -- Chaos and Conundrum

    NASA Astrophysics Data System (ADS)

    Jacobson, Robert A.

    2014-05-01

    From an analysis of Hubble Space Telescope data French et al. (2003 Icarus, 162, 143) found that the orbits of Prometheus and Pandora, which flank Saturn's ring, exhibited unexpected variations in their semimajor axes and mean motions. Goldreich and Rappaport (2003 Icarus, 162, 391) showed that those variations were caused by a chaotic interaction between the satellites. We report on the practical consequences that the chaos has on the production of ephemerides needed to support the Cassini mission and on the post Cassini ephemerides.Recently El Moutamid et al. (2014 Celest. Mech., 118, 235) proposed that the motions of three other satellites, Anthe, Methone, and Aegaeon could also be chaotic as a result of their mean motion resonances with Mimas. Coincidentally, the current orbits of the three satellites are a poor fit to the Cassini imaging data even though the direct perturbation of Mimas is included in the orbit computations. We discuss the status of our attempts to improve the orbit modelling for these satellites and the implications of their possibly chaotic behavior. Daphnis is a small satellite orbiting in the narrow (40 km) Keeler Gap in Saturn's rings. It was discovered in 2004 and found to have a near circular orbit in the ring gap. That orbit fits Cassini imaging data from 2004 to 2010 quite well, but it cannot fit the imaging acquired subsequent to late 2012. To fit the later data requires a circular orbit with a semimajor axis some 3 km larger. Moreover, no observations were made between 2010 and late 2012. We speculate on possible causes for the orbit change.

  8. Acoustic ray chaos and billiard system in Hamiltonian formalism (L)

    NASA Astrophysics Data System (ADS)

    Kawabe, Tetsuji; Aono, Keisuke; Shin-Ya, Masakazu

    2003-02-01

    The acoustic ray model with a strong connection to the billiard problem is presented within the framework of the Hamiltonian form. Introducing the background function into the sound-speed profile to confine all rays in a closed space, we obtain the ray trajectories consistent with a billiard picture. The ray chaos is observed when the perturbation due to inhomogeneity of the medium is taken into account. Based on the Poincaré surface of section and the Lyapunov exponents, we confirm that the chaos is characterized by almost the same structure as one observed in many Hamiltonian systems with two degrees of freedom.

  9. The edge of chaos: A nonlinear view of psychoanalytic technique.

    PubMed

    Galatzer-Levy, Robert M

    2016-04-01

    The field of nonlinear dynamics (or chaos theory) provides ways to expand concepts of psychoanalytic process that have implications for the technique of psychoanalysis. This paper describes how concepts of "the edge of chaos," emergence, attractors, and coupled oscillators can help shape analytic technique resulting in an approach to doing analysis which is at the same time freer and more firmly based in an enlarged understanding of the ways in which psychoanalysis works than some current recommendation about technique. Illustrations from a lengthy analysis of an analysand with obsessive-compulsive disorder show this approach in action. PMID:27030426

  10. Blessing and curse of chaos in numerical turbulence simulations

    NASA Astrophysics Data System (ADS)

    Lee, Jon

    1994-03-01

    Because of the trajectory instability, time reversal is not possible beyond a certain evolution time and hence the time irreversibility prevails under the finite-accuracy trajectory computation. This therefore provides a practical reconciliation of the dynamic reversibility and macroscopic irreversibility (blessing of chaos). On the other hand, the trajectory instability is also responsible for a limited evolution time, so that finite-accuracy computation would yield a pseudo-orbit which is totally unrelated to the true trajectory (curse of chaos). For the inviscid 2D flow, however, we can accurately compute the long- time average of flow quantities with a pseudo-orbit by invoking the ergodic theorem.

  11. Chaos: a topic for interdisciplinary education in physics

    NASA Astrophysics Data System (ADS)

    Bae, Saebyok

    2009-07-01

    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 seems useful and good. In addition, we discuss some issues which can be important to interdisciplinary education in physics: for example the possible difficulties in programme design, the expertise barriers of non-major fields, the role of non-theoretical education in understanding and the project-type team activities.

  12. Taming chaos with disorder in a pendulum array

    NASA Astrophysics Data System (ADS)

    Shew, Woodrow L.; Coy, Hanna A.; Lindner, John F.

    1999-08-01

    We designed and constructed an array of ten forced damped nonlinear pendulums. We drove the pivot of the pendulums in a vertical circle and torsionally coupled them with springs. We analyzed the motion using digitized videotape. The behavior of the real array closely mirrored the behavior of its computer simulation. For a homogeneous array of identical pendulums, the spatiotemporal dynamics was chaotic; for a heterogeneous array of nonidentical pendulums, the spatiotemporal dynamics was periodic. Such temporally fixed but spatially varying chaos control has been called "disorder taming chaos."

  13. Dynamic Ice-Water Interactions Form Europa's Chaos Terrains

    NASA Astrophysics Data System (ADS)

    Blankenship, D. D.; Schmidt, B. E.; Patterson, G. W.; Schenk, P.

    2011-12-01

    Unique to the surface of Europa, chaos terrain is diagnostic of the properties and dynamics of its icy shell. We present a new model that suggests large melt lenses form within the shell and that water-ice interactions above and within these lenses drive the production of chaos. This model is consistent with key observations of chaos, predicts observables for future missions, and indicates that the surface is likely still active today[1]. We apply lessons from ice-water interaction in the terrestrial cryosphere to hypothesize a dynamic lense-collapse model to for Europa's chaos terrain. Chaos terrain morphology, like that of Conamara chaos and Thera Macula, suggests a four-phase formation [1]: 1) Surface deflection occurs as ice melts over ascending thermal plumes, as regularly occurs on Earth as subglacial volcanoes activate. The same process can occur at Europa if thermal plumes cause pressure melt as they cross ice-impurity eutectics. 2) Resulting hydraulic gradients and driving forces produce a sealed, pressurized melt lense, akin to the hydraulic sealing of subglacial caldera lakes. On Europa, the water cannot escape the lense due to the horizontally continuous ice shell. 3) Extension of the brittle ice lid above the lense opens cracks, allowing for the ice to be hydrofractured by pressurized water. Fracture, brine injection and percolation within the ice and possible iceberg toppling produces ice-melange-like granular matrix material. 4) Refreezing of the melt lense and brine-filled pores and cracks within the matrix results in raised chaos. Brine soaking and injection concentrates the ice in brines and adds water volume to the shell. As this englacial water freezes, the now water-filled ice will expand, not unlike the process of forming pingos and other "expansion ice" phenomena on Earth. The refreezing can raise the surface and create the oft-observed matrix "domes" In this presentation, we describe how catastrophic ice-water interactions on Earth have

  14. Preface to the Focus Issue: Chaos Detection Methods and Predictability

    SciTech Connect

    Gottwald, Georg A.; Skokos, Charalampos

    2014-06-01

    This Focus Issue presents a collection of papers originating from the workshop Methods of Chaos Detection and Predictability: Theory and Applications held at the Max Planck Institute for the Physics of Complex Systems in Dresden, June 17–21, 2013. The main aim of this interdisciplinary workshop was to review comprehensively the theory and numerical implementation of the existing methods of chaos detection and predictability, as well as to report recent applications of these techniques to different scientific fields. The collection of twelve papers in this Focus Issue represents the wide range of applications, spanning mathematics, physics, astronomy, particle accelerator physics, meteorology and medical research. This Preface surveys the papers of this Issue.

  15. FAST TRACK COMMUNICATION: Kac Moody algebras and controlled chaos

    NASA Astrophysics Data System (ADS)

    Wesley, Daniel H.

    2007-02-01

    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 G2 holonomy.

  16. Subwavelength position sensing using nonlinear feedback and wave chaos.

    PubMed

    Cohen, Seth D; Cavalcante, Hugo L D de S; Gauthier, Daniel J

    2011-12-16

    We demonstrate a position-sensing technique that relies on the inherent sensitivity of chaos, where we illuminate a subwavelength object with a complex structured radio-frequency field generated using wave chaos and nonlinear feedback. We operate the system in a quasiperiodic state and analyze changes in the frequency content of the scalar voltage signal in the feedback loop. This allows us to extract the object's position with a one-dimensional resolution of ~λ/10,000 and a two-dimensional resolution of ~λ/300, where λ is the shortest wavelength of the illuminating source.

  17. PREFACE: The 27th International Conference on Phenomena in Ionized Gases (ICPIG)

    NASA Astrophysics Data System (ADS)

    Kroesen, Gerrit

    2006-05-01

    The 27th International Conference on Phenomena in Ionized Gases (ICPIG) was held in the conference resort of NH Koningshof in Veldhoven, near Eindhoven, The Netherlands, 17-22 July 2005. ICPIG is an important biennial event at which academics and industrialists working in low-temperature plasma science can meet. The 27th ICPIG was organized under the sponsorship of the International Union of Pure and Applied Chemistry (IUPAP), the Royal Dutch Academy of Sciences (KNAW), the Research School Centre for Plasma Physics and Radiation Technology (CPS), the Dutch Organization for Fundamental Research on Matter (FOM), Stichting Physica, the Dutch organization for Scientific Research (NWO), Philips Lighting, and the Eindhoven University of Technology. The scientific scope of this joint conference focused on both experimental and theoretical aspects of the physics of ionized gases as well as on industrial applications. It covered the following topics: • Kinetics, thermodynamics and transport phenomena • Elementary processes • Low-pressure glows • Coronas, sparks, surface discharges and high-pressure glows • Arc discharges • High-frequency discharges • Ionospheric, magnetospheric and astrophysical plasmas • Plasma diagnostic methods • Plasma wall interaction, electrode and surface effects • Physical aspects of plasma chemistry, plasma processing of surfaces and thin film technology • The generation and dynamics of plasma flows • Non-ideal plasmas, clusters and dusty plasmas • Waves and instabilities, including shock waves • Nonlinear phenomena, self-organization and chaos • Particle and laser beam interaction with plasmas • Plasma sources of radiation • Numerical modelling • Plasmas for environmental issues • Highly ionized, low-pressure plasmas (plasma thrusters, ion sources and surface treatment) • High-pressure, non-thermal plasmas. ICPIG was attended by close to 400 scientists from 41 countries. A selection of the invited papers is

  18. Aram Chaos: a Long Lived Subsurface Aqueous Environment with Strong Water Resources Potential for Human Missions on Mars

    NASA Technical Reports Server (NTRS)

    Sibille, L.; Mueller, R.; Niles, P. B.; Glotch, T.; Archer, P. D.; Bell, M. S.

    2015-01-01

    Aram Chaos, Mars is a crater 280 kilometers in diameter with elevations circa. minus 2 to minus 3 kilometers below datum that provides a compelling landing site for future human explorers as it features multiple scientific regions of interest (ROI) paired with a rich extensible Resource ROI that features poly-hydrated sulfates [1]. The geologic history of Aram Chaos suggests several past episodes of groundwater recharge and infilling by liquid water, ice, and other materials [1-3]. The creation of the fractured region with no known terrestrial equivalent may have been caused by melting of deep ice reservoirs that triggered the collapse of terrain followed by catastrophic water outflows over the region. Aram Chaos is of particular scientific interest because it is hypothesized that the chaotic terrain may be the source of water that contributed to the creation of nearby valleys such as Ares Vallis flowing toward Chryse Planitia. The liquid water was likely sourced as groundwater and therefore represents water derived from a protected subsurface environment making it a compelling astrobiological site [2]. The past history of water is also represented by high concentrations of hematite, Fe-oxyhydroxides, mono-hydrated and poly-hydrated sulfates [1, 2]. Poly-hydrated sulfates are likely to contain abundant water that evolves at temperatures below 500 degrees Centigrade thus conferring Aram Chaos a potentially high value for early in-situ resource utilization (ISRU) [4]. The geologic history also calls for future prospecting of deep ice deposits and possibly liquid water via deep drilling. The most recent stratigraphic units in the central part of Aram Chaos are not fractured, and are part of a dome-shaped formation that features bright, poorly-consolidated material that contains both hydrated sulfates and ferric oxides according to OMEGA (Observatoire pour la Minéralogie, l'Eau, les Glaces et l'Activité) data [5]. These surface material characteristics are

  19. Ikeda-like chaos on a dynamically filtered supercontinuum light source

    NASA Astrophysics Data System (ADS)

    Chembo, Yanne K.; Jacquot, Maxime; Dudley, John M.; Larger, Laurent

    2016-08-01

    We demonstrate temporal chaos in a color-selection mechanism from the visible spectrum of a supercontinuum light source. The color-selection mechanism is governed by an acousto-optoelectronic nonlinear delayed-feedback scheme modeled by an Ikeda-like equation. Initially motivated by the design of a broad audience live demonstrator in the framework of the International Year of Light 2015, the setup also provides a different experimental tool to investigate the dynamical complexity of delayed-feedback dynamics. Deterministic hyperchaos is analyzed here from the experimental time series. A projection method identifies the delay parameter, for which the chaotic strange attractor originally evolving in an infinite-dimensional phase space can be revealed in a two-dimensional subspace.

