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Sample records for deterministic chaos mathematics

  1. Multi-Strain Deterministic Chaos in Dengue Epidemiology, A Challenge for Computational Mathematics

    NASA Astrophysics Data System (ADS)

    Aguiar, Maíra; Kooi, Bob W.; Stollenwerk, Nico

    2009-09-01

    Recently, we have analysed epidemiological models of competing strains of pathogens and hence differences in transmission for first versus secondary infection due to interaction of the strains with previously aquired immunities, as has been described for dengue fever, known as antibody dependent enhancement (ADE). These models show a rich variety of dynamics through bifurcations up to deterministic chaos. Including temporary cross-immunity even enlarges the parameter range of such chaotic attractors, and also gives rise to various coexisting attractors, which are difficult to identify by standard numerical bifurcation programs using continuation methods. A combination of techniques, including classical bifurcation plots and Lyapunov exponent spectra has to be applied in comparison to get further insight into such dynamical structures. Especially, Lyapunov spectra, which quantify the predictability horizon in the epidemiological system, are computationally very demanding. We show ways to speed up computations of such Lyapunov spectra by a factor of more than ten by parallelizing previously used sequential C programs. Such fast computations of Lyapunov spectra will be especially of use in future investigations of seasonally forced versions of the present models, as they are needed for data analysis.

  2. 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.

  3. Are earthquakes an example of deterministic chaos?

    NASA Technical Reports Server (NTRS)

    Huang, Jie; Turcotte, Donald L.

    1990-01-01

    A simple mass-spring model is used to systematically examine the dynamical behavior introduced by fault zone heterogeneities. The model consists of two sliding blocks coupled to each other and to a constant velocity driver by elastic springs. The state of this system can be characterized by the positions of the two blocks relative to the driver. A simple static/dynamic friction law is used. When the system is symmetric, cyclic behavior is observed. For an asymmetric system, where the frictional forces for the two blocks are not equal, the solutions exhibit deterministic chaos. Chaotic windows occur repeatedly between regions of limit cycles on bifurcation diagrams. The model behavior is similar to that of the one-dimensional logistic map. The results provide substantial evidence that earthquakes are an example of deterministic chaos.

  4. Application of deterministic chaos analysis to investigating CFB hydrodynamics

    SciTech Connect

    Yin, C.; Luo, Z.; Li, X.; Fang, M.; Ni, M.; Cen, K.

    1997-12-31

    This paper presents an application of deterministic chaos analysis to the behavior of a gas-solid circulating fluidized bed (CFB). Two improvements for the traditional algorithm are put forward: a rule and the mathematical model are present to determine the no-scale interval, and an improved formula and the corresponding recurrence formula are given to calculate distance. Calculation results for different operating conditions indicate that the correlation dimension and Kolmogorov entropy can be employed to characterize fluidization regimes and their transitions, and may be used to detect abnormal conditions in CFB.

  5. Deterministic Chaos and Fractal Complexity in the Dynamics of Cardiovascular Behavior: Perspectives on a New Frontier

    PubMed Central

    Sharma, Vijay

    2009-01-01

    Physiological systems such as the cardiovascular system are capable of five kinds of behavior: equilibrium, periodicity, quasi-periodicity, deterministic chaos and random behavior. Systems adopt one or more these behaviors depending on the function they have evolved to perform. The emerging mathematical concepts of fractal mathematics and chaos theory are extending our ability to study physiological behavior. Fractal geometry is observed in the physical structure of pathways, networks and macroscopic structures such the vasculature and the His-Purkinje network of the heart. Fractal structure is also observed in processes in time, such as heart rate variability. Chaos theory describes the underlying dynamics of the system, and chaotic behavior is also observed at many levels, from effector molecules in the cell to heart function and blood pressure. This review discusses the role of fractal structure and chaos in the cardiovascular system at the level of the heart and blood vessels, and at the cellular level. Key functional consequences of these phenomena are highlighted, and a perspective provided on the possible evolutionary origins of chaotic behavior and fractal structure. The discussion is non-mathematical with an emphasis on the key underlying concepts. PMID:19812706

  6. Experimental evidence for deterministic chaos in thermal pulse combustion

    SciTech Connect

    Daw, C.S.; Thomas, J.F.; Richards, G.A.; Narayanaswami, L.L.

    1994-12-31

    Given the existence of chaotic oscillations in reacting chemical systems, it is reasonable to ask whether or not similar phenomena can occur in combustion. In this paper, the authors present experimental evidence that kinetically driven chaos occurs in a highly simplified thermal pulse combustor. The combustor is a well-stirred reactor with a tailpipe extending from one end. Fuel and air are injected into the combustion chamber through orifices in the end opposite the tailpipe. Propane with the fuel used in all cases. From the experimental data analyses, it is clear that deterministic chaos is an important factor in thermal pulse combustor dynamics. While the authors have only observed such behavior in this particular type combustor to date, they infer from their understanding of the origins of the chaos that it is likely to exist in other pulse combustors and even nonpulsing combustion. They speculate that realization of the importance of chaos in affecting flame stability could lead to significant changes in combustor design and control.

  7. Predictability of normal heart rhythms and deterministic chaos

    NASA Astrophysics Data System (ADS)

    Lefebvre, J. H.; Goodings, D. A.; Kamath, M. V.; Fallen, E. L.

    1993-04-01

    The evidence for deterministic chaos in normal heart rhythms is examined. Electrocardiograms were recorded of 29 subjects falling into four groups—a young healthy group, an older healthy group, and two groups of patients who had recently suffered an acute myocardial infarction. From the measured R-R intervals, a time series of 1000 first differences was constructed for each subject. The correlation integral of Grassberger and Procaccia was calculated for several subjects using these relatively short time series. No evidence was found for the existence of an attractor having a dimension less than about 4. However, a prediction method recently proposed by Sugihara and May and an autoregressive linear predictor both show that there is a measure of short-term predictability in the differenced R-R intervals. Further analysis revealed that the short-term predictability calculated by the Sugihara-May method is not consistent with the null hypothesis of a Gaussian random process. The evidence for a small amount of nonlinear dynamical behavior together with the short-term predictability suggest that there is an element of deterministic chaos in normal heart rhythms, although it is not strong or persistent. Finally, two useful parameters of the predictability curves are identified, namely, the `first step predictability' and the `predictability decay rate,' neither of which appears to be significantly correlated with the standard deviation of the R-R intervals.

  8. A three-variable model of deterministic chaos in the Belousov-Zhabotinsky reaction

    NASA Astrophysics Data System (ADS)

    Györgyi, László; Field, Richard J.

    1992-02-01

    CHAOS is exhibited by a wide variety of systems governed by nonlinear dynamic laws1-3. Its most striking feature is an apparent randomness which seems to contradict its deterministic origin. The best-studied chaotic chemical system is the Belousov-Zhabotinsky (BZ) reaction4-6 in a continuous-flow stirred-tank reactor (CSTR). Here we present a simple mechanism for the BZ reaction which allows us to develop a description in terms of a set of differential equations containing only three variables, the minimum number required to generate chaos in a continuous (non-iterative) dynamical system2. In common with experiments, our model shows aperiodicity and transitions between periodicity and chaos near bifurcations between oscillatory and steady-state behaviour, which occur at both low and high CSTR flow rates. While remaining closely related to a real chaotic chemical system, our model is sufficiently simple to allow detailed mathematical analysis. It also reproduces many other features of the BZ reaction better than does the simple Oregonator7 (which cannot produce chaos).

  9. Deterministic Chaos in the X-ray Sources

    NASA Astrophysics Data System (ADS)

    Grzedzielski, M.; Sukova, P.; Janiuk, A.

    2015-12-01

    Hardly any of the observed black hole accretion disks in X-ray binaries and active galaxies shows constant flux. When the local stochastic variations of the disk occur at specific regions where a resonant behaviour takes place, there appear the quasi-periodic oscillations (QPOs). If the global structure of the flow and its non-linear hydrodynamics affects the fluctuations, the variability is chaotic in the sense of deterministic chaos. Our aim is to solve a problem of the stochastic versus deterministic nature of the black hole binary variabilities. We use both observational and analytic methods. We use the recurrence analysis and we study the occurence of long diagonal lines in the recurrence plot of observed data series and compare it to the surrogate series. We analyze here the data of two X-ray binaries - XTE J1550-564 and GX 339-4 observed by Rossi X-ray Timing Explorer. In these sources, the non-linear variability is expected because of the global conditions (such as the mean accretion rate) leading to the possible instability of an accretion disk. The thermal-viscous instability and fluctuations around the fixed-point solution occurs at high accretion rate, when the radiation pressure gives dominant contribution to the stress tensor.

  10. Deterministic Chaos in Open Well-stirred Bray-Liebhafsky Reaction System

    NASA Astrophysics Data System (ADS)

    Kolar-Anić, Ljiljana; Vukojević, Vladana; Pejić, Nataša; Grozdić, Tomislav; Anić, Slobodan

    2004-12-01

    Dynamics of the Bray-Liebhafsky (BL) oscillatory reaction is analyzed in a Continuously-fed well-Stirred Thank Reactor (CSTR). Deterministic chaos is found under different conditions, when temperature and acidity are chosen as control parameters. Dynamic patterns observed in real experiments are also numerically simulated.

  11. Topological characterization of deterministic chaos: enforcing orientation preservation.

    PubMed

    Lefranc, Marc; Morant, Pierre-Emmanuel; Nizette, Michel

    2008-02-28

    The determinism principle, which states that dynamical state completely determines future time evolution, is a keystone of nonlinear dynamics and chaos theory. Since it precludes that two state space trajectories intersect, it is a core ingredient of a topological analysis of chaos based on a knot-theoretic characterization of unstable periodic orbits embedded in a strange attractor. However, knot theory can be applied only to three-dimensional systems. Still, determinism applies in any dimension. We propose an alternative framework in which this principle is enforced by constructing an orientation-preserving dynamics on triangulated surfaces and find that in three dimensions our approach numerically predicts the correct topological entropies for periodic orbits of the horseshoe map. PMID:17698472

  12. 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.

  13. A Unit on Deterministic Chaos for Student Teachers

    ERIC Educational Resources Information Center

    Stavrou, D.; Assimopoulos, S.; Skordoulis, C.