  20. Chaos in the classroom: Exposing gifted elementary school children to chaos and fractals

    NASA Astrophysics Data System (ADS)

    Adams, Helen M.; Russ, John C.

    1992-09-01

    A unit of study for gifted 4th and 5th graders is described on the subject of mathematical periodicity and chaos and the underlying physical processes which produce these phenomena. A variety of hands-on experiments and the use of various data analysis tools and computer aids provide students with powerful raw material for their analysis, interpretation, and understanding. The concepts of simple periodic motion (e.g., a pendulum), complex superposition of motions (e.g., the vibrations in musical instruments), and chaotic sequences (e.g., stock prices) are covered, with numerous practical examples. Opportunities to involve related activities emphasizing language arts, history, and graphic art are included. The student response to the material is documented.

  1. A cubic map chaos criterion theorem with applications in generalized synchronization based pseudorandom number generator and image encryption.

    PubMed

    Yang, Xiuping; Min, Lequan; Wang, Xue

    2015-05-01

    This paper sets up a chaos criterion theorem on a kind of cubic polynomial discrete maps. Using this theorem, Zhou-Song's chaos criterion theorem on quadratic polynomial discrete maps and generalized synchronization (GS) theorem construct an eight-dimensional chaotic GS system. Numerical simulations have been carried out to verify the effectiveness of theoretical results. The chaotic GS system is used to design a chaos-based pseudorandom number generator (CPRNG). Using FIPS 140-2 test suit/Generalized FIPS 140-2, test suit tests the randomness of two 1000 key streams consisting of 20 000 bits generated by the CPRNG, respectively. The results show that there are 99.9%/98.5% key streams to have passed the FIPS 140-2 test suit/Generalized FIPS 140-2 test. Numerical simulations show that the different keystreams have an average 50.001% same codes. The key space of the CPRNG is larger than 2(1345). As an application of the CPRNG, this study gives an image encryption example. Experimental results show that the linear coefficients between the plaintext and the ciphertext and the decrypted ciphertexts via the 100 key streams with perturbed keys are less than 0.00428. The result suggests that the decrypted texts via the keystreams generated via perturbed keys of the CPRNG are almost completely independent on the original image text, and brute attacks are needed to break the cryptographic system.

  2. Series-nonuniform rational B-spline signal feedback: From chaos to any embedded periodic orbit or target point

    SciTech Connect

    Shao, Chenxi Xue, Yong; Fang, Fang; Bai, Fangzhou; Yin, Peifeng; Wang, Binghong

    2015-07-15

    The self-controlling feedback control method requires an external periodic oscillator with special design, which is technically challenging. This paper proposes a chaos control method based on time series non-uniform rational B-splines (SNURBS for short) signal feedback. It first builds the chaos phase diagram or chaotic attractor with the sampled chaotic time series and any target orbit can then be explicitly chosen according to the actual demand. Second, we use the discrete timing sequence selected from the specific target orbit to build the corresponding external SNURBS chaos periodic signal, whose difference from the system current output is used as the feedback control signal. Finally, by properly adjusting the feedback weight, we can quickly lead the system to an expected status. We demonstrate both the effectiveness and efficiency of our method by applying it to two classic chaotic systems, i.e., the Van der Pol oscillator and the Lorenz chaotic system. Further, our experimental results show that compared with delayed feedback control, our method takes less time to obtain the target point or periodic orbit (from the starting point) and that its parameters can be fine-tuned more easily.

  3. A cubic map chaos criterion theorem with applications in generalized synchronization based pseudorandom number generator and image encryption

    SciTech Connect

    Yang, Xiuping Min, Lequan Wang, Xue

    2015-05-15

    This paper sets up a chaos criterion theorem on a kind of cubic polynomial discrete maps. Using this theorem, Zhou-Song's chaos criterion theorem on quadratic polynomial discrete maps and generalized synchronization (GS) theorem construct an eight-dimensional chaotic GS system. Numerical simulations have been carried out to verify the effectiveness of theoretical results. The chaotic GS system is used to design a chaos-based pseudorandom number generator (CPRNG). Using FIPS 140-2 test suit/Generalized FIPS 140-2, test suit tests the randomness of two 1000 key streams consisting of 20 000 bits generated by the CPRNG, respectively. The results show that there are 99.9%/98.5% key streams to have passed the FIPS 140-2 test suit/Generalized FIPS 140-2 test. Numerical simulations show that the different keystreams have an average 50.001% same codes. The key space of the CPRNG is larger than 2{sup 1345}. As an application of the CPRNG, this study gives an image encryption example. Experimental results show that the linear coefficients between the plaintext and the ciphertext and the decrypted ciphertexts via the 100 key streams with perturbed keys are less than 0.00428. The result suggests that the decrypted texts via the keystreams generated via perturbed keys of the CPRNG are almost completely independent on the original image text, and brute attacks are needed to break the cryptographic system.

  4. Nonlinear dynamics analysis of a self-organizing recurrent neural network: chaos waning.

    PubMed

    Eser, Jürgen; Zheng, Pengsheng; Triesch, Jochen

    2014-01-01

    Self-organization is thought to play an important role in structuring nervous systems. It frequently arises as a consequence of plasticity mechanisms in neural networks: connectivity determines network dynamics which in turn feed back on network structure through various forms of plasticity. Recently, self-organizing recurrent neural network models (SORNs) have been shown to learn non-trivial structure in their inputs and to reproduce the experimentally observed statistics and fluctuations of synaptic connection strengths in cortex and hippocampus. However, the dynamics in these networks and how they change with network evolution are still poorly understood. Here we investigate the degree of chaos in SORNs by studying how the networks' self-organization changes their response to small perturbations. We study the effect of perturbations to the excitatory-to-excitatory weight matrix on connection strengths and on unit activities. We find that the network dynamics, characterized by an estimate of the maximum Lyapunov exponent, becomes less chaotic during its self-organization, developing into a regime where only few perturbations become amplified. We also find that due to the mixing of discrete and (quasi-)continuous variables in SORNs, small perturbations to the synaptic weights may become amplified only after a substantial delay, a phenomenon we propose to call deferred chaos.

  5. Chaos and microbial systems. Final project report, July 1989--July 1992

    SciTech Connect

    Kot, M.

    1992-10-01

    The field of nonlinear dynamics has generated a variety of new techniques for identifying order in seemingly chaotic systems. These techniques have led to new insights for several ecological and epidemiological systems, most notably childhood disease epidemics. To better test the efficacy and relevance of these new techniques to population biology research with two components namely a mathematical analysis of some simple microbial models with chaotic dynamics; and experimental (chemostat) population studies to evaluate the accuracy of these models. I have completed a thorough analysis of the forced double-Monod model and of the phase-locking route to chaos that it exhibits. I have also analyzed a simpler pulsed system with mass action kinetics and a period-doubling route to chaos. This research also motivated detailed analyses of discrete-time predator-prey and dispersal models, and a fast new method for computing fractal dimension. My colleagues and I have assembled a complete laboratory system to determine the appropriateness of the forced double-Monod model. We have tested assays for concentration and density and have performed a variety of diagnostic tests on this system. We have measured growth parameters for bacteria and for protozoa in chemostat.

  6. Observation of Hamiltonian chaos and its control in wave particle interaction

    NASA Astrophysics Data System (ADS)

    Doveil, F.; Macor, A.; Aïssi, A.

    2007-12-01

    Wave-particle interactions are central in plasma physics. They can be studied in a traveling wave tube (TWT) to avoid intrinsic plasma noise. This led to detailed experimental analysis of the self-consistent interaction between unstable waves and an either cold or warm beam. More recently a test cold electron beam has been used to observe its non-self-consistent interaction with externally excited wave(s). The velocity distribution function of the electron beam is recorded with a trochoidal energy analyzer at the output of the TWT. An arbitrary waveform generator is used to launch a prescribed spectrum of waves along the slow wave structure (a 4 m long helix) of the TWT. The nonlinear synchronization of particles by a single wave responsible for Landau damping is observed. The resonant velocity domain associated with a single wave is also observed, as well as the transition to large scale chaos when the resonant domains of two waves and their secondary resonances overlap. This transition exhibits a 'devil's staircase' behavior when increasing the excitation amplitude in agreement with numerical simulation. A new strategy for control of chaos by building barriers of transport which prevent electrons from escaping from a given velocity region as well as its robustness are successfully tested. The underlying concepts extend far beyond the field of electron devices and plasma physics.

  7. Deterministic temporal chaos from a mid-infrared external cavity quantum cascade lasers

    NASA Astrophysics Data System (ADS)

    Grillot, Frédéric; Jumpertz, Louise; Schires, Kevin; Carras, Mathieu; Sciamanna, Marc

    2016-02-01

    Quantum cascade lasers (QCLs) are unipolar semiconductor lasers offering access to wavelengths from the mid-infrared (IR) to the terahertz domain and promising impact on various applications such as free-space communications, high-resolution spectroscopy, LIDAR remote sensing or optical countermeasures. Unlike bipolar semiconductor lasers, stimulated emission in QCLs is obtained via electronic transitions between discrete energy states inside the conduction band. Recent technological progress has led to QCLs operating in pulsed or continuous wave mode, at room temperature in single- or multi-mode operation, with high powers up to a few watts for mid-IR devices. This spectacular development raises multiple interrogations on the stability of QCLs as little is known on their dynamical properties. Very recently, experiments based on optical spectrum measurements have unveiled the existence of five distinct feedback regimes without, however, identifying the complex dynamics dwelling within the QCL. In this article we provide the first experimental evidence of a route to chaos in a QCL emitting at mid-IR wavelength. When applying optical feedback with an increasing strength, the QCL dynamics bifurcate to periodic dynamics at the external cavity frequency and later to chaos without an undamping of relaxation oscillations, hence contrasting with the well-known scenarios occurring in interband laser diodes.

  8. Sleep Quality Estimation based on Chaos Analysis for Heart Rate Variability

    NASA Astrophysics Data System (ADS)

    Fukuda, Toshio; Wakuda, Yuki; Hasegawa, Yasuhisa; Arai, Fumihito; Kawaguchi, Mitsuo; Noda, Akiko

    In this paper, we propose an algorithm to estimate sleep quality based on a heart rate variability using chaos analysis. Polysomnography(PSG) is a conventional and reliable system to diagnose sleep disorder and to evaluate its severity and therapeatic effect, by estimating sleep quality based on multiple channels. However, a recording process requires a lot of time and a controlled environment for measurement and then an analyzing process of PSG data is hard work because the huge sensed data should be manually evaluated. On the other hand, it is focused that some people make a mistake or cause an accident due to lost of regular sleep and of homeostasis these days. Therefore a simple home system for checking own sleep is required and then the estimation algorithm for the system should be developed. Therefore we propose an algorithm to estimate sleep quality based only on a heart rate variability which can be measured by a simple sensor such as a pressure sensor and an infrared sensor in an uncontrolled environment, by experimentally finding the relationship between chaos indices and sleep quality. The system including the estimation algorithm can inform patterns and quality of own daily sleep to a user, and then the user can previously arranges his life schedule, pays more attention based on sleep results and consult with a doctor.

  9. Chaos and thermal noise in the rf-biased Josephson junction

    SciTech Connect

    Kautz, R.L.

    1985-07-01

    The effect of thermal noise on chaotic behavior in the rf-biased Josephson junction is studied through digital simulations. In instances for which chaotic behavior occurs in the noise-free system, it is found that the dynamics of the system are almost unchanged by the addition of thermal noise unless the level of thermal noise exceeds that of the chaotic state. In instances for which the only stable states of the noise-free system are periodic solutions, small amounts of thermal noise can induce the junction to hop between two different dynamical states, producing a low-frequency noise level much higher than that of the thermal noise. Such noise-induced hopping can occur either between two periodic solutions or between a periodic solution and a metastable chaotic solution. When a metastable chaotic state is involved, temperatures somewhat higher than those which produce hopping can destablize the periodic solution to the point where the system spends virtually all of its time in the metastable chaotic state, creating noise-induced chaos. The similarities between chaotic behavior at zero temperature and noise-induced chaos are sufficiently strong that it may be difficult to distinguish the two cases experimentally.

  10. 13th International Conference on Chlamydomonas

    SciTech Connect

    Silflow, Carolyn D.

    2014-03-11

    The 13th International Conference on Chlamydomonas (EMBO Workshop on the Cell and Molecular Biology of Chlamydomonas) was held May 27 to June 1, 2008 in Hyeres, France. The conference was the biennial meeting for all researchers studying the green algal systems Chlamydomonas and Volvox. The conference brought together approximately 200 investigators from around the world (North America, Asia, Europe and Australia) representing different fields and disciplines (cell biology, genetics, biochemistry, biophysics, plant physiology, genomics). It provided an opportunity for investigators from different countries to share methodologies and to discuss recent results with a focus on the Chlamydomonas experimental system.