    2013-01-01

    A unit aiming to introduce pre-service teachers of primary education to the limited predictability of deterministic chaotic systems is presented. The unit is based on a commercial chaotic pendulum system connected with a data acquisition interface. The capabilities and difficulties in understanding the notion of limited predictability of 18…

  14. The deterministic chaos and random noise in turbulent jet

    SciTech Connect

    Yao, Tian-Liang; Liu, Hai-Feng Xu, Jian-Liang; Li, Wei-Feng

    2014-06-01

    A turbulent flow is usually treated as a superposition of coherent structure and incoherent turbulence. In this paper, the largest Lyapunov exponent and the random noise in the near field of round jet and plane jet are estimated with our previously proposed method of chaotic time series analysis [T. L. Yao, et al., Chaos 22, 033102 (2012)]. The results show that the largest Lyapunov exponents of the round jet and plane jet are in direct proportion to the reciprocal of the integral time scale of turbulence, which is in accordance with the results of the dimensional analysis, and the proportionality coefficients are equal. In addition, the random noise of the round jet and plane jet has the same linear relation with the Kolmogorov velocity scale of turbulence. As a result, the random noise may well be from the incoherent disturbance in turbulence, and the coherent structure in turbulence may well follow the rule of chaotic motion.

  15. The Claude Bernard Lecture, 1989 - Deterministic chaos: The science and the fiction

    NASA Astrophysics Data System (ADS)

    Ruelle, D.

    1990-02-01

    A general review of the ideas of chaos is presented. Particular attention is given to the problem of finding out whether or not various time evolutions observed in nature correspond to low-dimensional deterministic dynamics. The 'dimensions' of the order 6 that are obtained are found to be very close to the upper bound 2log(10)N permitted by the Grassberger-Procaccia algorithm (1983).

  16. 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.

  17. Maxwell Demon Dynamics: Deterministic Chaos, the Szilard Map, and the Intelligence of Thermodynamic Systems.

    PubMed

    Boyd, Alexander B; Crutchfield, James P

    2016-05-13

    We introduce a deterministic chaotic system-the Szilard map-that encapsulates the measurement, control, and erasure protocol by which Maxwellian demons extract work from a heat reservoir. Implementing the demon's control function in a dynamical embodiment, our construction symmetrizes the demon and the thermodynamic system, allowing one to explore their functionality and recover the fundamental trade-off between the thermodynamic costs of dissipation due to measurement and those due to erasure. The map's degree of chaos-captured by the Kolmogorov-Sinai entropy-is the rate of energy extraction from the heat bath. Moreover, an engine's statistical complexity quantifies the minimum necessary system memory for it to function. In this way, dynamical instability in the control protocol plays an essential and constructive role in intelligent thermodynamic systems. PMID:27232011

  18. Nonlinear Time Series Analysis of Nodulation Factor Induced Calcium Oscillations: Evidence for Deterministic Chaos?

    PubMed Central

    Hazledine, Saul; Sun, Jongho; Wysham, Derin; Downie, J. Allan; Oldroyd, Giles E. D.; Morris, Richard J.

    2009-01-01

    Legume plants form beneficial symbiotic interactions with nitrogen fixing bacteria (called rhizobia), with the rhizobia being accommodated in unique structures on the roots of the host plant. The legume/rhizobial symbiosis is responsible for a significant proportion of the global biologically available nitrogen. The initiation of this symbiosis is governed by a characteristic calcium oscillation within the plant root hair cells and this signal is activated by the rhizobia. Recent analyses on calcium time series data have suggested that stochastic effects have a large role to play in defining the nature of the oscillations. The use of multiple nonlinear time series techniques, however, suggests an alternative interpretation, namely deterministic chaos. We provide an extensive, nonlinear time series analysis on the nature of this calcium oscillation response. We build up evidence through a series of techniques that test for determinism, quantify linear and nonlinear components, and measure the local divergence of the system. Chaos is common in nature and it seems plausible that properties of chaotic dynamics might be exploited by biological systems to control processes within the cell. Systems possessing chaotic control mechanisms are more robust in the sense that the enhanced flexibility allows more rapid response to environmental changes with less energetic costs. The desired behaviour could be most efficiently targeted in this manner, supporting some intriguing speculations about nonlinear mechanisms in biological signaling. PMID:19675679

  19. Deterministic Chaos: Proposal of an Informal Educational Activity Aimed at High School Students

    ERIC Educational Resources Information Center

    Greco, Valeria; Spagnolo, Salvatore

    2016-01-01

    Chaos theory is not present in the Italian school curricula and textbooks in spite of being present in many topics of classical physics and in everyday life. Chaotic dynamics, in fact, are involved in phenomena easily accessible to everyone or in events experienced by most people in their lives (the dripping of a faucet which keeps people awoken…

  20. Neural nets with terminal chaos for simulation of non-deterministic patterns

    NASA Technical Reports Server (NTRS)

    Zak, Michail

    1993-01-01

    Models for simulating some aspects of neural intelligence are presented and discussed. Special attention is given to terminal neurodynamics as a particular architecture of terminal dynamics suitable for modeling information flows. Applications of terminal chaos to information fusion as well as to planning and modeling coordination among neurons in biological systems are disussed.

  1. Sensitivity analysis in a Lassa fever deterministic mathematical model

    NASA Astrophysics Data System (ADS)

    Abdullahi, Mohammed Baba; Doko, Umar Chado; Mamuda, Mamman

    2015-05-01

    Lassa virus that causes the Lassa fever is on the list of potential bio-weapons agents. It was recently imported into Germany, the Netherlands, the United Kingdom and the United States as a consequence of the rapid growth of international traffic. A model with five mutually exclusive compartments related to Lassa fever is presented and the basic reproduction number analyzed. A sensitivity analysis of the deterministic model is performed. This is done in order to determine the relative importance of the model parameters to the disease transmission. The result of the sensitivity analysis shows that the most sensitive parameter is the human immigration, followed by human recovery rate, then person to person contact. This suggests that control strategies should target human immigration, effective drugs for treatment and education to reduced person to person contact.

  2. Evidence for deterministic chaos as the origin of electrical tree breakdown structures in polymeric insulation

    NASA Astrophysics Data System (ADS)

    Dodd, S. J.; Dissado, L. A.; Champion, J. V.; Alison, J. M.

    1995-12-01

    Electrical discharges were measured during the propagation stage of electrical tree breakdown in an epoxy resin. An analysis of their number sequence provides strong evidence for the existence of an underlying deterministic chaotic mechanism. The fractal dimension of the tree and that of the reconstructed attractor and Lyapunov exponent were found to be related. The higher fractal dimension tree (dt~1.9) is associated with an attractor dimension df~3.1 and Lyapunov exponent λ~0.008 bit/s. The lower fractal dimension tree (dt~1.5) is associated with values of df~3.56 and λ~0.028 bit/s. No evidence for the presence of random stochastic processes, an essential ingredient of the dielectric breakdown model, has been found.

  3. Maxwell Demon Dynamics: Deterministic Chaos, the Szilard Map, and the Intelligence of Thermodynamic Systems

    NASA Astrophysics Data System (ADS)

    Boyd, Alexander B.; Crutchfield, James P.

    2016-05-01

    We introduce a deterministic chaotic system—the Szilard map—that encapsulates the measurement, control, and erasure protocol by which Maxwellian demons extract work from a heat reservoir. Implementing the demon's control function in a dynamical embodiment, our construction symmetrizes the demon and the thermodynamic system, allowing one to explore their functionality and recover the fundamental trade-off between the thermodynamic costs of dissipation due to measurement and those due to erasure. The map's degree of chaos—captured by the Kolmogorov-Sinai entropy—is the rate of energy extraction from the heat bath. Moreover, an engine's statistical complexity quantifies the minimum necessary system memory for it to function. In this way, dynamical instability in the control protocol plays an essential and constructive role in intelligent thermodynamic systems.

  4. Fascination of chaos

    NASA Astrophysics Data System (ADS)

    Loskutov, Alexander

    2010-12-01

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

  5. 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.

  6. 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

  7. Heart pathology determination from electrocardiogram signals by application of deterministic chaos mathematics. CRADA final report

    SciTech Connect

    Clapp, N.E.; Hively, L.M.; Stickney, R.E.

    1999-03-01

    It is well known that the electrical signals generated by the heart exhibit nonlinear, chaotic dynamics. A number of heart pathologies alter heartbeat dynamics and/or the electrical properties of the heart, which, in turn, alter electrocardiogram signals. Electrocardiogram techniques in common use for diagnosing pathologies have limited sensitivity and specificity. This leads to a relatively high misdiagnosis rate for ventricular fibrillation. It is also known that the linear analysis tools utilized (such as fast Fourier transforms and linear statistics) are limited in their ability to find subtle changes or characteristic signatures in nonlinear chaotic electrocardiogram signals. In contrast, the authors` research indicates that chaotic time-series analysis tools that they have developed allow quantification of the nonlinear nature of dynamic systems in the form of nonlinear statistics, and also enable characteristic signatures to be identified. The goal of this project is to modify these tools to increase and enhance the medically useful information obtained from electrocardiogram signals through the application of chaotic time series analysis tools. In the one year of the project, the tools have been extended to enhance the capabilities for detecting ventricular fibrillation. Chaotic time-series analysis provides a means to increase sensitivity in detecting general heart dynamics. Oak Ridge National Laboratory specialists have worked with Physio-Control and their medical collaborators to extend the capabilities of state-of-the-art electrocardiogram systems and interpretation of results.

  8. 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)

  9. Application of deterministic chaos theory to local instantaneous temperature, pressure, and heat transfer coefficients in a gas fluidized bed

    SciTech Connect

    Karamavruc, A.I.; Clark, N.N.

    1996-09-01

    A stainless steel heat transfer tube, carrying a hot water flow, was placed in a cold bubbling fluidized bed. The tube was instrumented in the circumferential direction with five fast-responding surface thermocouples and a vertical pressure differential sensor. The local temperature and pressure data were measured simultaneously at a frequency of 120 Hz. Additionally, the local instantaneous heat transfer coefficient was evaluated by solving the transient two-dimensional heat conduction equation across the tube wall numerically. The mutual information function (MIF) has been applied to the signals to observe the relationship between points separated in time. MIF was also used to provide the most appropriate time delay constant {tau} to reconstruct an m-dimensional phase portrait of the one-dimensional time series. The distinct variation of MIF around the tube indicates the variations of solid-surface contact in the circumferential direction. The correlation coefficient was evaluated to calculate the correlation exponent {nu}, which is closely related to the fractal dimension. The correlation exponent is a measure of the strange attractor. The minimum embedding dimension as well as the degrees of freedom of the system were evaluated via the correlation coefficient. Kolmogorov entropies of the signals were approximated by using the correlation coefficient. Kolmogorov entropy considers the inherent multi-dimensional nature of chaotic data. A positive estimation of Kolmogorov entropy is an indication of the chaotic nature of the signal. The Kolmogorov entropies of the temperature data around the tube were found to be between 10 bits/s and 24 bits/s. A comparison between the signals has shown that the local instantaneous heat transfer coefficient exhibits a higher degree of chaos than the local temperature and pressure signals.