  11. The General Conference Mennonites.

    ERIC Educational Resources Information Center

    Ediger, Marlow

    General Conference Mennonites and Old Order Amish are compared and contrasted in the areas of physical appearance, religious beliefs, formal education, methods of farming, and home settings. General Conference Mennonites and Amish differ in physical appearance and especially in dress. The General Conference Mennonite men and women dress the same…

  12. Parent Conferences. Beginnings Workshop.

    ERIC Educational Resources Information Center

    Duffy, Roslyn; And Others

    1997-01-01

    Presents six workshop sessions on parent conferences: (1) "Parents' Perspectives on Conferencing" (R. Duffy); (2) "Three Way Conferences" (G. Zeller); (3) "Conferencing with Parents of Infants" (K. Albrecht); (4) "Conferencing with Parents of School-Agers" (L. G. Miller); (5) "Cross Cultural Conferences" (J. Gonzalez-Mena); and (6) "Working with…

  13. The GAIA Hypothesis and Chaos in Daisyworld.

    NASA Astrophysics Data System (ADS)

    Flynn, Cathal Michael

    1993-01-01

    To correctly model the climate it is necessary to include the effects of the biosphere. The Gaia hypothesis claims that the earth's living matter, air, oceans, and land form a complex system which has the capacity to regulate the earth's climate. A model developed by Lovelock and Watson to demonstrate the Gaia hypothesis is explained and the results of their work are reviewed. Only steady state behavior is observed in the Daisyworld model. The work of Zeng et al. on the presence of chaos in Daisyworld is reviewed as an introduction to our own work. The presence of oscillatory and even chaotic behavior in this Daisyworld model brings into question the Gaia hypothesis. We develop a model of two-dimensional crystal growth called Crystalworld. The Crystalworld model is similar to the Daisyworld model in that there is a coupling between the growing entities and their environment via temperature. The results of this model are similar to that of the Daisyworld model. We present the results of another modified model of Daisyworld which we developed. This modified model takes into account the finite response time of the daisies to changes in the planet's climatic conditions. With a generation time introduced into the model equations, while retaining the differential equation format, it is found that the system can show oscillatory and chaotic behavior. These results show that any climate-biosphere model must contain a time delay and that such a time delay leads to behavior which contradicts the Gaia hypothesis. In order to determine the effects of introducing more species we develop a model with two species of daisies and a parasite species. For this Parasite-Daisyworld model steady state, periodic and chaotic behavior is found. A comparison between the results of this model and that of Zeng et al. is made. The results of the Parasite-Daisyworld model show that increasing the number of species does not lead to increased regulation. This contradicts the Gaia hypothesis and

  14. Chaos at the Heart of Orion

    NASA Technical Reports Server (NTRS)

    2006-01-01

    NASA's Spitzer and Hubble Space Telescopes have teamed up to expose the chaos that baby stars are creating 1,500 light-years away in a cosmic cloud called the Orion nebula.

    This striking infrared and visible-light composite indicates that four monstrously massive stars at the center of the cloud may be the main culprits in the familiar Orion constellation. The stars are collectively called the 'Trapezium.' Their community can be identified as the yellow smudge near the center of the image.

    Swirls of green in Hubble's ultraviolet and visible-light view reveal hydrogen and sulfur gas that have been heated and ionized by intense ultraviolet radiation from the Trapezium's stars. Meanwhile, Spitzer's infrared view exposes carbon-rich molecules called polycyclic aromatic hydrocarbons in the cloud. These organic molecules have been illuminated by the Trapezium's stars, and are shown in the composite as wisps of red and orange. On Earth, polycyclic aromatic hydrocarbons are found on burnt toast and in automobile exhaust.

    Together, the telescopes expose the stars in Orion as a rainbow of dots sprinkled throughout the image. Orange-yellow dots revealed by Spitzer are actually infant stars deeply embedded in a cocoon of dust and gas. Hubble showed less embedded stars as specks of green, and foreground stars as blue spots.

    Stellar winds from clusters of newborn stars scattered throughout the cloud etched all of the well-defined ridges and cavities in Orion. The large cavity near the right of the image was most likely carved by winds from the Trapezium's stars.

    Located 1,500 light-years away from Earth, the Orion nebula is the brightest spot in the sword of the Orion, or the 'Hunter' constellation. The cosmic cloud is also our closest massive star-formation factory, and astronomers believe it contains more than 1,000 young stars.

    The Orion constellation is a familiar sight in the fall and winter night sky in the northern hemisphere. The nebula

  15. Order Amidst Chaos of Star's Explosion

    NASA Technical Reports Server (NTRS)

    2006-01-01

    [figure removed for brevity, see original site] Click on the image for movie of Order Amidst Chaos of Star's Explosion

    This artist's animation shows the explosion of a massive star, the remains of which are named Cassiopeia A. NASA's Spitzer Space Telescope found evidence that the star exploded with some degree of order, preserving chunks of its onion-like layers as it blasted apart.

    Cassiopeia A is what is known as a supernova remnant. The original star, about 15 to 20 times more massive than our sun, died in a cataclysmic 'supernova' explosion viewable from Earth about 340 years ago. The remnant is located 10,000 light-years away in the constellation Cassiopeia.

    The movie begins by showing the star before it died, when its layers of elements (shown in different colors) were stacked neatly, with the heaviest at the core and the lightest at the top. The star is then shown blasting to smithereens. Spitzer found evidence that the star's original layers were preserved, flinging outward in all directions, but not at the same speeds. In other words, some chunks of the star sped outward faster than others, as illustrated by the animation.

    The movie ends with an actual picture of Cassiopeia A taken by Spitzer. The colored layers containing different elements are seen next to each other because they traveled at different speeds.

    The infrared observatory was able to see the tossed-out layers because they light up upon ramming into a 'reverse' shock wave created in the aftermath of the explosion. When a massive star explodes, it creates two types of shock waves. The forward shock wave darts out quickest, and, in the case of Cassiopeia A, is now traveling at supersonic speeds up to 7,500 kilometers per second (4,600 miles/second). The reverse shock wave is produced when the forward shock wave slams into a shell of surrounding material expelled before the star died. It tags along behind the forward shock wave at slightly slower speeds.

    Chunks

  16. BOOK REVIEW: Chaos: A Very Short Introduction

    NASA Astrophysics Data System (ADS)

    Klages, R.

    2007-07-01

    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

  17. Catastrophe, Chaos, and Complexity Models and Psychosocial Adjustment to Disability.

    ERIC Educational Resources Information Center

    Parker, Randall M.; Schaller, James; Hansmann, Sandra

    2003-01-01

    Rehabilitation professionals may unknowingly rely on stereotypes and specious beliefs when dealing with people with disabilities, despite the formulation of theories that suggest new models of the adjustment process. Suggests that Catastrophe, Chaos, and Complexity Theories hold considerable promise in this regard. This article reviews these…

  18. The Living Career: Complexity, Chaos, Connections and Career.

    ERIC Educational Resources Information Center

    Bloch, Deborah P.

    The purpose of this paper is to present a theory of career development drawn from current work in the physical and biological sciences, specifically work that is associated with chaos and complexity theories. The paper includes specific suggestions for practice based upon the theory and reflections of career professionals on its use. The theory…

  19. Chaos Modeling: Increasing Educational Researchers' Awareness of a New Tool.

    ERIC Educational Resources Information Center

    Bobner, Ronald F.; And Others

    Chaos theory is being used as a tool to study a wide variety of phenomena. It is a philosophical and empirical approach that attempts to explain relationships previously thought to be totally random. Although some relationships are truly random, many data appear to be random but reveal repeatable patterns of behavior under further investigation.…

  20. Careers Education: Evolving, Adapting and Building Resilience through Chaos

    ERIC Educational Resources Information Center

    Loader, Trent

    2011-01-01

    Career educators' ultimate goal, given the new career management paradigm, should be to ensure that students are career resilient when they leave their studies (from whatever year level). This article outlines the chaos theory of careers and resilience. It then goes on to describe a four-lesson unit of careers education work that attempts to…

  1. Applying Chaos Theory to Careers: Attraction and Attractors

    ERIC Educational Resources Information Center

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

    2007-01-01

    This article presents the Chaos Theory of Careers with particular reference to the concepts of "attraction" and "attractors". Attractors are defined in terms of characteristic trajectories, feedback mechanisms, end states, ordered boundedness, reality visions and equilibrium and fluctuation. The identified types of attractors (point, pendulum,…

  2. Chaos in learning a simple two-person game.

    PubMed

    Sato, Yuzuru; Akiyama, Eizo; Farmer, J Doyne

    2002-04-01

    We investigate the problem of learning to play the game of rock-paper-scissors. Each player attempts to improve her/his average score by adjusting the frequency of the three possible responses, using reinforcement learning. For the zero sum game the learning process displays Hamiltonian chaos. Thus, the learning trajectory can be simple or complex, depending on initial conditions. We also investigate the non-zero sum case and show that it can give rise to chaotic transients. This is, to our knowledge, the first demonstration of Hamiltonian chaos in learning a basic two-person game, extending earlier findings of chaotic attractors in dissipative systems. As we argue here, chaos provides an important self-consistency condition for determining when players will learn to behave as though they were fully rational. That chaos can occur in learning a simple game indicates one should use caution in assuming real people will learn to play a game according to a Nash equilibrium strategy.

  3. Planning in Higher Education: A Model from Chaos Theory.

    ERIC Educational Resources Information Center

    Cutright, Marc

    This paper proposes a metaphoric perspective based on chaos theory for strategic planning by institutions of higher education. It offers 10 propositions for planning: (1) the ideal outcome of planning is planning, not a plan; (2) planning begins with a distillation of the institution's key values and purposes; (3) the widest possible universe of…

  4. Group Chaos Theory: A Metaphor and Model for Group Work

    ERIC Educational Resources Information Center

    Rivera, Edil Torres; Wilbur, Michael; Frank-Saraceni, James; Roberts-Wilbur, Janice; Phan, Loan T.; Garrett, Michael T.

    2005-01-01

    Group phenomena and interactions are described through the use of the chaos theory constructs and characteristics of sensitive dependence on initial conditions, phase space, turbulence, emergence, self-organization, dissipation, iteration, bifurcation, and attractors and fractals. These constructs and theoretical tenets are presented as applicable…

  5. Chaos in learning a simple two-person game.

    PubMed

    Sato, Yuzuru; Akiyama, Eizo; Farmer, J Doyne

    2002-04-01

    We investigate the problem of learning to play the game of rock-paper-scissors. Each player attempts to improve her/his average score by adjusting the frequency of the three possible responses, using reinforcement learning. For the zero sum game the learning process displays Hamiltonian chaos. Thus, the learning trajectory can be simple or complex, depending on initial conditions. We also investigate the non-zero sum case and show that it can give rise to chaotic transients. This is, to our knowledge, the first demonstration of Hamiltonian chaos in learning a basic two-person game, extending earlier findings of chaotic attractors in dissipative systems. As we argue here, chaos provides an important self-consistency condition for determining when players will learn to behave as though they were fully rational. That chaos can occur in learning a simple game indicates one should use caution in assuming real people will learn to play a game according to a Nash equilibrium strategy. PMID:11930020

  6. Review of Stephen Arons's "Short Route to Chaos."

    ERIC Educational Resources Information Center

    Glenn, Charles L.

    1998-01-01

    "Short Route to Chaos" criticizes the Goals 2000 program, related educational reforms, and the agenda of the Religious Right from the viewpoint of the secular Left. Arons supports school choice, school and teacher independence from government regulation of instructional content, publicly funded schools, and equity in funding. (SLD)

  7. Bifurcation and chaos in power systems: A survey

    SciTech Connect

    Varaiya, P.; Wu, F. . Dept. of Electrical Engineering and Computer Sciences); Chiang, H.D. . School of Electrical Engineering)

    1992-08-01

    The literature dealing with bifurcation and chaos in electric power systems is surveyed. A brief discussion of relevant mathematical concepts and results is included in order to make the presentation self-contained and readily accessible. The objective is to determine the extent and significance of power system behavior that can be understood by dynamic models exhibiting bifurcation and chaotic motion. Bifurcation denotes a qualitative change in system behavior. The study is divided into three parts dealing with static bifurcations, Hopf bifurcations, and chaos. Static bifurcation occurs when two or more equilibrium points coincide. Hopf bifurcation occurs when a periodic oscillation emerges from a stable equilibrium. These are both examples of local bifurcation - they are determined by the system behavior in a neighborhood of the equilibrium. Chaos emerges from a global bifurcation - a non-local change in the phase portrait of tile system. The following conclusions are reached. Even the simplest models of power systems exhibit both local and global bifurcations. Local bifurcations occur because power flow equations have multiple solutions. In models that only incorporate real power flow, the capacity of transmission systems is so large that local bifurcations although present are unlikely to be practically significant. However, in models where voltage is determined by reactive power flows, local bifurcations can dramatically shrink the stability region. These bifurcations may explain voltage collapse''. The simplest models also exhibit chaotic behavior. However, for analytical convenience, chaos has mostly been investigated in systems with unrealistic parameter values.

  8. Bifurcation and chaos in power systems: A survey. Final report

    SciTech Connect

    Varaiya, P.; Wu, F.; Chiang, H.D.