  10. 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...

  11. 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.

  12. Boolean chaos

    NASA Astrophysics Data System (ADS)

    Zhang, Rui; de S. Cavalcante, Hugo L. D.; Gao, Zheng; Gauthier, Daniel J.; Socolar, Joshua E. S.; Adams, Matthew M.; Lathrop, Daniel P.

    2009-10-01

    We observe deterministic chaos in a simple network of electronic logic gates that are not regulated by a clocking signal. The resulting power spectrum is ultrawide band, extending from dc to beyond 2 GHz. The observed behavior is reproduced qualitatively using an autonomously updating Boolean model with signal propagation times that depend on the recent history of the gates and filtering of pulses of short duration, whose presence is confirmed experimentally. Electronic Boolean chaos may find application as an ultrawide-band source of radio waves.

  13. 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

  14. 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

  15. 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)

  16. Teaching Deterministic Chaos through Music.

    ERIC Educational Resources Information Center

    Chacon, R.; And Others

    1992-01-01

    Presents music education as a setting for teaching nonlinear dynamics and chaotic behavior connected with fixed-point and limit-cycle attractors. The aim is not music composition but a first approach to an interdisciplinary tool suitable for a single-session class, at either the secondary or undergraduate level, for the introduction of these…

  17. Children’s looking preference for biological motion may be related to an affinity for mathematical chaos

    PubMed Central

    Haworth, Joshua L.; Kyvelidou, Anastasia; Fisher, Wayne; Stergiou, Nicholas

    2015-01-01

    Recognition of biological motion is pervasive in early child development. Further, viewing the movement behavior of others is a primary component of a child’s acquisition of complex, robust movement repertoires, through imitation and real-time coordinated action. We theorize that inherent to biological movements are particular qualities of mathematical chaos and complexity. We further posit that this character affords the rich and complex inter-dynamics throughout early motor development. Specifically, we explored whether children’s preference for biological motion may be related to an affinity for mathematical chaos. Cross recurrence quantification analysis (cRQA) was used to investigate the coordination of gaze and posture with various temporal structures (periodic, chaotic, and aperiodic) of the motion of an oscillating visual stimulus. Children appear to competently perceive and respond to chaotic motion, both in rate (cRQA-percent determinism) and duration (cRQA-maxline) of coordination. We interpret this to indicate that children not only recognize chaotic motion structures, but also have a preference for coordination with them. Further, stratification of our sample (by age) uncovers the suggestion that this preference may become refined with age. PMID:25852600

  18. Introduction to the focus issue: Fifty years of chaos: Applied and theoretical

    NASA Astrophysics Data System (ADS)

    Hikihara, Takashi; Holmes, Philip; Kambe, Tsutomu; Rega, Giuseppe

    2012-12-01

    The discovery of deterministic chaos in the late nineteenth century, its subsequent study, and the development of mathematical and computational methods for its analysis have substantially influenced the sciences. Chaos is, however, only one phenomenon in the larger area of dynamical systems theory. This Focus Issue collects 13 papers, from authors and research groups representing the mathematical, physical, and biological sciences, that were presented at a symposium held at Kyoto University from November 28 to December 2, 2011. The symposium, sponsored by the International Union of Theoretical and Applied Mechanics, was called 50 Years of Chaos: Applied and Theoretical. Following some historical remarks to provide a background for the last 50 years, and for chaos, this Introduction surveys the papers and identifies some common themes that appear in them and in the theory of dynamical systems.

  19. Chaos, dynamical structure and climate variability

    SciTech Connect

    Stewart, H.B.

    1995-09-01

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

  20. Uncertainty quantification in simulations of epidemics using polynomial chaos.

    PubMed

    Santonja, F; Chen-Charpentier, B

    2012-01-01

    Mathematical models based on ordinary differential equations are a useful tool to study the processes involved in epidemiology. Many models consider that the parameters are deterministic variables. But in practice, the transmission parameters present large variability and it is not possible to determine them exactly, and it is necessary to introduce randomness. In this paper, we present an application of the polynomial chaos approach to epidemiological mathematical models based on ordinary differential equations with random coefficients. Taking into account the variability of the transmission parameters of the model, this approach allows us to obtain an auxiliary system of differential equations, which is then integrated numerically to obtain the first-and the second-order moments of the output stochastic processes. A sensitivity analysis based on the polynomial chaos approach is also performed to determine which parameters have the greatest influence on the results. As an example, we will apply the approach to an obesity epidemic model. PMID:22927889

  1. 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.

  2. "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…

  3. Deterministic Brownian Motion

    NASA Astrophysics Data System (ADS)

    Trefan, Gyorgy

    1993-01-01

    The goal of this thesis is to contribute to the ambitious program of the foundation of developing statistical physics using chaos. We build a deterministic model of Brownian motion and provide a microscopic derivation of the Fokker-Planck equation. Since the Brownian motion of a particle is the result of the competing processes of diffusion and dissipation, we create a model where both diffusion and dissipation originate from the same deterministic mechanism--the deterministic interaction of that particle with its environment. We show that standard diffusion which is the basis of the Fokker-Planck equation rests on the Central Limit Theorem, and, consequently, on the possibility of deriving it from a deterministic process with a quickly decaying correlation function. The sensitive dependence on initial conditions, one of the defining properties of chaos insures this rapid decay. We carefully address the problem of deriving dissipation from the interaction of a particle with a fully deterministic nonlinear bath, that we term the booster. We show that the solution of this problem essentially rests on the linear response of a booster to an external perturbation. This raises a long-standing problem concerned with Kubo's Linear Response Theory and the strong criticism against it by van Kampen. Kubo's theory is based on a perturbation treatment of the Liouville equation, which, in turn, is expected to be totally equivalent to a first-order perturbation treatment of single trajectories. Since the boosters are chaotic, and chaos is essential to generate diffusion, the single trajectories are highly unstable and do not respond linearly to weak external perturbation. We adopt chaotic maps as boosters of a Brownian particle, and therefore address the problem of the response of a chaotic booster to an external perturbation. We notice that a fully chaotic map is characterized by an invariant measure which is a continuous function of the control parameters of the map

  4. 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…

  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. 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

  7. 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.

  8. Chaos without nonlinear dynamics.

    PubMed

    Corron, Ned J; Hayes, Scott T; Pethel, Shawn D; Blakely, Jonathan N

    2006-07-14

    A linear, second-order filter driven by randomly polarized pulses is shown to generate a waveform that is chaotic under time reversal. That is, the filter output exhibits determinism and a positive Lyapunov exponent when viewed backward in time. The filter is demonstrated experimentally using a passive electronic circuit, and the resulting waveform exhibits a Lorenz-like butterfly structure. This phenomenon suggests that chaos may be connected to physical theories whose underlying framework is not that of a traditional deterministic nonlinear dynamical system. PMID:16907450

  9. 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…

  10. 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.…

  11. Titration of chaos with added noise

    PubMed Central

    Poon, Chi-Sang; Barahona, Mauricio

    2001-01-01

    Deterministic chaos has been implicated in numerous natural and man-made complex phenomena ranging from quantum to astronomical scales and in disciplines as diverse as meteorology, physiology, ecology, and economics. However, the lack of a definitive test of chaos vs. random noise in experimental time series has led to considerable controversy in many fields. Here we propose a numerical titration procedure as a simple “litmus test” for highly sensitive, specific, and robust detection of chaos in short noisy data without the need for intensive surrogate data testing. We show that the controlled addition of white or colored noise to a signal with a preexisting noise floor results in a titration index that: (i) faithfully tracks the onset of deterministic chaos in all standard bifurcation routes to chaos; and (ii) gives a relative measure of chaos intensity. Such reliable detection and quantification of chaos under severe conditions of relatively low signal-to-noise ratio is of great interest, as it may open potential practical ways of identifying, forecasting, and controlling complex behaviors in a wide variety of physical, biomedical, and socioeconomic systems. PMID:11416195

  12. 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

  13. 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.

  14. 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.

  15. Proceedings of the 2nd Experimental Chaos Conference

    NASA Astrophysics Data System (ADS)

    Ditto, William; Pecora, Lou; Shlesinger, Michael; Spano, Mark; Vohra, Sandeep

    1995-02-01

    The Table of Contents for the full book PDF is as follows: * Introduction * Spatiotemporal Phenomena * Experimental Studies of Chaotic Mixing * Using Random Maps in the Analysis of Experimental Fluid Flows * Transition to Spatiotemporal Chaos in a Reaction-Diffusion System * Ion-Dynamical Chaos in Plasmas * Optics * Chaos in a Synchronously Driven Optical Resonator * Chaos, Patterns and Defects in Stimulated Scattering Phenomena * Test of the Normal Form for a Subcritical Bifurcation * Observation of Bifurcations and Chaos in a Driven Fiber Optic Coil * Applications -- Communications * Robustness and Signal Recovery in a Synchronized Chaotic System * Synchronizing Nonautonomous Chaotic Circuits * Synchronization of Pulse-Coupled Chaotic Oscillators * Ocean Transmission Effects on Chaotic Signals * Controlling Symbolic Dynamics for Communication * Applications -- Control * Analysis of Nonlinear Actuators Using Chaotic Waveforms * Controlling Chaos in a Quasiperiodic Electronic System * Control of Chaos in a CO2 Laser * General Research * Video-Based Analysis of Bifurcation Phenomena in Radio-Frequency-Excited Inert Gas Plasmas * Transition from Soliton to Chaotic Motion During the Impact of a Nonlinear Structure * Sonoluminescence in a Single Bubble: Periodic, Quasiperiodic and Chaotic Light Source * Quantum Chaos Experiments Using Microwave Cavities * Experiments on Quantum Chaos With and Without Time Reversibility * When Small Noise Imposed on Deterministic Dynamics Becomes Important * Biology * Chaos Control for Cardiac Arrhythmias * Irregularities in Spike Trains of Cat Retinal Ganglion Cells * Broad-Band Synchronization in Monkey Neocortex * Applicability of Correlation Dimension Calculations to Blood Pressure Signal in Rats * Tests for Deterministic Chaos in Noisy Time Series * The Crayfish Mechanoreceptor Cell: A Biological Example of Stochastic Resonance * Chemistry * Chaos During Heterogeneous Chemical Reactions * Stabilizing and Tracking Unstable Periodic

  16. The Deterministic Information Bottleneck

    NASA Astrophysics Data System (ADS)

    Strouse, D. J.; Schwab, David

    2015-03-01

    A fundamental and ubiquitous task that all organisms face is prediction of the future based on past sensory experience. Since an individual's memory resources are limited and costly, however, there is a tradeoff between memory cost and predictive payoff. The information bottleneck (IB) method (Tishby, Pereira, & Bialek 2000) formulates this tradeoff as a mathematical optimization problem using an information theoretic cost function. IB encourages storing as few bits of past sensory input as possible while selectively preserving the bits that are most predictive of the future. Here we introduce an alternative formulation of the IB method, which we call the deterministic information bottleneck (DIB). First, we argue for an alternative cost function, which better represents the biologically-motivated goal of minimizing required memory resources. Then, we show that this seemingly minor change has the dramatic effect of converting the optimal memory encoder from stochastic to deterministic. Next, we propose an iterative algorithm for solving the DIB problem. Additionally, we compare the IB and DIB methods on a variety of synthetic datasets, and examine the performance of retinal ganglion cell populations relative to the optimal encoding strategy for each problem.

  17. 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)

  18. 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

  19. 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

  20. Chaos in an imperfectly premixed model combustor.

    PubMed

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

    2015-02-01

    This article reports nonlinear bifurcations observed in a laboratory scale, turbulent combustor operating under imperfectly premixed mode with global equivalence ratio as the control parameter. The results indicate that the dynamics of thermoacoustic instability correspond to quasi-periodic bifurcation to low-dimensional, deterministic chaos, a route that is common to a variety of dissipative nonlinear systems. The results support the recent identification of bifurcation scenarios in a laminar premixed flame combustor (Kabiraj et al., Chaos: Interdiscip. J. Nonlinear Sci. 22, 023129 (2012)) and extend the observation to a practically relevant combustor configuration. PMID:25725637

  1. 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.

  2. 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.

  3. The information geometry of chaos

    NASA Astrophysics Data System (ADS)

    Cafaro, Carlo

    2008-10-01

    In this Thesis, we propose a new theoretical information-geometric framework (IGAC, Information Geometrodynamical Approach to Chaos) suitable to characterize chaotic dynamical behavior of arbitrary complex systems. First, the problem being investigated is defined; its motivation and relevance are discussed. The basic tools of information physics and the relevant mathematical tools employed in this work are introduced. The basic aspects of Entropic Dynamics (ED) are reviewed. ED is an information-constrained dynamics developed by Ariel Caticha to investigate the possibility that laws of physics---either classical or quantum---may emerge as macroscopic manifestations of underlying microscopic statistical structures. ED is of primary importance in our IGAC. The notion of chaos in classical and quantum physics is introduced. Special focus is devoted to the conventional Riemannian geometrodynamical approach to chaos (Jacobi geometrodynamics) and to the Zurek-Paz quantum chaos criterion of linear entropy growth. After presenting this background material, we show that the ED formalism is not purely an abstract mathematical framework, but is indeed a general theoretical scheme from which conventional Newtonian dynamics is obtained as a special limiting case. The major elements of our IGAC and the novel notion of information geometrodynamical entropy (IGE) are introduced by studying two "toy models". To illustrate the potential power of our IGAC, one application is presented. An information-geometric analogue of the Zurek-Paz quantum chaos criterion of linear entropy growth is suggested. Finally, concluding remarks emphasizing strengths and weak points of our approach are presented and possible further research directions are addressed. At this stage of its development, IGAC remains an ambitious unifying information-geometric theoretical construct for the study of chaotic dynamics with several unsolved problems. However, based on our recent findings, we believe it already

  4. Traffic chaotic dynamics modeling and analysis of deterministic network

    NASA Astrophysics Data System (ADS)

    Wu, Weiqiang; Huang, Ning; Wu, Zhitao

    2016-07-01

    Network traffic is an important and direct acting factor of network reliability and performance. To understand the behaviors of network traffic, chaotic dynamics models were proposed and helped to analyze nondeterministic network a lot. The previous research thought that the chaotic dynamics behavior was caused by random factors, and the deterministic networks would not exhibit chaotic dynamics behavior because of lacking of random factors. In this paper, we first adopted chaos theory to analyze traffic data collected from a typical deterministic network testbed — avionics full duplex switched Ethernet (AFDX, a typical deterministic network) testbed, and found that the chaotic dynamics behavior also existed in deterministic network. Then in order to explore the chaos generating mechanism, we applied the mean field theory to construct the traffic dynamics equation (TDE) for deterministic network traffic modeling without any network random factors. Through studying the derived TDE, we proposed that chaotic dynamics was one of the nature properties of network traffic, and it also could be looked as the action effect of TDE control parameters. A network simulation was performed and the results verified that the network congestion resulted in the chaotic dynamics for a deterministic network, which was identical with expectation of TDE. Our research will be helpful to analyze the traffic complicated dynamics behavior for deterministic network and contribute to network reliability designing and analysis.

  5. What Can We Learn from Chaos Theory? An Alternative Approach to Instructional Systems Design.

    ERIC Educational Resources Information Center

    You, Yeongmahn

    1993-01-01

    Explains chaos theory; compares a conventional instructional systems design (ISD) approach with chaos theory and dynamic nonlinear systems, including deterministic predictability and indeterministic unpredictability and negative and positive feedback; explores theoretical implications for developing an alternative ISD model; and recommends future…

  6. Chaos and Forecasting - Proceedings of the Royal Society Discussion Meeting

    NASA Astrophysics Data System (ADS)

    Tong, Howell

    1995-04-01

    The Table of Contents for the full book PDF is as follows: * Preface * Orthogonal Projection, Embedding Dimension and Sample Size in Chaotic Time Series from a Statistical Perspective * A Theory of Correlation Dimension for Stationary Time Series * On Prediction and Chaos in Stochastic Systems * Locally Optimized Prediction of Nonlinear Systems: Stochastic and Deterministic * A Poisson Distribution for the BDS Test Statistic for Independence in a Time Series * Chaos and Nonlinear Forecastability in Economics and Finance * Paradigm Change in Prediction * Predicting Nonuniform Chaotic Attractors in an Enzyme Reaction * Chaos in Geophysical Fluids * Chaotic Modulation of the Solar Cycle * Fractal Nature in Earthquake Phenomena and its Simple Models * Singular Vectors and the Predictability of Weather and Climate * Prediction as a Criterion for Classifying Natural Time Series * Measuring and Characterising Spatial Patterns, Dynamics and Chaos in Spatially-Extended Dynamical Systems and Ecologies * Non-Linear Forecasting and Chaos in Ecology and Epidemiology: Measles as a Case Study

  7. 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.

  8. Chaos in plasma simulation and experiment

    SciTech Connect

    Watts, C.; Newman, D.E.; Sprott, J.C.

    1993-09-01

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

  9. 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.

  10. Oscillation and chaos in pitting corrosion of steel

    SciTech Connect

    Hernandez, M.A.; Rodriguez, F.J.; Garcia, E.; Boerio, F.J.

    1999-11-01

    The potential and current oscillations during pitting corrosion of steel in NaCl solution were studied. Detailed analysis using numerical diagnostics developed to characterize complex time series clearly shows that the irregularity in these time series corresponds to deterministic chaos, rather than to random noise. The chaotic oscillations were characterized by power spectral densities, phase space and Lyapunov exponents.

  11. 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…

  12. 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)

  13. 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…

  14. Deterministic Walks with Choice

    SciTech Connect

    Beeler, Katy E.; Berenhaut, Kenneth S.; Cooper, Joshua N.; Hunter, Meagan N.; Barr, Peter S.

    2014-01-10

    This paper studies deterministic movement over toroidal grids, integrating local information, bounded memory and choice at individual nodes. The research is motivated by recent work on deterministic random walks, and applications in multi-agent systems. Several results regarding passing tokens through toroidal grids are discussed, as well as some open questions.

  15. 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)

  16. Applying Chaos Theory to School Reform.

    ERIC Educational Resources Information Center

    Wertheimer, Richard; Zinga, Mario

    1998-01-01

    Presents a case study of the ideology, strategies and process of the "Common Knowledge: Pittsburgh" project in its attempt at school reform in an urban school district. Reflects on the project's activities, and uses its experience to develop a conceptual framework based on chaos theory, as developed in mathematics and science, for discussing…

  17. 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.

  18. 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. PMID:17747421

  19. Colored Chaos

    NASA Technical Reports Server (NTRS)

    2004-01-01

    [figure removed for brevity, see original site]

    Released 7 May 2004 This daytime visible color image was collected on May 30, 2002 during the Southern Fall season in Atlantis Chaos.

    The THEMIS VIS camera is capable of capturing color images of the martian surface using its five different color filters. In this mode of operation, the spatial resolution and coverage of the image must be reduced to accommodate the additional data volume produced from the use of multiple filters. To make a color image, three of the five filter images (each in grayscale) are selected. Each is contrast enhanced and then converted to a red, green, or blue intensity image. These three images are then combined to produce a full color, single image. Because the THEMIS color filters don't span the full range of colors seen by the human eye, a color THEMIS image does not represent true color. Also, because each single-filter image is contrast enhanced before inclusion in the three-color image, the apparent color variation of the scene is exaggerated. Nevertheless, the color variation that does appear is representative of some change in color, however subtle, in the actual scene. Note that the long edges of THEMIS color images typically contain color artifacts that do not represent surface variation.

    Image information: VIS instrument. Latitude -34.5, Longitude 183.6 East (176.4 West). 38 meter/pixel resolution.

    Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time.

    NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of

  20. Auream Chaos

    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 was collected during Southern Fall and shows part of the Aureum Chaos.

    Image information: VIS instrument. Latitude -3.6, Longitude 332.9 East (27.1 West). 35 meter/pixel resolution.

    Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time.

    NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission

  1. 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.

  2. 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.

  3. CHAOS AND STOCHASTICITY IN DETERMINISTICALLY GENERATED MULTIFRACTAL MEASURES. (R824780)

    EPA Science Inventory

    The perspectives, information and conclusions conveyed in research project abstracts, progress reports, final reports, journal abstracts and journal publications convey the viewpoints of the principal investigator and may not represent the views and policies of ORD and EPA. Concl...

  4. Turbulent Fluid Motion 6: Turbulence, Nonlinear Dynamics, and Deterministic Chaos

    NASA Technical Reports Server (NTRS)

    Deissler, Robert G.

    1996-01-01

    Several turbulent and nonturbulent solutions of the Navier-Stokes equations are obtained. The unaveraged equations are used numerically in conjunction with tools and concepts from nonlinear dynamics, including time series, phase portraits, Poincare sections, Liapunov exponents, power spectra, and strange attractors. Initially neighboring solutions for a low-Reynolds-number fully developed turbulence are compared. The turbulence is sustained by a nonrandom time-independent external force. The solutions, on the average, separate exponentially with time, having a positive Liapunov exponent. Thus, the turbulence is characterized as chaotic. In a search for solutions which contrast with the turbulent ones, the Reynolds number (or strength of the forcing) is reduced. Several qualitatively different flows are noted. These are, respectively, fully chaotic, complex periodic, weakly chaotic, simple periodic, and fixed-point. Of these, we classify only the fully chaotic flows as turbulent. Those flows have both a positive Liapunov exponent and Poincare sections without pattern. By contrast, the weakly chaotic flows, although having positive Liapunov exponents, have some pattern in their Poincare sections. The fixed-point and periodic flows are nonturbulent, since turbulence, as generally understood, is both time-dependent and aperiodic.

  5. Deterministic representation of chaos with application to turbulence

    NASA Technical Reports Server (NTRS)

    Zak, M.

    1987-01-01

    Chaotic motions of nonlinear dynamical systems are decomposed into mean components and fluctuations. The approach is based upon the concept that the fluctuations driven by the instability of the original (unperturbed) motion grow until a new stable state is approached. The Reynolds-type equations written for continuous as well as for finite-degrees-of-freedom dynamical systems are closed by using this stabilization principle. The theory is applied to conservative systems, to strange attractors and to turbulent motions.

  6. 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.

  7. Exploring dynamical systems and chaos using the logistic map model of population change

    NASA Astrophysics Data System (ADS)

    Groff, Jeffrey R.

    2013-10-01

    The logistic map difference equation is encountered in the theoretical ecology literature as a mathematical model of population change for organisms with non-overlapping generations and density-dependent dynamics influenced solely by intraspecific interactions. This article presents the logistic map as a simple model suitable for introducing students to the properties of dynamical systems including periodic orbits, bifurcations, and deterministic chaos. After a brief historical and mathematical introduction to models of population change and the logistic map, the article summarizes the logistic map activities I teach in my introductory physics laboratories for non-physics majors. The logistic map laboratory introduces the many bioscience students in my courses to a foundational model in population ecology that has inspired ecologists to recognize the importance of nonlinear dynamics in real populations. Although I use this activity in courses for non-majors, the logistic map model of population change could also be taught to physics majors to introduce properties of dynamical systems while demonstrating an application of mathematical modeling outside of traditional physics.

  8. Wiener Chaos expansions and numerical solutions of randomly forced equations of fluid mechanics

    SciTech Connect

    Hou, Thomas Y. . E-mail: hou@ama.caltech.edu; Luo Wuan; Rozovskii, Boris; Zhou Haomin

    2006-08-10

    In this paper, we propose a numerical method based on Wiener Chaos expansion and apply it to solve the stochastic Burgers and Navier-Stokes equations driven by Brownian motion. The main advantage of the Wiener Chaos approach is that it allows for the separation of random and deterministic effects in a rigorous and effective manner. The separation principle effectively reduces a stochastic equation to its associated propagator, a system of deterministic equations for the coefficients of the Wiener Chaos expansion. Simple formulas for statistical moments of the stochastic solution are presented. These formulas only involve the solutions of the propagator. We demonstrate that for short time solutions the numerical methods based on the Wiener Chaos expansion are more efficient and accurate than those based on the Monte Carlo simulations.

  9. Chaos in String Cosmology

    NASA Astrophysics Data System (ADS)

    Damour, Thibault

    We briefly review recent work which established the existence of chaos in the generic cosmological solutions of the tree-level low-energy effective actions coming out of string theory, and linked this chaos to the Weyl groups of some hyperbolic Kac-Moody algebras.

  10. Chaos in string cosmology

    NASA Astrophysics Data System (ADS)

    Damour, T.

    2003-10-01

    We briefly review two aspects of string cosmology: 1) the presence of chaos in the generic cosmological solutions of the tree-level low-energy effective actions coming out of string theory, and 2) the remarkable link between the latter chaos and the Weyl groups of some hyperbolic Kac-Moody algebras.

  11. String Cosmology and Chaos

    NASA Astrophysics Data System (ADS)

    Damour, Thibault

    We briefly review two aspects of string cosmology: (1) the presence of chaos in the generic cosmological solutions of the tree-level low-energy effective actions coming out of string theory, and (2) the remarkable link between the latter chaos and the Weyl groups of some hyperbolic Kac-Moody algebras.

  12. 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.

  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. Spatiotemporal Chaos Induces Extreme Events in an Extended Microcavity Laser

    NASA Astrophysics Data System (ADS)

    Selmi, F.; Coulibaly, S.; Loghmari, Z.; Sagnes, I.; Beaudoin, G.; Clerc, M. G.; Barbay, S.

    2016-01-01

    Extreme events such as rogue waves in optics and fluids are often associated with the merging dynamics of coherent structures. We present experimental and numerical results on the physics of extreme event appearance in a spatially extended semiconductor microcavity laser with an intracavity saturable absorber. This system can display deterministic irregular dynamics only, thanks to spatial coupling through diffraction of light. We have identified parameter regions where extreme events are encountered and established the origin of this dynamics in the emergence of deterministic spatiotemporal chaos, through the correspondence between the proportion of extreme events and the dimension of the strange attractor.

  16. Spatiotemporal Chaos Induces Extreme Events in an Extended Microcavity Laser.

    PubMed

    Selmi, F; Coulibaly, S; Loghmari, Z; Sagnes, I; Beaudoin, G; Clerc, M G; Barbay, S

    2016-01-01

    Extreme events such as rogue waves in optics and fluids are often associated with the merging dynamics of coherent structures. We present experimental and numerical results on the physics of extreme event appearance in a spatially extended semiconductor microcavity laser with an intracavity saturable absorber. This system can display deterministic irregular dynamics only, thanks to spatial coupling through diffraction of light. We have identified parameter regions where extreme events are encountered and established the origin of this dynamics in the emergence of deterministic spatiotemporal chaos, through the correspondence between the proportion of extreme events and the dimension of the strange attractor. PMID:26799020

  17. [Importance of chaos research for psychosomatic medicine].

    PubMed

    Wyss, D

    1993-01-01

    After a critical review of the many unsettled questions in psychosomatic medicine the author emphasizes the importance of the results of the so-called-research in mathematics, physics, biology and internal medicine. He developed various models for a deeper understanding not only of health and sickness but specially of the body/soul-problem and demonstrates the importance and fertility of the chaos-investigation for the psychosomatic medicine. PMID:8212774

  18. Statistical properties of deterministic Bernoulli flows

    SciTech Connect

    Radunskaya, A.E.

    1992-12-31

    This thesis presents several new theorems about the stability and the statistical properties of deterministic chaotic flows. Many concrete systems known to exhibit deterministic chaos have so far been shown to be of a class known as Bernoulli Flows. This class of flows is characterized by the Finitely Determined property, which can be checked in specific cases. The first theorem says that these flows can be modeled arbitrarily well for all time by continuous-time finite state Markov processes. In other words it is theoretically possible to model the flow arbitrarily well by a computer equipped with a roulette wheel. There follows a stability result, which says that one can distort the measurements made on the processes without affecting the approximation. These results are than applied to the problem of distinguishing deterministic chaos from stochastic processes in the analysis of time series. The second part of the thesis deals with a specific set of examples. Although it has been possible to analyze specific systems to determine whether they lie in the class of Bernoulli systems, the standard techniques rely on the construction of expanding and contracting fibers in the phase space of the system. These fibers are then used to coordinatize the phase space and to prove the existence of a hyperbolic structure. Unfortunately such methods may fail in the general case, where smoothness conditions and a small singular set cannot be assumed. For example, suppose the standard billiard flow on a square table with a perfectly round obstacle, which is known to be Bernoulli, is replaced by a similar flow on a table with a bumpy fractal-like obstacle: a model perhaps closer to nature. It is shown that these fibers no longer exist and hence cannot be used in the standard manner to prove Bernoulliness or ergodicity. But, one can use the fact that the class of Bernoulli flows is closed in the d-bar metric to show that this billard flow with a bumpy obstacle is in fact Bernoulli.

  19. 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

  20. 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.

  1. Deterministic hierarchical networks

    NASA Astrophysics Data System (ADS)

    Barrière, L.; Comellas, F.; Dalfó, C.; Fiol, M. A.

    2016-06-01

    It has been shown that many networks associated with complex systems are small-world (they have both a large local clustering coefficient and a small diameter) and also scale-free (the degrees are distributed according to a power law). Moreover, these networks are very often hierarchical, as they describe the modularity of the systems that are modeled. Most of the studies for complex networks are based on stochastic methods. However, a deterministic method, with an exact determination of the main relevant parameters of the networks, has proven useful. Indeed, this approach complements and enhances the probabilistic and simulation techniques and, therefore, it provides a better understanding of the modeled systems. In this paper we find the radius, diameter, clustering coefficient and degree distribution of a generic family of deterministic hierarchical small-world scale-free networks that has been considered for modeling real-life complex systems.

  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 stellar streams

    NASA Astrophysics Data System (ADS)

    Price-Whelan, Adrian M.; Johnston, Kathryn V.; Valluri, Monica; Pearson, Sarah; Kupper, Andreas Hans Wilhelm; Hogg, David W.