    1992-08-01

    The literature dealing with bifurcation and chaos in electric power systems is surveyed. A brief discussion of relevant mathematical concepts and results is included in order to make the presentation self-contained and readily accessible. The objective is to determine the extent and significance of power system behavior that can be understood by dynamic models exhibiting bifurcation and chaotic motion. Bifurcation denotes a qualitative change in system behavior. The study is divided into three parts dealing with static bifurcations, Hopf bifurcations, and chaos. Static bifurcation occurs when two or more equilibrium points coincide. Hopf bifurcation occurs when a periodic oscillation emerges from a stable equilibrium. These are both examples of local bifurcation - they are determined by the system behavior in a neighborhood of the equilibrium. Chaos emerges from a global bifurcation - a non-local change in the phase portrait of tile system. The following conclusions are reached. Even the simplest models of power systems exhibit both local and global bifurcations. Local bifurcations occur because power flow equations have multiple solutions. In models that only incorporate real power flow, the capacity of transmission systems is so large that local bifurcations although present are unlikely to be practically significant. However, in models where voltage is determined by reactive power flows, local bifurcations can dramatically shrink the stability region. These bifurcations may explain ``voltage collapse``. The simplest models also exhibit chaotic behavior. However, for analytical convenience, chaos has mostly been investigated in systems with unrealistic parameter values.

  9. Does the transition to chaos determine the dynamic aperture

    SciTech Connect

    Jowett, J.M.

    1986-06-01

    We review the important notion of the dynamic aperture of a storage ring with emphasis on its relation to general ideas of dynamical instability, notably the transition to chaos. Practical approaches to the problem are compared. We suggest a somewhat novel quantitative guide to the old problem of choosing machine tunes based on a heuristic blend of KAM theory and resonance selection rules.

  10. Change in Chaos: Seven Lessons Learned from Katrina

    ERIC Educational Resources Information Center

    Carr-Chellman, Alison A.; Beabout, Brian; Alkandari, Khaled A.; Almeida, Luis C.; Gursoy, Husra T.; Ma, Ziyan; Modak, Rucha S.; Pastore, Raymond S.

    2008-01-01

    This article discusses seven lessons learned from Katrina, suggesting that after chaos: (1) there is hope; (2) there is a strong atmosphere of indeterminacy; (3) things tend to break apart and reform in somewhat similar ways but with different values; (4) there is a desire for organization, leadership, and familiarity; (5) there is a sense of…

  11. Positive Maladjustment as a Transition from Chaos to Order

    ERIC Educational Resources Information Center

    Laycraft, Krystyna

    2009-01-01

    Dabrowski's theory of positive disintegration describes patterns and explains mechanisms of human development and has been successfully applied to understanding of gifted individuals. This article shows how the concepts of chaos theory and self-organization such as the sensitivity to initial conditions, positive and negative feedback, bifurcation…

  12. Ecosystem Simulations and Chaos on the Graphing Calculator

    ERIC Educational Resources Information Center

    Sinn, Robb

    2007-01-01

    An eighth grade algebra class used graphing calculators to simulate ecosystems. One simulation introduced mathematical chaos. The activities exposed the students to nonlinear patterns and modeling. The rate-of-change investigations related the ideas of intercept and slope to the changing equilibrium. The chaotic model intrigued them and was useful…

  13. Organisational Leadership and Chaos Theory: Let's Be Careful

    ERIC Educational Resources Information Center

    Galbraith, Peter

    2004-01-01

    This article addresses issues associated with applications of ideas from "chaos theory" to educational administration and leadership as found in the literature. Implications are considered in relation to claims concerning the behaviour of non-linear dynamic systems, and to the nature of the interpretations and recommendations that are made. To aid…

  14. Poincaré's contributions to chance and chaos.

    NASA Astrophysics Data System (ADS)

    Szebehely, V.

    In this paper a short and condensed biography of Henri Poincaré is presented with detailed information concerning several biographical references. This is followed by a review of his publications emphasizing his work in celestial mechanics and on the problem of three bodies. His article "Le Hasard" is reviewed in detail discussing his contributions to chaos.

  15. SLAC: A Tool for Addressing Chaos in the Ecology Classroom

    ERIC Educational Resources Information Center

    Hamilton, A. J.

    2005-01-01

    Until the early 1970s, ecologists generally assumed that erratic fluctuations observed in natural populations were a product of stochastic noise. It is now known that extremely complex dynamics can arise from basic deterministic processes. This field of study is generally called chaos theory. Here, a computer program, SLAC (Stability, Limits, And…

  16. Optimal control for stochastic systems with polynomial chaos

    NASA Astrophysics Data System (ADS)

    Gallagher, David James

    Assuring robustness of control system performance against model uncertainty is a significant component of control design. Current methods for developing a robust controller, however, are typically either too conservative or too computationally expensive. This thesis uses generalized polynomial chaos alongside finite-horizon optimal control as a new method of robust control design for a stochastic system. Since the equations for the mean and variance of the response can be expressed in terms of coefficients from a polynomial chaos expansion, optimizing a polynomial chaos expansion can be used to optimize the mean and variance, thus providing robust responses in a stochastic system. This thesis first provides a review of the concepts and literature then the rationale as well as the derivation of the proposed robust control method. Three examples are given to show the effectiveness of the new control method and are discussed. In particular, the final example demonstrates the applicability of using polynomial chaos to provide robust control for a stochastic soft landing problem.

  17. Microcomputer Simulation of Nonlinear Systems: From Oscillations to Chaos.

    ERIC Educational Resources Information Center

    Raw, Cecil J. G.; Stacey, Larry M.

    1989-01-01

    Presents two short microcomputer programs which illustrate features of nonlinear dynamics, including steady states, periodic oscillations, period doubling, and chaos. Logistic maps are explained, inclusion in undergraduate chemistry and physics courses to teach nonlinear equations is discussed, and applications in social and biological sciences…

  18. Toward Therapeutic Autopoiesis: Chaos, Complexity, and Narrative Therapy.

    ERIC Educational Resources Information Center

    Chen, Mei-whei

    The paradigm of modern psychology has been the determinism of Newtonian physics. That model earns psychology status as a science yet tunnels it to a linear way of unraveling human functioning. Responding to demands for a more holistic approach to psychological practice, it is necessary to redefine the "self" and other terms. Chaos, complexity, and…

  19. Learning Dialogically: The Art of Chaos-Informed Transformation

    ERIC Educational Resources Information Center

    van Eijnatten, Frans M.; van Galen, Maarten C.; Fitzgerald, Laurie A.

    2003-01-01

    A decision to don the chaos lens, adopt dialogue as its primary mode of communication, and to recognize the power of the organizational mind has fundamentally and irreversibly changed the way a Dutch capital-equipment manufacturer operates in its rapidly complexifying global marketplace. Beginning in September 1999, the focus of an ever widening…

  20. Parametric resonance induced chaos in magnetic damped driven pendulum

    NASA Astrophysics Data System (ADS)

    Khomeriki, Giorgi

    2016-07-01

    A damped driven pendulum with a magnetic driving force, appearing from a solenoid, where ac current flows is considered. The solenoid acts on the magnet, which is located at a free end of the pendulum. In this system the existence and interrelation of chaos and parametric resonance is theoretically examined. Derived analytical results are supported by numerical simulations and conducted experiments.

  1. Thinking about Chaos: Non-Quantitative Approaches to Teacher Education.

    ERIC Educational Resources Information Center

    Rockler, Michael J.

    1991-01-01

    Explains the chaos theory and its effect on education, relating it to quantum physics. The article suggests implications for education (predictions about student achievement are limited, the brain learns in nonlinear ways, and the knowledge base in teacher education needs modification to account for recent discoveries in science and mathematics).…

  2. What Does Chaos Theory Have to Offer Educational Administration?

    ERIC Educational Resources Information Center

    Blair, Billie Goode

    1993-01-01

    Chaos theory, based on quantum physics research, boasts six central concepts: the butterfly effect, onset of turbulence, dissipative structures, random shocks, strange attractors, and recursive symmetries and feedback mechanisms. This article examines five principals' daily experiences, focusing on participants' efforts to generate meaning from a…

  3. Constrained Quantum Mechanics: Chaos in Non-Planar Billiards

    ERIC Educational Resources Information Center

    Salazar, R.; Tellez, G.

    2012-01-01

    We illustrate some of the techniques to identify chaos signatures at the quantum level using as guiding examples some systems where a particle is constrained to move on a radial symmetric, but non-planar, surface. In particular, two systems are studied: the case of a cone with an arbitrary contour or "dunce hat billiard" and the rectangular…

  4. Jurassic Management: Chaos and Management Development in Educational Institutions.

    ERIC Educational Resources Information Center

    Gunter, Helen

    1995-01-01

    Investigates the failure of "Jurassic" management: visioning, consensus value systems, proactively created teams, and development planning. Applied chaos theory can help self-managing schools and colleges avoid disaster and improve their management-development programs. Survival in turbulent times is based on educational managers' capacity to make…

  5. SECULAR CHAOS AND THE PRODUCTION OF HOT JUPITERS

    SciTech Connect

    Wu Yanqin; Lithwick, Yoram

    2011-07-10

    In a planetary system with two or more well-spaced, eccentric, inclined planets, secular interactions may lead to chaos. The innermost planet may gradually become very eccentric and/or inclined as a result of the secular degrees of freedom drifting toward equipartition of angular momentum deficit. Secular chaos is known to be responsible for the eventual destabilization of Mercury in our own solar system. Here we focus on systems with three giant planets. We characterize the secular chaos and demonstrate the criterion for it to occur, but leave a detailed understanding of secular chaos to a companion paper. After an extended period of eccentricity diffusion, the inner planet's pericenter can approach the star to within a few stellar radii. Strong tidal interactions and ensuing tidal dissipation extract orbital energy from the planet and pull it inward, creating a hot Jupiter. In contrast to other proposed channels for the production of hot Jupiters, such a scenario (which we term 'secular migration') explains a range of observations: the pile-up of hot Jupiters at 3 day orbital periods, the fact that hot Jupiters are in general less massive than other radial velocity planets, that they may have misaligned inclinations with respect to stellar spin, and that they have few easily detectable companions (but may have giant companions in distant orbits). Secular migration can also explain close-in planets as low in mass as Neptune; and an aborted secular migration can explain the 'warm Jupiters' at intermediate distances. In addition, the frequency of hot Jupiters formed via secular migration increases with stellar age. We further suggest that secular chaos may be responsible for the observed eccentricities of giant planets at larger distances and that these planets could exhibit significant spin-orbit misalignment.

  6. Secular Chaos and the Production of Hot Jupiters

    NASA Astrophysics Data System (ADS)

    Wu, Yanqin; Lithwick, Yoram

    2011-07-01

    In a planetary system with two or more well-spaced, eccentric, inclined planets, secular interactions may lead to chaos. The innermost planet may gradually become very eccentric and/or inclined as a result of the secular degrees of freedom drifting toward equipartition of angular momentum deficit. Secular chaos is known to be responsible for the eventual destabilization of Mercury in our own solar system. Here we focus on systems with three giant planets. We characterize the secular chaos and demonstrate the criterion for it to occur, but leave a detailed understanding of secular chaos to a companion paper. After an extended period of eccentricity diffusion, the inner planet's pericenter can approach the star to within a few stellar radii. Strong tidal interactions and ensuing tidal dissipation extract orbital energy from the planet and pull it inward, creating a hot Jupiter. In contrast to other proposed channels for the production of hot Jupiters, such a scenario (which we term "secular migration") explains a range of observations: the pile-up of hot Jupiters at 3 day orbital periods, the fact that hot Jupiters are in general less massive than other radial velocity planets, that they may have misaligned inclinations with respect to stellar spin, and that they have few easily detectable companions (but may have giant companions in distant orbits). Secular migration can also explain close-in planets as low in mass as Neptune; and an aborted secular migration can explain the "warm Jupiters" at intermediate distances. In addition, the frequency of hot Jupiters formed via secular migration increases with stellar age. We further suggest that secular chaos may be responsible for the observed eccentricities of giant planets at larger distances and that these planets could exhibit significant spin-orbit misalignment.

  7. "I Had Seen Order and Chaos, but Had Thought They Were Different." The Challenges of the Chaos Theory for Career Development

    ERIC Educational Resources Information Center

    Pryor, Robert; Bright, Jim

    2004-01-01

    This paper highlights five challenges to the accepted wisdom in career development theory and practice. It presents the chaos theory of careers and argues that the chaos theory provides a more complete and authentic account of human behaviour. The paper argues that positivism, reductionism and assumptions of linearity are inappropriate for…

  8. Gypsum and Associated Sulfates in Iani Chaos, Mars

    NASA Astrophysics Data System (ADS)

    Gilmore, M. S.; Greenwood, J. P.

    2009-12-01

    We have mapped layered deposits in Iani Chaos, part of the Margaritifer - Ares Valles outflow system in the southern hemisphere of Mars. These deposits have high thermal inertia relative to their surroundings and they often appear bright in visible images. Context Camera (CTX) and High Resolution Imaging Science Experiment (HiRise) data show the deposits to typically have a fractured and polygonal texture at the 1 - 10 m scale and preserve few craters. The deposits are commonly layered at the several meter scale and may form cliffs that are actively eroding into blocks and rockfalls. Three primary deposits of these materials are present in Iani covering a total area of ~6000 km2 (approximately the size of Great Salt Lake). The deposits lie in topographic lows within Iani and form mounds of material 100s of meters high (range ~ 0 - 1 km). Bright, layered deposits are recognized within the mounds that comprise the chaos terrain itself. The layered deposits within the mounds are conformable to exposed layered deposits suggesting that the deposits are exposed by differential weathering (likely along fractures) between the chaos mounds. In central Iani, a second generation of layered deposits embay the eroded mounds of the chaos formation. Analysis of Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) data for this site positively identifies gypsum (CaSO4●H2O) in the post-chaos layered deposits. Sulfates also comprise the chaos terrain itself. The spectra of these sulfates are consistent with kieserite (MgSO4●H2O) in a mixture containing additional minerals. The stratigraphy at Iani requires at least two episodes of sulfate formation, separated by an uncomformity. We propose the following geologic sequence for Iani Chaos: 1) Formation of Mg (and possibly other sulfates and evaporite minerals) by evaporation of water. 3) Emplacement of non-evaporite materials in the region. 4) Formation of chaos terrain, presumably due to subsurface failure. 5) Erosion of

  9. Staying Innovative and Change-Focused in the New Economy. A Collection of Special Papers Generated for the 2001 International Career Development Conference (Seattle, Washington, November 7-11, 2001).

    ERIC Educational Resources Information Center

    Walz, Garry R., Ed.; Knowdell, Richard, Ed.; Kirkman, Chris, Ed.

    This publication is designed to broaden exposure to the ideas presented at the 2001 International Career Development Conference. It provides authors with an international forum for communicating their current research, proposals, and projects to the international career development community. The articles in this symposium include: (1) "Chaos,…

  10. Outflow channel sources, reactivation, and chaos formation, Xanthe Terra, Mars

    USGS Publications Warehouse

    Rodriguez, J.A.P.; Sasaki, S.; Kuzmin, R.O.; Dohm, J.M.; Tanaka, K.L.; Miyamoto, H.; Kurita, K.; Komatsu, G.; Fairen, A.G.; Ferris, J.C.

    2005-01-01

    The undulating, warped, and densely fractured surfaces of highland regions east of Valles Marineris (located north of the eastern Aureum Chaos, east of the Hydraotes Chaos, and south of the Hydaspis Chaos) resulted from extensional surface warping related to ground subsidence, caused when pressurized water confined in subterranean caverns was released to the surface. Water emanations formed crater lakes and resulted in channeling episodes involved in the excavation of Ares, Tiu, and Simud Valles of the eastern part of the circum-Chryse outflow channel system. Progressive surface subsidence and associated reduction of the subsurface cavernous volume, and/or episodes of magmatic-driven activity, led to increases of the hydrostatic pressure, resulting in reactivation of both catastrophic and non-catastrophic outflow activity. Ancient cratered highland and basin materials that underwent large-scale subsidence grade into densely fractured terrains. Collapse of rock materials in these regions resulted in the formation of chaotic terrains, which occur in and near the headwaters of the eastern circum-Chryse outflow channels. The deepest chaotic terrain in the Hydaspis Chaos region resulted from the collapse of pre-existing outflow channel floors. The release of volatiles and related collapse may have included water emanations not necessarily linked to catastrophic outflow. Basal warming related to dike intrusions, thermokarst activity involving wet sediments and/or dissected ice-enriched country rock, permafrost exposed to the atmosphere by extensional tectonism and channel incision, and/or the injection of water into porous floor material, may have enhanced outflow channel floor instability and subsequent collapse. In addition to the possible genetic linkage to outflow channel development dating back to at least the Late Noachian, clear disruption of impact craters with pristine ejecta blankets and rims, as well as preservation of fine tectonic fabrics, suggest that

  11. A novel image encryption algorithm using chaos and reversible cellular automata

    NASA Astrophysics Data System (ADS)

    Wang, Xingyuan; Luan, Dapeng

    2013-11-01

    In this paper, a novel image encryption scheme is proposed based on reversible cellular automata (RCA) combining chaos. In this algorithm, an intertwining logistic map with complex behavior and periodic boundary reversible cellular automata are used. We split each pixel of image into units of 4 bits, then adopt pseudorandom key stream generated by the intertwining logistic map to permute these units in confusion stage. And in diffusion stage, two-dimensional reversible cellular automata which are discrete dynamical systems are applied to iterate many rounds to achieve diffusion on bit-level, in which we only consider the higher 4 bits in a pixel because the higher 4 bits carry almost the information of an image. Theoretical analysis and experimental results demonstrate the proposed algorithm achieves a high security level and processes good performance against common attacks like differential attack and statistical attack. This algorithm belongs to the class of symmetric systems.

  12. The circular fountain: liquid merry-go-round and benchmark for spatiotemporal chaos

    NASA Astrophysics Data System (ADS)

    Brunet, Philippe; Flesselles, Jean-Marc; Limat, Laurent

    1999-11-01

    A circular dish being continuously filled with viscous fluid through a hole placed in its center makes a simple overflowing fountain. Within appropriate experimental conditions (nature of the fluid and flow rate), a regular pattern of liquid columns is selected. A variety of stable dynamical modes may be excited and lead to oscillation, drift or spatiotemporal chaos of all or part of the pattern. Despite numerous attempts, the underlying mechanisms are still unknown. Two ways to tackle the problem are considered. Firstly the amplitude equations approach, which has proven its efficiency in the past to describe the spatiotemporal behavior of one dimensional periodic patterns; here, our experiment shows that new theoretical inputs are necessary. Secondly a fluid mechanic approach based on the evaluation of the different contributions to the fluid motion. Both approaches provide different insights to the problem.

  13. Deterministic chaos in the Belousov-Zhabotinsky reaction: Experiments and simulations

    NASA Astrophysics Data System (ADS)

    Zhang, Dongmei; Györgyi, László; Peltier, William R.

    1993-10-01

    An account of the experimental discovery of complex dynamical behavior in the continuous-flow, stirred tank reactor (CSTR) Belousov-Zhabotinsky (BZ) reaction, as well as numerical simulations based on the BZ chemistry are given. The most recent four- and three-variable models that are deduced from the well-accepted, updated chemical mechanism of the BZ reaction and which exhibit robust chaotic states are summarized. Chaos has been observed in experiments and simulations embedded in the regions of complexities at both low and high flow rates. The deterministic nature of the observed aperiodicities at low flow rates is unequivocally established. However, controversy still remains in the interpretation of certain aperiodicities observed at high flow rates.

  14. Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers.

    PubMed

    Hirano, Kunihito; Yamazaki, Taiki; Morikatsu, Shinichiro; Okumura, Haruka; Aida, Hiroki; Uchida, Atsushi; Yoshimori, Shigeru; Yoshimura, Kazuyuki; Harayama, Takahisa; Davis, Peter

    2010-03-15

    We experimentally demonstrate random bit generation using multi-bit samples of bandwidth-enhanced chaos in semiconductor lasers. Chaotic fluctuation of laser output is generated in a semiconductor laser with optical feedback and the chaotic output is injected into a second semiconductor laser to obtain a chaotic intensity signal with bandwidth enhanced up to 16 GHz. The chaotic signal is converted to an 8-bit digital signal by sampling with a digital oscilloscope at 12.5 Giga samples per second (GS/s). Random bits are generated by bitwise exclusive-OR operation on corresponding bits in samples of the chaotic signal and its time-delayed signal. Statistical tests verify the randomness of bit sequences obtained using 1 to 6 bits per sample, corresponding to fast random bit generation rates from 12.5 to 75 Gigabit per second (Gb/s) ( = 6 bit x 12.5 GS/s).

  15. PAPR reduction based on chaos combined with SLM technique in optical OFDM IM/DD system

    NASA Astrophysics Data System (ADS)

    Xiao, Yaoqiang; Chen, Ming; Li, Fan; Tang, Jin; Liu, Yi; Chen, Lin

    2015-01-01

    This paper proposes a method to decrease the PAPR of 16-quadrature-amplitude-modulation (16QAM) orthogonal-frequency-division-multiplexing (OFDM) signal. The method is to combine chaos with selected mapping (CSLM) technique so that the chaotic sequences are able to control generation of phase rotation factors. The research has utilized this method to transmit OFDM signal along 100 km long single-mode fiber in an IM/DD system to test OFDM signal performance. Our experimental results show that the receiver sensitivity is improved by about 1.4 dB when a 3.28 GB/s OFDM signal at a bit error rate of 1 × 10-3 is launched by transmission power at 2, 6, 8 and 10 dBm, respectively. Moreover, comparison with traditional SLM technique, the CSLM technique can improve the BER of the system.

  16. PREFACE: 10th Joint Conference on Chemistry

    NASA Astrophysics Data System (ADS)

    2016-02-01

    The 10th Joint Conference on Chemistry is an international conference organized by 4 chemistry departments of 4 universities in central Java, Indonesia. The universities are Sebelas Maret University, Diponegoro University, Semarang State University and Soedirman University. The venue was at Solo, Indonesia, at September 8-9, 2015. The total conference participants are 133 including the invited speakers. The conference emphasized the multidisciplinary chemical issue and impact of today's sustainable chemistry which covering the following topics: • Material innovation for sustainable goals • Development of renewable and sustainable energy based on chemistry • New drug design, experimental and theoretical methods • Green synthesis and characterization of material (from molecule to functionalized materials) • Catalysis as core technology in industry • Natural product isolation and optimization

  17. Li-Yorke Chaos in Hybrid Systems on a Time Scale

    NASA Astrophysics Data System (ADS)

    Akhmet, Marat; Fen, Mehmet Onur

    2015-12-01

    By using the reduction technique to impulsive differential equations [Akhmet & Turan, 2006], we rigorously prove the presence of chaos in dynamic equations on time scales (DETS). The results of the present study are based on the Li-Yorke definition of chaos. This is the first time in the literature that chaos is obtained for DETS. An illustrative example is presented by means of a Duffing equation on a time scale.

  18. Laser dynamical reservoir computing with consistency: an approach of a chaos mask signal.

    PubMed

    Nakayama, Joma; Kanno, Kazutaka; Uchida, Atsushi

    2016-04-18

    We numerically investigate reservoir computing based on the consistency of a semiconductor laser subjected to optical feedback and injection. We introduce a chaos mask signal as an input temporal mask for reservoir computing and perform a time-series prediction task. We compare the errors of the task obtained from the chaos mask signal with those obtained from other digital and analog masks. The performance of the prediction task can be improved by using the chaos mask signal due to complex dynamical response.

  19. Controlling chaos in some laser systems via variable coupling and feedback time delays

    NASA Astrophysics Data System (ADS)

    Shahverdiev, E. M.

    2016-09-01

    We study numerically a system of two lasers cross-coupled optoelectronically with a time delay where the output intensity of each laser modulates the pump current of the other laser. We demonstrate control of chaos via variable coupling time delay by converting the laser intensity chaos to the steady-state. We also show that wavelength chaos in an electrically tunable distributed Bragg reflector (DBR) laser diode with a feedback loop that can be controlled via variable feedback time delay.

  20. Randomness versus deterministic chaos: Effect on invasion percolation clusters

    NASA Astrophysics Data System (ADS)

    Peng, Chung-Kang; Prakash, Sona; Herrmann, Hans J.; Stanley, H. Eugene

    1990-10-01

    What is the difference between randomness and chaos \\? Although one can define randomness and one can define chaos, one cannot easily assess the difference in a practical situation. Here we compare the results of these two antipodal approaches on a specific example. Specifically, we study how well the logistic map in its chaotic regime can be used as quasirandom number generator by calculating pertinent properties of a well-known random process: invasion percolation. Only if λ>λ*1 (the first reverse bifurcation point) is a smooth extrapolation in system size possible, and percolation exponents are retrieved. If λ≠1, a sequential filling of the lattice with the random numbers generates a measurable anisotropy in the growth sequence of the clusters, due to short-range correlations.

  1. Impulse-induced localized control of chaos in starlike networks.

    PubMed

    Chacón, Ricardo; Palmero, Faustino; Cuevas-Maraver, Jesús

    2016-06-01

    Locally decreasing the impulse transmitted by periodic pulses is shown to be a reliable method of taming chaos in starlike networks of dissipative nonlinear oscillators, leading to both synchronous periodic states and equilibria (oscillation death). Specifically, the paradigmatic model of damped kicked rotators is studied in which it is assumed that when the rotators are driven synchronously, i.e., all driving pulses transmit the same impulse, the networks display chaotic dynamics. It is found that the taming effect of decreasing the impulse transmitted by the pulses acting on particular nodes strongly depends on their number and degree of connectivity. A theoretical analysis is given explaining the basic physical mechanism as well as the main features of the chaos-control scenario. PMID:27415258

  2. Organized and Disorganized Chaos a New Dynamics in Peace Intelligence

    NASA Astrophysics Data System (ADS)

    Erçetin, Şefika Şule; Tekin, Ali; Açıkalın, Şuay Nilhan

    "How to prevent wars" can be considered as reason behind the foundation of field international relations. In other words, after two devastating war humanity realized that we should learn peaceful coexistence. That's why last 50 years were dedicated to peace which have been the most controversial and gripping notion in all disciplines. Within this context, the notion of sustainable peace becomes more important in last years. On the other hand, chaos and its application in social life- actually our real universe gave insight people to understand social facts with dynamic systems and chaos theory. So, this chapter will be a new and fresh to have sustainable peace with peace intelligence. Peace intelligence is completely new phenomena which coined by Şefika Şule Erçetin.