    2016-01-01

    Cosmological simulations predict that dark matter halos around galaxies should be triaxial in shape with universal density profiles. A significant number of orbits in such systems are chaotic, though it is commonly assumed that chaos is not dynamically relevant for galaxy halos because the timescales over which chaos is computed to be important are generally long relative to the dynamical time. In recent work, we showed that even when chaos is not important for restructuring the global structure of a galaxy, chaos can greatly enhance the density evolution and alter the morphologies of stellar streams over just a few orbital times by causing streams to 'fan out.' This occurs because the orbits of the stars in stellar streams have small distributions of fundamental frequencies and are therefore sensitive to mild chaos that modulates the frequencies on small-scales over much faster timescales. This suggests that the morphology of tidal streams alone can be used to estimate the significance of chaos along the orbits of the progenitor systems, thereby placing constraints on the global properties of the gravitational potential. I will explain our theoretical understanding of this phenomenon and discuss implications for a recently discovered stellar stream (the Ophiuchus stream) that may be on a chaotic orbit in the inner Milky Way due to the influence of the time-dependent, triaxial potential of the Galactic bar.

  5. Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series

    NASA Astrophysics Data System (ADS)

    Sugihara, George; May, Robert M.

    1990-04-01

    An approach is presented for making short-term predictions about the trajectories of chaotic dynamical systems. The method is applied to data on measles, chickenpox, and marine phytoplankton populations, to show how apparent noise associated with deterministic chaos can be distinguished from sampling error and other sources of externally induced environmental noise.

  6. Deterministic Bilinear System Identification

    NASA Astrophysics Data System (ADS)

    Lee, Cheh-Han; Juang, Jer-Nan

    2013-12-01

    A unified identification method is proposed for system realization of a deterministic continuous-time/discrete-time bilinear models from input and output measurement data. A generalized Hankel matrix is formed with the output measurements obtained by applying a set of repeated input sequences to a bilinear system. A computational procedure is developed to extract a time varying discrete-time state-space model from the generalized Hankel matrix. The bilinear system models are realized by transforming the identified time varying discrete-time model to the bilinear models. Numerical simulations are given to show the effectiveness of the proposed identification method.

  7. Semi-deterministic reasoning

    SciTech Connect

    Chengjiang Mao

    1996-12-31

    In typical AI systems, we employ so-called non-deterministic reasoning (NDR), which resorts to some systematic search with backtracking in the search spaces defined by knowledge bases (KBs). An eminent property of NDR is that it facilitates programming, especially programming for those difficult AI problems such as natural language processing for which it is difficult to find algorithms to tell computers what to do at every step. However, poor efficiency of NDR is still an open problem. Our work aims at overcoming this efficiency problem.

  8. Blue tongue - A modelling examination of fundamentals - Seasonality and chaos.

    PubMed

    Thornley, John H M; France, James

    2016-08-21

    A deterministic mathematical model is developed for the dynamics of bluetongue disease within a single farm. The purpose is to examine widely the possible behaviours which may occur. This is important because of the increasing impact of blue tongue due to global warming. The model incorporates a recently suggested modification of logistic growth for the vectors which can greatly affect early disease dynamics and employs a variable number of up to 10 sequential pools for incubating vectors and for incubating and infectious hosts. Ten sequential pools represent the possible loss of immunity of recovered hosts over a 3-year period. After formally describing the model, the impact of the two logistic growth scenarios considered is examined in Section 3.1. The scenarios are applied with parameters that give identical long-term consequences but the early dynamics can be greatly affected. In the two scenarios, the effect of varying the assumed constant birth rate (scenario 1) or constant mortality rates (scenario 2) is considered. If the recovered (and immune) hosts, are assumed to lose their immunity, then, given particular values of the host-vector coupling constants, the system can exhibit autonomous oscillations (Section 3.2). Seasonality is represented by air temperature, and it is assumed that air temperatures below a threshold can increase vector mortality (Section 3.3). Adding seasonal effects on mortality to the autonomous oscillations resulting from recovered and resistant hosts losing immunity can give rise to chaos (Section 3.4). This could help explain the unusual persistence and re-occurrence of the disease. Finally (Section 3.5), the roles of host birth and mortality rates in examined, particularly in relation to placental transmission of the virus to offspring. It is concluded that the latter does not make an appreciable contribution to disease dynamics. PMID:27155045

  9. 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.

  10. Are earthquakes deterministic or chaotic?

    NASA Astrophysics Data System (ADS)

    Rundle, John B.; Julian, Bruce R.; Turcotte, Donald L.

    During the last decade, physicists and applied mathematicians have made substantial headway in understanding the dynamics of complex nonlinear systems. Progress has been possible due to the development of several new tools, including the renormalization group approach, phase portraits, and scaling methods (fractals). At the same time, mathematical geophysicists interested in earthquakes have begun to utilize these same concepts to generate models of faults and fractures.In order to bring these scientific communities together, it was decided to convene the workshop, Physics of Earthquake Faults: Deterministic or Chaotic?, held February 12-15, at the Asilomar conference center near Monterey, Calif. Thirty-six Earth scientists met with 15 physicists and applied mathematicians to discuss how recent advances in nonlinear systems might be applied to better understand earthquakes. Funding was provided by the Geodynamics Branch of the National Aeronautics and Space Administration, the National Science Foundation, and the Office of Basic Energy Sciences of the U.S. Department of Energy. Organizational and logistical support were provided by the U.S. Geological Survey.

  11. 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.

  12. The Mathematical Modeling of Chaotic Social Structures.

    ERIC Educational Resources Information Center

    Marion, Russ; Richardson, Michael D.

    Chaos theory describes the way systems change over time. It proposes that systems governed by physical laws can undergo transitions to a highly irregular form of behavior and that although chaotic behavior appears random, it is governed by strict mathematical conditions. This paper applies chaos theory to administrative and organizational issues.…

  13. 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…

  14. 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

  15. Distinguishing Error from Chaos in Ecological Time Series

    NASA Astrophysics Data System (ADS)

    Sugihara, George; Grenfell, Bryan; May, Robert M.

    1990-11-01

    Over the years, there has been much discussion about the relative importance of environmental and biological factors in regulating natural populations. Often it is thought that environmental factors are associated with stochastic fluctuations in population density, and biological ones with deterministic regulation. We revisit these ideas in the light of recent work on chaos and nonlinear systems. We show that completely deterministic regulatory factors can lead to apparently random fluctuations in population density, and we then develop a new method (that can be applied to limited data sets) to make practical distinctions between apparently noisy dynamics produced by low-dimensional chaos and population variation that in fact derives from random (high-dimensional)noise, such as environmental stochasticity or sampling error. To show its practical use, the method is first applied to models where the dynamics are known. We then apply the method to several sets of real data, including newly analysed data on the incidence of measles in the United Kingdom. Here the additional problems of secular trends and spatial effects are explored. In particular, we find that on a city-by-city scale measles exhibits low-dimensional chaos (as has previously been found for measles in New York City), whereas on a larger, country-wide scale the dynamics appear as a noisy two-year cycle. In addition to shedding light on the basic dynamics of some nonlinear biological systems, this work dramatizes how the scale on which data is collected and analysed can affect the conclusions drawn.

  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. 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)

  18. Geometry in the large and hyperbolic chaos

    SciTech Connect

    Hasslacher, B.; Mainieri, R.

    1998-11-01

    This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The authors calculated observables in strongly chaotic systems. This is difficult to do because of a lack of a workable orbit classification for such systems. This is due to global geometrical information from the original dynamical system being entangled in an unknown way throughout the orbit sequence. They used geometrical methods from modern mathematics and recent connections between global geometry and modern quantum field theory to study the natural geometrical objects belonging to hard chaos-hyperbolic manifolds.

  19. 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.

  20. Quantum Correlations, Chaos and Information

    NASA Astrophysics Data System (ADS)

    Madhok, Vaibhav

    Quantum chaos is the study of quantum systems whose classical description is chaotic. How does chaos manifest itself in the quantum world? In this spirit, we study the dynamical generation of entanglement as a signature of chaos in a system of periodically kicked coupled-tops, where chaos and entanglement arise from the same physical mechanism. The long-time entanglement as a function of the position of an initially localized wave packet very closely correlates with the classical phase space surface of section - it is nearly uniform in the chaotic sea, and reproduces the detailed structure of the regular islands. The uniform value in the chaotic sea is explained by the random state conjecture. As classically chaotic dynamics take localized distributions in phase space to random distributions, quantized versions take localized coherent states to pseudo-random states in Hilbert space. Such random states are highly entangled, with an average value near that of the maximally entangled state. For a map with global chaos, we derive that value based on new analytic results for the entropy of random states. For a mixed phase space, we use the Percival conjecture to identify a "chaotic subspace" of the Hilbert space. The typical entanglement, averaged over the unitarily invariant Haar measure in this subspace, agrees with the long-time averaged entanglement for initial states in the chaotic sea. In all cases the dynamically generated entanglement is that of a random complex vector, even though the system is time-reversal invariant, and the Floquet operator is a member of the circular orthogonal ensemble. Continuing on our journey to find the footprints of chaos in the quantum world, we explore quantum signatures of classical chaos by studying the rate of information gain in quantum tomography. The measurement record is obtained as a sequence of expectation values of a Hermitian operator evolving under repeated application of the Floquet operator of the quantum kicked top on

  1. Large-Scale Chaos and Fluctuations in Active Nematics

    NASA Astrophysics Data System (ADS)

    Ngo, Sandrine; Peshkov, Anton; Aranson, Igor S.; Bertin, Eric; Ginelli, Francesco; Chaté, Hugues

    2014-07-01

    We show that dry active nematics, e.g., collections of shaken elongated granular particles, exhibit large-scale spatiotemporal chaos made of interacting dense, ordered, bandlike structures in a parameter region including the linear onset of nematic order. These results are obtained from the study of both the well-known (deterministic) hydrodynamic equations describing these systems and of the self-propelled particle model they were derived from. We prove, in particular, that the chaos stems from the generic instability of the band solution of the hydrodynamic equations. Revisiting the status of the strong fluctuations and long-range correlations in the particle model, we show that the giant number fluctuations observed in the chaotic phase are a trivial consequence of density segregation. However anomalous, curvature-driven number fluctuations are present in the homogeneous quasiordered nematic phase and characterized by a nontrivial scaling exponent.

  2. Spreading of atomic wave packets and semiclassical chaos

    NASA Astrophysics Data System (ADS)

    Argonov, V. Yu.

    2010-12-01

    The correspondence between the statistical properties of the evolution of a quantum system and Lyapunov instability and the chaos of its semiclassical analog has been demonstrated. The results of the analyses of atomic motion in a laser field in the semiclassical approximation (dynamics is described by several nonlinear equations) and without this approximation (dynamics is described by an infinite system of linear equations) are compared. In the ranges of the parameters for which the semiclassical dynamics of point-like atoms is unstable, the fast "spreading" of quantized wave packets in the momentum space is observed. Thus, deterministic chaos "imitates" the statistics of the quantum nondeterministic effects, although the semiclassical and quantum solutions are fundamentally different.

  3. Spreading of atomic wave packets and semiclassical chaos

    NASA Astrophysics Data System (ADS)

    Argonov, V. Yu.

    2009-12-01

    The correspondence between the statistical properties of the evolution of a quantum system and Lyapunov instability and the chaos of its semiclassical analog has been demonstrated. The results of the analyses of atomic motion in a laser field in the semiclassical approximation (dynamics is described by several nonlinear equations) and without this approximation (dynamics is described by an infinite system of linear equations) are compared. In the ranges of the parameters for which the semiclassical dynamics of point-like atoms is unstable, the fast “spreading” of quantized wave packets in the momentum space is observed. Thus, deterministic chaos “imitates” the statistics of the quantum nondeterministic effects, although the semiclassical and quantum solutions are fundamentally different.

  4. 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.

  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. 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.

  8. 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.

  9. 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

  10. Phase chaos in coupled oscillators.

    PubMed

    Popovych, Oleksandr V; Maistrenko, Yuri L; Tass, Peter A

    2005-06-01

    A complex high-dimensional chaotic behavior, phase chaos, is found in the finite-dimensional Kuramoto model of coupled phase oscillators. This type of chaos is characterized by half of the spectrum of Lyapunov exponents being positive and the Lyapunov dimension equaling almost the total system dimension. Intriguingly, the strongest phase chaos occurs for intermediate-size ensembles. Phase chaos is a common property of networks of oscillators of very different natures, such as phase oscillators, limit-cycle oscillators, and chaotic oscillators, e.g., Rössler systems. PMID:16089804

  11. Phase chaos in coupled oscillators

    NASA Astrophysics Data System (ADS)

    Popovych, Oleksandr V.; Maistrenko, Yuri L.; Tass, Peter A.

    2005-06-01

    A complex high-dimensional chaotic behavior, phase chaos, is found in the finite-dimensional Kuramoto model of coupled phase oscillators. This type of chaos is characterized by half of the spectrum of Lyapunov exponents being positive and the Lyapunov dimension equaling almost the total system dimension. Intriguingly, the strongest phase chaos occurs for intermediate-size ensembles. Phase chaos is a common property of networks of oscillators of very different natures, such as phase oscillators, limit-cycle oscillators, and chaotic oscillators, e.g., Rössler systems.

  12. 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

  13. 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.

  14. 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

  15. 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.

  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. Deterministic methods in radiation transport

    SciTech Connect

    Rice, A.F.; Roussin, R.W.

    1992-06-01

    The Seminar on Deterministic Methods in Radiation Transport was held February 4--5, 1992, in Oak Ridge, Tennessee. Eleven presentations were made and the full papers are published in this report, along with three that were submitted but not given orally. These papers represent a good overview of the state of the art in the deterministic solution of radiation transport problems for a variety of applications of current interest to the Radiation Shielding Information Center user community.

  18. 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.

  19. 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…

  20. 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…

  1. From deterministic cellular automata to coupled map lattices

    NASA Astrophysics Data System (ADS)

    García-Morales, Vladimir

    2016-07-01

    A general mathematical method is presented for the systematic construction of coupled map lattices (CMLs) out of deterministic cellular automata (CAs). The entire CA rule space is addressed by means of a universal map for CAs that we have recently derived and that is not dependent on any freely adjustable parameters. The CMLs thus constructed are termed real-valued deterministic cellular automata (RDCA) and encompass all deterministic CAs in rule space in the asymptotic limit κ \\to 0 of a continuous parameter κ. Thus, RDCAs generalize CAs in such a way that they constitute CMLs when κ is finite and nonvanishing. In the limit κ \\to ∞ all RDCAs are shown to exhibit a global homogeneous fixed-point that attracts all initial conditions. A new bifurcation is discovered for RDCAs and its location is exactly determined from the linear stability analysis of the global quiescent state. In this bifurcation, fuzziness gradually begins to intrude in a purely deterministic CA-like dynamics. The mathematical method presented allows to get insight in some highly nontrivial behavior found after the bifurcation.

  2. Generalized Polynomial Chaos Based Uncertainty Quantification for Planning MRgLITT Procedures

    PubMed Central

    Fahrenholtz, S.; Stafford, R. J.; Maier, F.; Hazle, J. D.; Fuentes, D.

    2014-01-01

    Purpose A generalized polynomial chaos (gPC) method is used to incorporate constitutive parameter uncertainties within the Pennes representation of bioheat transfer phenomena. The stochastic temperature predictions of the mathematical model are critically evaluated against MR thermometry data for planning MR-guided Laser Induced Thermal Therapies (MRgLITT). Methods Pennes bioheat transfer model coupled with a diffusion theory approximation of laser tissue interaction was implemented as the underlying deterministic kernel. A probabilistic sensitivity study was used to identify parameters that provide the most variance in temperature output. Confidence intervals of the temperature predictions are compared to MR temperature imaging (MRTI) obtained during phantom and in vivo canine (n=4) MRgLITT experiments. The gPC predictions were quantitatively compared to MRTI data using probabilistic linear and temporal profiles as well as 2-D 60 °C isotherms. Results Within the range of physically meaningful constitutive values relevant to the ablative temperature regime of MRgLITT, the sensitivity study indicated that the optical parameters, particularly the anisotropy factor, created the most variance in the stochastic model's output temperature prediction. Further, within the statistical sense considered, a nonlinear model of the temperature and damage dependent perfusion, absorption, and scattering is captured within the confidence intervals of the linear gPC method. Multivariate stochastic model predictions using parameters with the dominant sensitivities show good agreement with experimental MRTI data. Conclusions Given parameter uncertainties and mathematical modeling approximations of the Pennes bioheat model, the statistical framework demonstrates conservative estimates of the therapeutic heating and has potential for use as a computational prediction tool for thermal therapy planning. PMID:23692295

  3. Chaos, brain and divided consciousness.

    PubMed

    Bob, Petr

    2007-01-01

    with schizophrenia and depression. Increased level of psychopathological symptoms indicates close relationship to the right-left EDA asymmetry and asymmetry of information entropy calculated by non-linear recurrence quantification analysis of EDA records. Because epileptiform activity has specific chaotic behaviour and calculated information entropy from EDA records reflects the complexity of the deterministic structure in the system there is a relevant assumption that unilaterally increased complexity may produce interhemispheric disbalance and increased chaoticity which hypothetically may serve as a dynamic source of epileptiform discharges related to trauma induced kindling mechanism. Specific form of chaotic inner organization which cannot be explained only as a consequence of external causality support also psychophysiological data that lead to the so-called self-organizing theory of dreaming by Kahn and Hobson. This study suggests that self-organizing theory of dreaming is particularly important with respect to problem of memory formation and processing during dissociative states characteristic for dreams. Recent data and also findings of this study support the research utility of chaos theory in psychology and neuroscience, and also its conceptual view of dynamic ordering factors and self-organization underlying psychological processes and brain physiology. PMID:17867519

  4. [Shedding light on chaos theory].

    PubMed

    Chou, Shieu-Ming

    2004-06-01

    Gleick (1987) said that only three twentieth century scientific theories would be important enough to continue be of use in the twenty-first century: The Theory of Relativity, Quantum Theory, and Chaos Theory. Chaos Theory has become a craze which is being used to forge a new scientific system. It has also been extensively applied in a variety of professions. The purpose of this article is to introduce chaos theory and its nursing applications. Chaos is a sign of regular order. This is to say that chaos theory emphasizes the intrinsic potential for regular order within disordered phenomena. It is to be hoped that this article will inspire more nursing scientists to apply this concept to clinical, research, or administrative fields in our profession. PMID:15211774

  5. 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.

  6. Transition from low to high dimensional chaos in a group of pulsations recorded in a broad radiowave interval

    NASA Astrophysics Data System (ADS)

    Méndez Berhondo, Adolfo L.; Zlobec, Paolo; Díaz Rodríguez, Ana K.

    2015-06-01

    We examined the dynamic characteristics of the time series regarding a group of pulsations in broadband spectrum at metric waveband solar radio emission. The data were recorded with the radio polarimeter of the INAF-Trieste Astronomical Observatory at July 17, 2002. The aim is to determine if the underlying process of these pulsations can be describe as a periodic, deterministic chaos or stochastic. The pulsations under inquiry in present paper are rather rare, as we found only one example of similar ones reported in the literature. Unlike most of the previously works where the analyses was done to a broadband pulsating events at one single frequency, we examine the pulsation event as it evolves both in time and in frequency. We found that the dynamics underlying the generation of pulsations can be characterized by a deterministic chaotic process which increases the dimension of chaos with frequency showing a transition from low-dimensional to high-dimensional deterministic chaotic system.

  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. 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.

  9. 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.

  10. PT -symmetry Wave Chaos

    NASA Astrophysics Data System (ADS)

    West, Carl T.; Kottos, Tsampikos; Prosen, Tomaz

    2010-03-01

    We study a new class of chaotic systems with dynamical localization, where gain/loss processes break the hermiticity, while allowing for parity-time PT symmetry. For a value γPT of the gain/loss parameter the spectrum undergoes a spontaneous phase transition from real (exact phase) to complex values (broken phase). We develop a one parameter scaling theory for γPT, and show that chaos assists the exact PT-phase. Our results will have applications to the design of optical elements with PT-symmetry.