  3. Impulse-induced localized control of chaos in starlike networks

    NASA Astrophysics Data System (ADS)

    Chacón, Ricardo; Palmero, Faustino; Cuevas-Maraver, Jesús

    2016-06-01

    Locally decreasing the impulse transmitted by periodic pulses is shown to be a reliable method of taming chaos in starlike networks of dissipative nonlinear oscillators, leading to both synchronous periodic states and equilibria (oscillation death). Specifically, the paradigmatic model of damped kicked rotators is studied in which it is assumed that when the rotators are driven synchronously, i.e., all driving pulses transmit the same impulse, the networks display chaotic dynamics. It is found that the taming effect of decreasing the impulse transmitted by the pulses acting on particular nodes strongly depends on their number and degree of connectivity. A theoretical analysis is given explaining the basic physical mechanism as well as the main features of the chaos-control scenario.

  4. Impulse-induced localized control of chaos in starlike networks.

    PubMed

    Chacón, Ricardo; Palmero, Faustino; Cuevas-Maraver, Jesús

    2016-06-01

    Locally decreasing the impulse transmitted by periodic pulses is shown to be a reliable method of taming chaos in starlike networks of dissipative nonlinear oscillators, leading to both synchronous periodic states and equilibria (oscillation death). Specifically, the paradigmatic model of damped kicked rotators is studied in which it is assumed that when the rotators are driven synchronously, i.e., all driving pulses transmit the same impulse, the networks display chaotic dynamics. It is found that the taming effect of decreasing the impulse transmitted by the pulses acting on particular nodes strongly depends on their number and degree of connectivity. A theoretical analysis is given explaining the basic physical mechanism as well as the main features of the chaos-control scenario.

  5. 'Chaos, restitution and quest': one woman's journey through menopause.

    PubMed

    Nosek, Marcianna; Kennedy, Holly Powell; Gudmundsdottir, Maria

    2012-09-01

    Menopause, a natural stage in a woman's reproductive life, is not an illness; yet some women experience severe enough symptoms to cause a breakdown in the body similar to illness or other major health disruptions. As part of a larger narrative analysis investigation of distress during menopause, this case study presents one woman's transformational journey through menopause, analysed through Frank's health and illness narratives - chaos, restitution and quest. The narratives were retranscribed using Labov's elements of a true story and Gee's poetic restructuring. This report of one woman's experience of distress during the menopause transition describes a poetic chaos narrative of incessant night sweats resulting in a loss of physicality and a deep-rooted belief in self-healing; a restitution narrative of restored health that mandated the surrender to a new healing discourse, experienced simultaneously as a victory and a defeat; and a quest narrative of seeking meaning, insight and new-found values and identities. PMID:22471763

  6. Stimulus-dependent suppression of chaos in recurrent neural networks

    SciTech Connect

    Rajan, Kanaka; Abbott, L. F.; Sompolinsky, Haim

    2010-07-15

    Neuronal activity arises from an interaction between ongoing firing generated spontaneously by neural circuits and responses driven by external stimuli. Using mean-field analysis, we ask how a neural network that intrinsically generates chaotic patterns of activity can remain sensitive to extrinsic input. We find that inputs not only drive network responses, but they also actively suppress ongoing activity, ultimately leading to a phase transition in which chaos is completely eliminated. The critical input intensity at the phase transition is a nonmonotonic function of stimulus frequency, revealing a 'resonant' frequency at which the input is most effective at suppressing chaos even though the power spectrum of the spontaneous activity peaks at zero and falls exponentially. A prediction of our analysis is that the variance of neural responses should be most strongly suppressed at frequencies matching the range over which many sensory systems operate.

  7. Granular chaos and mixing: Whirled in a grain of sand

    SciTech Connect

    Shinbrot, Troy

    2015-09-15

    In this paper, we overview examples of chaos in granular flows. We begin by reviewing several remarkable behaviors that have intrigued researchers over the past few decades, and we then focus on three areas in which chaos plays an intrinsic role in granular behavior. First, we discuss pattern formation in vibrated beds, which we show is a direct result of chaotic scattering combined with dynamical dissipation. Next, we consider stick-slip motion, which involves chaotic scattering on the micro-scale, and which results in complex and as yet unexplained peculiarities on the macro-scale. Finally, we examine granular mixing, which we show combines micro-scale chaotic scattering and macro-scale stick-slip motion into behaviors that are well described by dynamical systems tools, such as iterative mappings.

  8. Computational complexity of symbolic dynamics at the onset of chaos

    NASA Astrophysics Data System (ADS)

    Lakdawala, Porus

    1996-05-01

    In a variety of studies of dynamical systems, the edge of order and chaos has been singled out as a region of complexity. It was suggested by Wolfram, on the basis of qualitative behavior of cellular automata, that the computational basis for modeling this region is the universal Turing machine. In this paper, following a suggestion of Crutchfield, we try to show that the Turing machine model may often be too powerful as a computational model to describe the boundary of order and chaos. In particular we study the region of the first accumulation of period doubling in unimodal and bimodal maps of the interval, from the point of view of language theory. We show that in relation to the ``extended'' Chomsky hierarchy, the relevant computational model in the unimodal case is the nested stack automaton or the related indexed languages, while the bimodal case is modeled by the linear bounded automaton or the related context-sensitive languages.

  9. Quantum biology on the edge of quantum chaos.

    PubMed

    Vattay, Gabor; Kauffman, Stuart; Niiranen, Samuli

    2014-01-01

    We give a new explanation for why some biological systems can stay quantum coherent for a long time at room temperature, one of the fundamental puzzles of quantum biology. We show that systems with the right level of complexity between chaos and regularity can increase their coherence time by orders of magnitude. Systems near Critical Quantum Chaos or Metal-Insulator Transition (MIT) can have long coherence times and coherent transport at the same time. The new theory tested in a realistic light harvesting system model can reproduce the scaling of critical fluctuations reported in recent experiments. Scaling of return probability in the FMO light harvesting complex shows the signs of universal return probability decay observed at critical MIT. The results may open up new possibilities to design low loss energy and information transport systems in this Poised Realm hovering reversibly between quantum coherence and classicality.

  10. Genomes: At the edge of Chaos with maximum information capacity

    NASA Astrophysics Data System (ADS)

    Kong, Sing-Guan; Chen, Hong-Da; Torda, Andrew; Lee, H. C.

    We propose an order index, ϕ, which quantifies the notion of "life at the edge of chaos" when applied to genome sequences. It maps genomes to a number from 0 (random and of infinite length) to 1 (fully ordered) and applies regardless of sequence length and base composition. The 786 complete genomic sequences in GenBank were found to have ϕ values in a very narrow range, 0.037 ± 0.027. We show this implies that genomes are halfway towards being completely random, namely, at the edge of chaos. We argue that this narrow range represents the neighborhood of a fixed-point in the space of sequences, and genomes are driven there by the dynamics of a robust, predominantly neutral evolution process...

  11. Intermittency and transient chaos from simple frequency-dependent selection.

    PubMed

    Gavrilets, S; Hastings, A

    1995-08-22

    Frequency-dependent selection is an important determinant of the evolution of gametophytic self-incompatibility systems in plants, aposematic (warning) and cryptic coloration, systems of mimicry, competitive interactions among members of a population, mating preferences, predator-prey and host-parasite interactions, aggression and other behavioural traits. Past theoretical studies of frequency-dependent selection have shown it to be a plausible mechanism for the maintenance of genetic variability in natural populations. Here, through an analysis of a simple deterministic model for frequency-dependent selection, we demonstrate that complex dynamic behaviour is possible under a broad range of parameter values. In particular we show that the model exhibits not only cycles and chaos but also, for a more restricted set of parameters, transient chaos and intermittency: alterations between an apparently deterministic behaviour and apparently chaotic fluctuations. This behaviour, which has not been stressed within the population genetics literature, provides an explanation for erratic dynamics of gene frequencies.

  12. Intermittency and chaos in intracavity doubled lasers. II

    SciTech Connect

    James, G.E.; Harrell, E.M. II ); Roy, R. )

    1990-03-01

    We describe the nonlinear dynamics of intracavity doubled multimode lasers. Baer (J. Opt. Soc. Am. B 3, 1175 (1986)) observed irregular amplitude fluctuations in a multimode yttrium aluminum garnet laser with an intracavity potassium titanyl phosphate frequency-doubling crystal; we identify type-III intermittency as the route to chaos. Subsequently, Oka and Kubota (Opt. Lett. 13, 805 (1988)) demonstrated the stabilization of such a laser by the introduction of a quarter wave plate into the cavity. A generalized model of rate equations for this case is introduced. It is shown that a second route to chaos through a Hopf bifurcation, synchronization, and period-doubling sequence occurs on rotation of the quarter wave plate within the cavity. In addition, we predict that the laser output may be stable for particular lengths of the doubling crystal.

  13. Control of complex dynamics and chaos in distributed parameter systems

    SciTech Connect

    Chakravarti, S.; Marek, M.; Ray, W.H.

    1995-12-31

    This paper discusses a methodology for controlling complex dynamics and chaos in distributed parameter systems. The reaction-diffusion system with Brusselator kinetics, where the torus-doubling or quasi-periodic (two characteristic incommensurate frequencies) route to chaos exists in a defined range of parameter values, is used as an example. Poincare maps are used for characterization of quasi-periodic and chaotic attractors. The dominant modes or topos, which are inherent properties of the system, are identified by means of the Singular Value Decomposition. Tested modal feedback control schemas based on identified dominant spatial modes confirm the possibility of stabilization of simple quasi-periodic trajectories in the complex quasi-periodic or chaotic spatiotemporal patterns.

  14. Pattern dynamics and spatiotemporal chaos in the quantum Zakharov equations

    SciTech Connect

    Misra, A. P.; Shukla, P. K.

    2009-05-15

    The dynamical behavior of the nonlinear interaction of quantum Langmuir waves (QLWs) and quantum ion-acoustic waves (QIAWs) is studied in the one-dimensional quantum Zakharov equations. Numerical simulations of coupled QLWs and QIAWs reveal that many coherent solitary patterns can be excited and saturated via the modulational instability of unstable harmonic modes excited by a modulation wave number of monoenergetic QLWs. The evolution of such solitary patterns may undergo the states of spatially partial coherence (SPC), coexistence of temporal chaos and spatiotemporal chaos (STC), as well as STC. The SPC state is essentially due to ion-acoustic wave emission and due to quantum diffraction, while the STC is caused by the combined effects of SPC and quantum diffraction, as well as by collisions and fusions among patterns in stochastic motion. The energy in the system is strongly redistributed, which may switch on the onset of weak turbulence in dense quantum plasmas.

  15. Verification of chaotic behavior in an experimental loudspeaker.

    PubMed

    Reiss, Joshua D; Djurek, Ivan; Petosic, Antonio; Djurek, Danijel

    2008-10-01

    The dynamics of an experimental electrodynamic loudspeaker is studied by using the tools of chaos theory and time series analysis. Delay time, embedding dimension, fractal dimension, and other empirical quantities are determined from experimental data. Particular attention is paid to issues of stationarity in a system in order to identify sources of uncertainty. Lyapunov exponents and fractal dimension are measured using several independent techniques. Results are compared in order to establish independent confirmation of low dimensional dynamics and a positive dominant Lyapunov exponent. We thus show that the loudspeaker may function as a chaotic system suitable for low dimensional modeling and the application of chaos control techniques.

  16. Coupled lasers: phase versus chaos synchronization.

    PubMed

    Reidler, I; Nixon, M; Aviad, Y; Guberman, S; Friesem, A A; Rosenbluh, M; Davidson, N; Kanter, I

    2013-10-15

    The synchronization of chaotic lasers and the optical phase synchronization of light originating in multiple coupled lasers have both been extensively studied. However, the interplay between these two phenomena, especially at the network level, is unexplored. Here, we experimentally compare these phenomena by controlling the heterogeneity of the coupling delay times of two lasers. While chaotic lasers exhibit deterioration in synchronization as the time delay heterogeneity increases, phase synchronization is found to be independent of heterogeneity. The experimental results are found to be in agreement with numerical simulations for semiconductor lasers.

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

    NASA Astrophysics Data System (ADS)

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

    2016-09-01

    A new arbitrary Polynomial Chaos (aPC) method is presented for moderately high-dimensional problems characterised by limited input data availability. The proposed methodology improves the algorithm of aPC and extends the method, that was previously only introduced as tensor product expansion, to moderately high-dimensional stochastic problems. The fundamental idea of aPC is to use the statistical moments of the input random variables to develop the polynomial chaos expansion. This approach provides the possibility to propagate continuous or discrete probability density functions and also histograms (data sets) as long as their moments exist, are finite and the determinant of the moment matrix is strictly positive. For cases with limited data availability, this approach avoids bias and fitting errors caused by wrong assumptions. In this work, an alternative way to calculate the aPC is suggested, which provides the optimal polynomials, Gaussian quadrature collocation points and weights from the moments using only a handful of matrix operations on the Hankel matrix of moments. It can therefore be implemented without requiring prior knowledge about statistical data analysis or a detailed understanding of the mathematics of polynomial chaos expansions. The extension to more input variables suggested in this work, is an anisotropic and adaptive version of Smolyak's algorithm that is solely based on the moments of the input probability distributions. It is referred to as SAMBA (PC), which is short for Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos. It is illustrated that for moderately high-dimensional problems (up to 20 different input variables or histograms) SAMBA can significantly simplify the calculation of sparse Gaussian quadrature rules. SAMBA's efficiency for multivariate functions with regard to data availability is further demonstrated by analysing higher order convergence and accuracy for a set of nonlinear test functions with 2, 5 and 10

  18. Geology and origin of Europa's "Mitten" feature (Murias Chaos)

    USGS Publications Warehouse

    Figueredo, P.H.; Chuang, F.C.; Rathbun, J.; Kirk, R.L.; Greeley, R.

    2002-01-01

    The "Mitten" (provisionally named Murias Chaos by the International Astronomical Union) is a region of elevated chaos-like terrain in the leading hemisphere of Europa. Its origin had been explained under the currently debated theories of melting through a thin lithosphere or convection within a thick one. Galileo observations reveal several characteristics that suggest that the Mitten is distinct from typical chaos terrain and point to a different formational process. Photoclinometric elevation estimates suggest that the Mitten is slightly elevated with respect to the surrounding terrain; geologic relations indicate that it must have raised significantly from the plains in its past, resembling disrupted domes on Europa's trailing hemisphere. Moreover, the Mitten material appears to have extruded onto the plains and flowed for tens of kilometers. The area subsequently subsided as a result of isostatic adjustment, viscous relaxation, and/or plains loading. Using plate flexure models, we estimated the elastic lithosphere in the area to be several kilometers thick. We propose that the Mitten originated by the ascent and extrusion of a large thermal diapir. Thermal-mechanical modeling shows that a Mitten-sized plume would remain sufficiently warm and buoyant to pierce through the crust and flow unconfined on the surface. Such a diapir probably had an initial radius between 5 and 8 km and an initial depth of 20-40 km, consistent with a thick-lithosphere model. In this scenario the Mitten appears to represent the surface expression of the rare ascent of a large diapir, in contrast to lenticulae and chaos terrain, which may form by isolated and clustered small diapirs, respectively.

  19. Geology and Origin of Europa's Mitten Feature (Murias Chaos)

    NASA Technical Reports Server (NTRS)

    Figueredo, P. H.; Chuang, F. C.; Rathbun, J.; Kirk, R. L.; Greeley, R.

    2002-01-01

    The "Mitten" (provisionally named Murias Chaos by the International Astronomical Union) is a region of elevated chaos-like terrain in the leading hemisphere of Europa. Its origin had been explained under the currently debated theories of melting through a thin lithosphere or convection within a thick one. Galileo observations reveal several characteristics that suggest that the Mitten is distinct from typical chaos terrain and point to a different formational process. Photoclinometric elevation estimates suggest that the Mitten is slightly elevated with respect to the surrounding terrain; geologic relations indicate that it must have raised significantly from the plains in its past, resembling disrupted domes on Europa's trailing hemisphere. Moreover, the Mitten material appears to have extruded onto the plains and flowed for tens of kilometers. The area subsequently subsided as a result of isostatic adjustment, viscous relaxation, and/or plains loading. Using plate flexure models, we estimated the elastic lithosphere in the area to be several kilometers thick. We propose that the Mitten originated by the ascent and extrusion of a large thermal diapir. Thermal-mechanical modeling shows that a Mitten-sized plume would remain sufficiently warm and buoyant to pierce through the crust and flow unconfined on the surface. Such a diapir probably had an initial radius between 5 and 8 km and an initial depth of 20-40 km, consistent with a thick-lithosphere model. In this scenario the Mitten appears to represent the surface expression of the rare ascent of a large diapir, in contrast to lenticulae and chaos terrain, which may form by isolated and clustered small diapirs, respectively.

  20. Chaos detection tools: The LP-VIcode and its applications

    NASA Astrophysics Data System (ADS)

    Darriba, L. A.; Maffione, N. P.; Cincotta, P. M.; Giordano, C. M.

    A very important topic in galactic dynamics is the detection of instabilities of a given system and the possible appearance of chaos. Such a chaotic bahaviour can be detected and studied by means of variational chaos in- dicators (CIs). The CIs are based on the study of the evolution of initial deviation vectors, which makes these techniques specially sensitive to in- dicate the presence of chaos. Notwithstanding their special sensitiveness to identify chaos, the CIs are still good alternatives to determine also the resonance web. On the other hand, the so-called spectral analysis methods are based on the study of some quantity (e.g. the frequency) on a single orbit, which turns these techniques very efficient for the determination of the resonant struc- ture of the system. The analysis of the interaction among chaotic and regular components as well as the determination of the resonant structure of the Hamiltonian leads to a deeper understanding of the system's dynamics. Despite the advan- tages of the simultaneous application of both types of techniques, many researchers keep applying only one of them. Herein, we present an alpha version of a program coded in Fortran, the LP-VIcode. Although the code is in a developing stage, it can compute several CIs, and here we apply it together with the Frequency Modified Fourier Transform (FMFT) (Sidlichovský & Nesvorný 1996) to study the stationary space (Schwarzchild 1993) of an average realistic Hamiltonian model (Muzzio et al. 2005). Using the LP-VIcode, in Maffione et al. (2011b) and Darriba et al. (sub- mitted) the authors suggest an efficient package of CIs to study a general Hamiltonian. Here the research is extended to show that the complemen- tary use of the LP-VIcode and the spectral analysis methods is highly rec- ommended to study a realistic Hamiltonian model.

  1. Classical and quantum chaos in a circular billiard with a straight cut

    SciTech Connect

    Ree, S.; Reichl, L.E.

    1999-08-01

    We study classical and quantum dynamics of a particle in a circular billiard with a straight cut. Classically, this system can be integrable, nonintegrable with {ital soft chaos}, or nonintegrable with {ital hard chaos} as we vary the size of the cut. We plot Poincar{acute e} surfaces of section to study chaos. Quantum mechanically, we look at Husimi plots, and also use the quantum web, the technique primarily used in spin systems so far, to try to see differences in quantum manifestations of soft and hard chaos. {copyright} {ital 1999} {ital The American Physical Society}

  2. Simulation experiments to generate broadband chaos using dual-wavelength optically injected Fabry-Perot laser

    NASA Astrophysics Data System (ADS)

    Obaid, Hafiz Muhammad; Khawar Islam, Muhammad; Obaid Ullah, Muhammad

    2016-08-01

    Broadband chaos can be generated by beating two wavelengths in a hybrid arrangement of Fabry-Perot (FP) Laser and Fiber ring cavity by injecting dual wavelengths. The bandwidth of generated chaos can be controlled by detuning different modes of FP Laser for beating. The bandwidth of generated chaos increased to many folds depending upon the injected strength and wavelength spacing matched to FP laser modes. The bandwidth enhancement in different simulation experiments conducted is optimized by varying different parameters of FP laser and cavity. The waveforms are analyzed and Lyapunov exponents are calculated in order to validate the existence of high bandwidth non-pulsating chaos.

  3. Symptoms of chaos in observed oscillations near a bifurcation with noise

    NASA Astrophysics Data System (ADS)

    Harding, Robert H.; Ross, John

    1988-10-01

    We examine an experimental transition from periodic to aperiodic and back to periodic dynamics in the combustion of acetaldehyde(ACH) in a continuous stirred tank reactor (CSTR) with power spectra, autocorrelation functions, phase portraits, Poincaŕe sections, the Wolf-Swift-Swinney-Vastano (WSSV) method for determining the largest Lyapounov exponent, and the Grassberger-Procaccia (GP) method for determining correlation dimension. Each technique gives some indications of a transition to chaos, but there are discrepancies in that the largest Lyapounov exponent is positive but does not converge and the GP method results in a correlation dimension between one and two for two aperiodic data sets. We explore in instructive detail possible explanations for false indications of chaos by comparing our results with calculations on the Rössler chaotic attractor and the van der Pol periodic attractor modified to examine the effects of uneven point distribution and three types of experimental noise. An uneven distribution of points results in a decreased range of length scales for convergence and a larger required embedding dimension for the GP method, but does not explain our experimental results. Observation noise (a Gaussian noise added to each term in the time series but not entering in the equations of motion) and constraint shift (the motion relaxes to an attractor but a constraint changes monotonically during the course of measurement) added to a periodic attractor both result in a low length scale cutoff below which the attractor dimension does not converge with embedding dimension, and above which it converges to 1. Constraint variation noise (a Gaussian noise is added to each term in the time series and enters into the equations of motion as a stochastic perturbation) does yield correlation dimensions between 1 and 2. The experimental transition shows many similarities to a Hopf bifurcation found in another experiment on the same system and to a theoretical Hopf

  4. Building CHAOS: An Operating System for Livermore Linux Clusters

    SciTech Connect

    Garlick, J E; Dunlap, C M

    2003-02-21

    The Livermore Computing (LC) Linux Integration and Development Project (the Linux Project) produces and supports the Clustered High Availability Operating System (CHAOS), a cluster operating environment based on Red Hat Linux. Each CHAOS release begins with a set of requirements and ends with a formally tested, packaged, and documented release suitable for use on LC's production Linux clusters. One characteristic of CHAOS is that component software packages come from different sources under varying degrees of project control. Some are developed by the Linux Project, some are developed by other LC projects, some are external open source projects, and some are commercial software packages. A challenge to the Linux Project is to adhere to release schedules and testing disciplines in a diverse, highly decentralized development environment. Communication channels are maintained for externally developed packages in order to obtain support, influence development decisions, and coordinate/understand release schedules. The Linux Project embraces open source by releasing locally developed packages under open source license, by collaborating with open source projects where mutually beneficial, and by preferring open source over proprietary software. Project members generally use open source development tools. The Linux Project requires system administrators and developers to work together to resolve problems that arise in production. This tight coupling of production and development is a key strategy for making a product that directly addresses LC's production requirements. It is another challenge to balance support and development activities in such a way that one does not overwhelm the other.

  5. Topological chaos, braiding and bifurcation of almost-cyclic sets

    NASA Astrophysics Data System (ADS)

    Grover, Piyush; Ross, Shane D.; Stremler, Mark A.; Kumar, Pankaj

    2012-12-01

    In certain two-dimensional time-dependent flows, the braiding of periodic orbits provides a way to analyze chaos in the system through application of the Thurston-Nielsen classification theorem (TNCT). We expand upon earlier work that introduced the application of the TNCT to braiding of almost-cyclic sets, which are individual components of almost-invariant sets [Stremler et al., "Topological chaos and periodic braiding of almost-cyclic sets," Phys. Rev. Lett. 106, 114101 (2011)]. In this context, almost-cyclic sets are periodic regions in the flow with high local residence time that act as stirrers or "ghost rods" around which the surrounding fluid appears to be stretched and folded. In the present work, we discuss the bifurcation of the almost-cyclic sets as a system parameter is varied, which results in a sequence of topologically distinct braids. We show that, for Stokes' flow in a lid-driven cavity, these various braids give good lower bounds on the topological entropy over the respective parameter regimes in which they exist. We make the case that a topological analysis based on spatiotemporal braiding of almost-cyclic sets can be used for analyzing chaos in fluid flows. Hence, we further develop a connection between set-oriented statistical methods and topological methods, which promises to be an important analysis tool in the study of complex systems.

  6. A period-doubling cascade precedes chaos for planar maps.

    PubMed

    Sander, Evelyn; Yorke, James A

    2013-09-01

    A period-doubling cascade is often seen in numerical studies of those smooth (one-parameter families of) maps for which as the parameter is varied, the map transitions from one without chaos to one with chaos. Our emphasis in this paper is on establishing the existence of such a cascade for many maps with phase space dimension 2. We use continuation methods to show the following: under certain general assumptions, if at one parameter there are only finitely many periodic orbits, and at another parameter value there is chaos, then between those two parameter values there must be a cascade. We investigate only families that are generic in the sense that all periodic orbit bifurcations are generic. Our method of proof in showing there is one cascade is to show there must be infinitely many cascades. We discuss in detail two-dimensional families like those which arise as a time-2π maps for the Duffing equation and the forced damped pendulum equation. PMID:24089949

  7. Controlling chaos in balanced neural circuits with input spike trains

    NASA Astrophysics Data System (ADS)

    Engelken, Rainer; Wolf, Fred

    The cerebral cortex can be seen as a system of neural circuits driving each other with spike trains. Here we study how the statistics of these spike trains affects chaos in balanced target circuits.Earlier studies of chaos in balanced neural circuits either used a fixed input [van Vreeswijk, Sompolinsky 1996, Monteforte, Wolf 2010] or white noise [Lajoie et al. 2014]. We study dynamical stability of balanced networks driven by input spike trains with variable statistics. The analytically obtained Jacobian enables us to calculate the complete Lyapunov spectrum. We solved the dynamics in event-based simulations and calculated Lyapunov spectra, entropy production rate and attractor dimension. We vary correlations, irregularity, coupling strength and spike rate of the input and action potential onset rapidness of recurrent neurons.We generally find a suppression of chaos by input spike trains. This is strengthened by bursty and correlated input spike trains and increased action potential onset rapidness. We find a link between response reliability and the Lyapunov spectrum. Our study extends findings in chaotic rate models [Molgedey et al. 1992] to spiking neuron models and opens a novel avenue to study the role of projections in shaping the dynamics of large neural circuits.

  8. Lambda and the edge of chaos in recurrent neural networks.

    PubMed

    Seifter, Jared; Reggia, James A

    2015-01-01

    The idea that there is an edge of chaos, a region in the space of dynamical systems having special meaning for complex living entities, has a long history in artificial life. The significance of this region was first emphasized in cellular automata models when a single simple measure, λCA, identified it as a transitional region between order and chaos. Here we introduce a parameter λNN that is inspired by λCA but is defined for recurrent neural networks. We show through a series of systematic computational experiments that λNN generally orders the dynamical behaviors of randomly connected/weighted recurrent neural networks in the same way that λCA does for cellular automata. By extending this ordering to larger values of λNN than has typically been done with λCA and cellular automata, we find that a second edge-of-chaos region exists on the opposite side of the chaotic region. These basic results are found to hold under different assumptions about network connectivity, but vary substantially in their details. The results show that the basic concept underlying the lambda parameter can usefully be extended to other types of complex dynamical systems than just cellular automata.

  9. Structured chaos in a devil's staircase of the Josephson junction

    SciTech Connect

    Shukrinov, Yu. M.; Botha, A. E.; Medvedeva, S. Yu.; Kolahchi, M. R.; Irie, A.

    2014-09-01

    The phase dynamics of Josephson junctions (JJs) under external electromagnetic radiation is studied through numerical simulations. Current-voltage characteristics, Lyapunov exponents, and Poincaré sections are analyzed in detail. It is found that the subharmonic Shapiro steps at certain parameters are separated by structured chaotic windows. By performing a linear regression on the linear part of the data, a fractal dimension of D = 0.868 is obtained, with an uncertainty of ±0.012. The chaotic regions exhibit scaling similarity, and it is shown that the devil's staircase of the system can form a backbone that unifies and explains the highly correlated and structured chaotic behavior. These features suggest a system possessing multiple complete devil's staircases. The onset of chaos for subharmonic steps occurs through the Feigenbaum period doubling scenario. Universality in the sequence of periodic windows is also demonstrated. Finally, the influence of the radiation and JJ parameters on the structured chaos is investigated, and it is concluded that the structured chaos is a stable formation over a wide range of parameter values.

  10. Urban chaos and replacement dynamics in nature and society

    NASA Astrophysics Data System (ADS)

    Chen, Yanguang

    2014-11-01

    Replacements resulting from competition are ubiquitous phenomena in both nature and society. The evolution of a self-organized system is always a physical process substituting one type of components for another type of components. A logistic model of replacement dynamics has been proposed in terms of technical innovation and urbanization, but it fails to arouse widespread attention in the academia. This paper is devoted to laying the foundations of general replacement principle by using analogy and induction. The empirical base of this study is urban replacement, including urbanization and urban growth. The sigmoid functions can be employed to model various processes of replacement. Many mathematical methods such as allometric scaling and head/tail breaks can be applied to analyzing the processes and patterns of replacement. Among varied sigmoid functions, the logistic function is the basic and the simplest model of replacement dynamics. A new finding is that replacement can be associated with chaos in a nonlinear system, e.g., urban chaos is just a part of replacement dynamics. The aim of developing replacement theory is at understanding complex interaction and conversion. This theory provides a new way of looking at urbanization, technological innovation and diffusion, Volterra-Lotka’s predator-prey interaction, man-land relation, and dynastic changes resulting from peasant uprising, and all that. Especially, the periodic oscillations and chaos of replacement dynamics can be used to explain and predict the catastrophic occurrences in the physical and human systems.

  11. Chaos, creativity, and substance abuse: the nonlinear dynamics of choice.

    PubMed

    Zausner, Tobi

    2011-04-01

    Artists create their work in conditions of disequilibrium, states of creative chaos that may appear turbulent but are capable of bringing forth new order. By absorbing information from the environment and discharging it negentropically as new work, artists can be modeled as dissipative systems. A characteristic of chaotic systems is a heightened sensitivity to stimuli, which can generate either positive experiences or negative ones that can lead some artists to substance abuse and misguided searches for a creative chaos. Alcohol and drug use along with inadequately addressed co-occurring emotional disorders interfere with artists' quest for the nonlinearity of creativity. Instead, metaphorically modeled by a limit cycle of addiction and then a spiral to disorder, the joys of a creative chaos become an elusive chimera for them rather than a fulfilling experience. Untreated mental illness and addiction to substances have shortened the lives of artists such as Vincent Van Gogh, Frida Kahlo, Henri de Toulouse-Lautrec, and Jackson Pollock, all of whom committed suicide. In contrast Edvard Munch and John Callahan, who chose to address their emotional problems and substance abuse, continued to live and remain creative. Choosing to access previously avoided moments of pain can activate the nonlinear power of self-transformation.

  12. Understanding of Arab Spring with Chaos Theory - Uprising or Revolution

    NASA Astrophysics Data System (ADS)

    Açıkalın, Şuay Nilhan; Bölücek, Cemal Alpgiray

    `Arab Spring' can be considered as one of the most remarkable events in the history of world politics. On December 18, 2010, a Tunisian young protestor burned himself in a public square of the city. This event triggered probably one of the most chaotic and long term uprisings in the Middle East. From the day of its initiation until the present, `Arab Spring' in the Middle East created unstable political situation and several uprisings. In this chapter, we will first give general information about chaos theory, and then we will examine the `butterfly effect' created by the Tunisian young protestor and process of Arab Spring in the Middle East regarding its extend and form in those countries within the framework of chaos theory. For the first part of this chapter, the spark created by the Tunisian young protestor and its effects can be analyzed under `butterfly effect' perspective within chaos theory, arguing whether the events followed each other consecutively or randomly. The question is whether the incidents following each other have reasonable links of causality to one another, or the events defining the phenomena known as `Arab Spring' have no predictable reasons and outcomes regardless of the regional, social and political differences. The events caused the collapse of the regimes in Tunisia, Egypt and Libya; they had very serious outcomes.

  13. Structured chaos in a devil's staircase of the Josephson junction

    NASA Astrophysics Data System (ADS)

    Shukrinov, Yu. M.; Botha, A. E.; Medvedeva, S. Yu.; Kolahchi, M. R.; Irie, A.

    2014-09-01

    The phase dynamics of Josephson junctions (JJs) under external electromagnetic radiation is studied through numerical simulations. Current-voltage characteristics, Lyapunov exponents, and Poincaré sections are analyzed in detail. It is found that the subharmonic Shapiro steps at certain parameters are separated by structured chaotic windows. By performing a linear regression on the linear part of the data, a fractal dimension of D = 0.868 is obtained, with an uncertainty of ±0.012. The chaotic regions exhibit scaling similarity, and it is shown that the devil's staircase of the system can form a backbone that unifies and explains the highly correlated and structured chaotic behavior. These features suggest a system possessing multiple complete devil's staircases. The onset of chaos for subharmonic steps occurs through the Feigenbaum period doubling scenario. Universality in the sequence of periodic windows is also demonstrated. Finally, the influence of the radiation and JJ parameters on the structured chaos is investigated, and it is concluded that the structured chaos is a stable formation over a wide range of parameter values.

  14. Structured chaos in a devil's staircase of the Josephson junction.

    PubMed

    Shukrinov, Yu M; Botha, A E; Medvedeva, S Yu; Kolahchi, M R; Irie, A

    2014-09-01

    The phase dynamics of Josephson junctions (JJs) under external electromagnetic radiation is studied through numerical simulations. Current-voltage characteristics, Lyapunov exponents, and Poincaré sections are analyzed in detail. It is found that the subharmonic Shapiro steps at certain parameters are separated by structured chaotic windows. By performing a linear regression on the linear part of the data, a fractal dimension of D = 0.868 is obtained, with an uncertainty of ±0.012. The chaotic regions exhibit scaling similarity, and it is shown that the devil's staircase of the system can form a backbone that unifies and explains the highly correlated and structured chaotic behavior. These features suggest a system possessing multiple complete devil's staircases. The onset of chaos for subharmonic steps occurs through the Feigenbaum period doubling scenario. Universality in the sequence of periodic windows is also demonstrated. Finally, the influence of the radiation and JJ parameters on the structured chaos is investigated, and it is concluded that the structured chaos is a stable formation over a wide range of parameter values.

  15. Anderson Localization in Quantum Chaos: Scaling and Universality

    NASA Astrophysics Data System (ADS)

    García-García, A. M.; Wang, J.

    2007-10-01

    The one-parameter scaling theory is a powerful tool to investigate Anderson localization effects in disordered systems. In this paper we show that this theory can be adapted to the context of quantum chaos provided that the classical phase space is homogeneous, not mixed. The localization problem in this case is defined in momentum, not in real space. We then employ the one-parameter scaling theory to: (a) propose a precise characterization of the type of classical dynamics related to the Wigner-Dyson and Poisson statistics which also predicts in which situations Anderson localization corrections invalidate the relation between classical chaos and random matrix theory encoded in the Bohigas-Giannoni-Schmit conjecture, (b) to identify the universality class associated with the metal-insulator transition in quantum chaos. In low dimensions it is characterized by classical superdiffusion, in higher dimensions it has in general a quantum origin as in the case of disordered systems. We illustrate these two cases by studying 1d kicked rotors with non-analytical potentials and a 3d kicked rotor with a smooth potential.

  16. A period-doubling cascade precedes chaos for planar maps

    NASA Astrophysics Data System (ADS)

    Sander, Evelyn; Yorke, James A.

    2013-09-01

    A period-doubling cascade is often seen in numerical studies of those smooth (one-parameter families of) maps for which as the parameter is varied, the map transitions from one without chaos to one with chaos. Our emphasis in this paper is on establishing the existence of such a cascade for many maps with phase space dimension 2. We use continuation methods to show the following: under certain general assumptions, if at one parameter there are only finitely many periodic orbits, and at another parameter value there is chaos, then between those two parameter values there must be a cascade. We investigate only families that are generic in the sense that all periodic orbit bifurcations are generic. Our method of proof in showing there is one cascade is to show there must be infinitely many cascades. We discuss in detail two-dimensional families like those which arise as a time-2π maps for the Duffing equation and the forced damped pendulum equation.

  17. Microstate description of stable chaos in networks of spiking neurons

    NASA Astrophysics Data System (ADS)

    Puelma Touzel, Maximilian; Michael, Monteforte; Wolf, Fred

    2014-03-01

    Dynamic instabilities have been proposed to explain the decorrelation of stimulus-driven activity observed in sensory areas such as the olfactory bulb, but are sensitive to noise. Simple neuron models coupled through inhibition can nevertheless exhibit a negative maximum Lyapunov exponent, despite displaying irregular and asynchronous (AI) activity and having an exponential instability to finite-sized perturbations above a critical strength that scales with the size, density and activity of the circuit. This stable chaos, a phenomenon first found in coupled-map lattices, produces a large, finite set of locally-attracting, yet mutually-repelling AI spike sequences ideally suited for discrete, high-dimensional coding. We analyze the effects of finite-sized perturbations on the spiking microstate and reveal the mechanism underlying the stable chaos. From this, we can analytically derive the aforementioned scaling relations and estimate the critical value of previously observed transitions to conventional chaos. This work highlights the features of intra-neuron dynamics and inter-neuron coupling that generate this phase space structure, which might serve as an attractor reservoir that downstream networks can use to decode sensory input.

  18. 76 FR 64083 - Reliability Technical Conference; Notice of Technical Conference

    Federal Register 2010, 2011, 2012, 2013, 2014

    2011-10-17

    ... From the Federal Register Online via the Government Publishing Office DEPARTMENT OF ENERGY Federal Energy Regulatory Commission Reliability Technical Conference; Notice of Technical Conference Take notice that the Federal Energy Regulatory Commission will hold a Technical Conference on Tuesday, November...

  19. District Leadership Conference Planner.

    ERIC Educational Resources Information Center

    Washington State Coordinating Council for Occupational Education, Olympia.

    This manual provides usable guidelines and planning forms and materials for planning district leadership conferences, which were designed and initiated in Washington State to meet the problems in student enrollment and, consequently, Distributive Education Clubs of America membership. The conferences have become a useful means to increase…

  20. [Conference Time Kit.

    ERIC Educational Resources Information Center

    National School Public Relations Association, Washington, DC.

    This multimedia kit, for use with and by teachers from kindergarten through the upper elementary grades, consists of four components: 1) a filmstrip for teachers; 2) the 1970 edition of a handbook, "Conference Time for Teachers and Parents"; 3) a filmstrip for parents; 4) a supporting parent information leaflet "How To Confer Successfully with…