  11. Synthesizing folded band chaos.

    PubMed

    Corron, Ned J; Hayes, Scott T; Pethel, Shawn D; Blakely, Jonathan N

    2007-04-01

    A randomly driven linear filter that synthesizes Lorenz-like, reverse-time chaos is shown also to produce Rössler-like folded band wave forms when driven using a different encoding of the random source. The relationship between the topological entropy of the random source, dissipation in the linear filter, and the positive Lyapunov exponent for the reverse-time wave form is exposed. The two drive encodings are viewed as grammar restrictions on a more general encoding that produces a chaotic superset encompassing both the Lorenz butterfly and Rössler folded band paradigms of nonlinear dynamics. PMID:17500950

  12. 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

  13. Deterministic multidimensional nonuniform gap sampling

    NASA Astrophysics Data System (ADS)

    Worley, Bradley; Powers, Robert

    2015-12-01

    Born from empirical observations in nonuniformly sampled multidimensional NMR data relating to gaps between sampled points, the Poisson-gap sampling method has enjoyed widespread use in biomolecular NMR. While the majority of nonuniform sampling schemes are fully randomly drawn from probability densities that vary over a Nyquist grid, the Poisson-gap scheme employs constrained random deviates to minimize the gaps between sampled grid points. We describe a deterministic gap sampling method, based on the average behavior of Poisson-gap sampling, which performs comparably to its random counterpart with the additional benefit of completely deterministic behavior. We also introduce a general algorithm for multidimensional nonuniform sampling based on a gap equation, and apply it to yield a deterministic sampling scheme that combines burst-mode sampling features with those of Poisson-gap schemes. Finally, we derive a relationship between stochastic gap equations and the expectation value of their sampling probability densities.

  14. The Dripping Handrail Model: Transient Chaos in Accretion Systems

    NASA Technical Reports Server (NTRS)

    Young, Karl; Scargle, Jeffrey D.; Cuzzi, Jeffrey (Technical Monitor)

    1995-01-01

    We define and study a simple dynamical model for accretion systems, the "dripping handrail" (DHR). The time evolution of this spatially extended system is a mixture of periodic and apparently random (but actually deterministic) behavior. The nature of this mixture depends on the values of its physical parameters - the accretion rate, diffusion coefficient, and density threshold. The aperiodic component is a special kind of deterministic chaos called transient chaos. The model can simultaneously exhibit both the quasiperiodic oscillations (QPO) and very low frequency noise (VLFN) that characterize the power spectra of fluctuations of several classes of accretion systems in astronomy. For this reason, our model may be relevant to many such astrophysical systems, including binary stars with accretion onto a compact object - white dwarf, neutron star, or black hole - as well as active galactic nuclei. We describe the systematics of the DHR's temporal behavior, by exploring its physical parameter space using several diagnostics: power spectra, wavelet "scalegrams," and Lyapunov exponents. In addition, we note that for large accretion rates the DHR has periodic modes; the effective pulse shapes for these modes - evaluated by folding the time series at the known period - bear a resemblance to the similarly- determined shapes for some x-ray pulsars. The pulsing observed in some of these systems may be such periodic-mode accretion, and not due to pure rotation as in the standard pulsar model.

  15. 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.

  16. 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

  17. Chaos vs linear instability in the Vlasov equation: A fractal analysis characterization

    SciTech Connect

    Atalmi, A.; Baldo, M.; Burgio, G.F.; Rapisarda, A.

    1996-05-01

    In this paper we discuss the most recent results concerning the Vlasov dynamics inside the spinodal region. The chaotic behavior which follows an initial regular evolution is characterized through the calculation of the fractal dimension of the distribution of the final modes excited. The ambiguous role of the largest Lyapunov exponent for unstable systems is also critically reviewed. This investigation seems to confirm the crucial role played by deterministic chaos in nuclear multifragmentation. {copyright} {ital 1996 The American Physical Society.}

  18. 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.

  19. Deterministic models for traffic jams

    NASA Astrophysics Data System (ADS)

    Nagel, Kai; Herrmann, Hans J.

    1993-10-01

    We study several deterministic one-dimensional traffic models. For integer positions and velocities we find the typical high and low density phases separated by a simple transition. If positions and velocities are continuous variables the model shows self-organized critically driven by the slowest car.

  20. 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

  1. Genetic information and ecosystem health: arguments for the application of chaos theory to identify boundary conditions for ecosystem management.

    PubMed

    Stomp, A M

    1994-12-01

    To meet the demands for goods and services of an exponentially growing human population, global ecosystems will come under increasing human management. The hallmark of successful ecosystem management will be long-term ecosystem stability. Ecosystems and the genetic information and processes which underlie interactions of organisms with the environment in populations and communities exhibit behaviors which have nonlinear characteristics. Nonlinear mathematical formulations describing deterministic chaos have been used successfully to model such systems in physics, chemistry, economics, physiology, and epidemiology. This approach can be extended to ecotoxicology and can be used to investigate how changes in genetic information determine the behavior of populations and communities. This article seeks to provide the arguments for such an approach and to give initial direction to the search for the boundary conditions within which lies ecosystem stability. The identification of a theoretical framework for ecotoxicology and the parameters which drive the underlying model is a critical component in the formulation of a prioritized research agenda and appropriate ecosystem management policy and regulation. PMID:7713038

  2. Genetic information and ecosystem health: arguments for the application of chaos theory to identify boundary conditions for ecosystem management.

    PubMed Central

    Stomp, A M

    1994-01-01

    To meet the demands for goods and services of an exponentially growing human population, global ecosystems will come under increasing human management. The hallmark of successful ecosystem management will be long-term ecosystem stability. Ecosystems and the genetic information and processes which underlie interactions of organisms with the environment in populations and communities exhibit behaviors which have nonlinear characteristics. Nonlinear mathematical formulations describing deterministic chaos have been used successfully to model such systems in physics, chemistry, economics, physiology, and epidemiology. This approach can be extended to ecotoxicology and can be used to investigate how changes in genetic information determine the behavior of populations and communities. This article seeks to provide the arguments for such an approach and to give initial direction to the search for the boundary conditions within which lies ecosystem stability. The identification of a theoretical framework for ecotoxicology and the parameters which drive the underlying model is a critical component in the formulation of a prioritized research agenda and appropriate ecosystem management policy and regulation. PMID:7713038

  3. Deterministic and stochastic simulation and analysis of biochemical reaction networks the lactose operon example.

    PubMed

    Yildirim, Necmettin; Kazanci, Caner

    2011-01-01

    A brief introduction to mathematical modeling of biochemical regulatory reaction networks is presented. Both deterministic and stochastic modeling techniques are covered with examples from enzyme kinetics, coupled reaction networks with oscillatory dynamics and bistability. The Yildirim-Mackey model for lactose operon is used as an example to discuss and show how deterministic and stochastic methods can be used to investigate various aspects of this bacterial circuit. PMID:21187231

  4. Chaos-Dchroot Version 2

    Energy Science and Technology Software Center (ESTSC)

    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.

  5. Chaos in driven Alfven systems

    NASA Technical Reports Server (NTRS)

    Hada, T.; Kennel, C. F.; Buti, B.; Mjolhus, E.

    1990-01-01

    The chaos in a one-dimensional system, which would be nonlinear stationary Alfven waves in the absence of an external driver, is characterized. The evolution equations are numerically integrated for the transverse wave magnetic field amplitude and phase using the derivative nonlinear Schroedinger equation (DNLS), including resistive wave damping and a long-wavelength monochromatic, circularly polarized driver. A Poincare map analysis shows that, for the nondissipative (Hamiltonian) case, the solutions near the phase space (soliton) separatrices of this system become chaotic as the driver amplitude increases, and 'strong' chaos appears when the driver amplitude is large. The dissipative system exhibits a wealth of dynamical behavior, including quasiperiodic orbits, period-doubling bifurcations leading to chaos, sudden transitions to chaos, and several types of strange attractors.

  6. 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.

  7. Optical digital chaos cryptography

    NASA Astrophysics Data System (ADS)

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

    2007-10-01

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

  8. 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

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. Food chain chaos due to transcritical point

    NASA Astrophysics Data System (ADS)

    Deng, Bo; Hines, Gwendolen

    2003-06-01

    Chaotic dynamics of a classical prey-predator-superpredator ecological model are considered. Although much is known about the behavior of the model numerically, very few results have been proven analytically. A new analytical result is obtained. It is demonstrated that there exists a subset on which a singular Poincaré map generated by the model is conjugate to the shift map on two symbols. The existence of such a Poincaré map is due to two conditions: the assumption that each species has its own time scale ranging from fast for the prey to slow for the superpredator, and the existence of transcritical points, leading to the classical mathematical phenomenon of Pontryagin's delay of loss of stability. This chaos generating mechanism is new, neither suspected in abstract form nor recognized in numerical experiments in the literature.

  14. Deterministic relativistic quantum bit commitment

    NASA Astrophysics Data System (ADS)

    Adlam, Emily; Kent, Adrian

    2015-06-01

    We describe new unconditionally secure bit commitment schemes whose security is based on Minkowski causality and the monogamy of quantum entanglement. We first describe an ideal scheme that is purely deterministic, in the sense that neither party needs to generate any secret randomness at any stage. We also describe a variant that allows the committer to proceed deterministically, requires only local randomness generation from the receiver, and allows the commitment to be verified in the neighborhood of the unveiling point. We show that these schemes still offer near-perfect security in the presence of losses and errors, which can be made perfect if the committer uses an extra single random secret bit. We discuss scenarios where these advantages are significant.

  15. Implications of chaos, scale-invariance, and fractal statistics in geology

    NASA Technical Reports Server (NTRS)

    Turcotte, D. L.

    1990-01-01

    A set of three nonlinear total differential equations (Lorenz equations) exhibiting deterministic chaos is considered, and it is shown that these equations demonstrate that deterministic equations with deterministic initial conditions can yield stocastic solutions with fractal statistics. The logistic map, fractal distributions, and fragmentation are discussed. It is pointed out that well-defined fractal distributions of earthquakes are found both regionally and globally, and that the general applicability of the fractal relation for seismicity can provide the basis for a quantitative seismic hazard assessment. It is suggested that the governing physics of erosional topography is nonlinear and may be related to a fractal distribution of storms and floods that generate and renew erosional feature such as gullies and drainage systems.

  16. Losers in the 'Rock-Paper-Scissors' game: The role of non-hierarchical competition and chaos as biodiversity sustaining agents in aquatic systems

    EPA Science Inventory

    Processes occurring within small areas (patch-scale) that influence species richness and spatial heterogeneity of larger areas (landscape-scale) have long been an interest of ecologists. This research focused on the role of patch-scale deterministic chaos arising in phytoplankton...

  17. Robustness analysis of an air heating plant and control law by using polynomial chaos

    SciTech Connect

    Colón, Diego; Ferreira, Murillo A. S.; Bueno, Átila M.; Balthazar, José M.; Rosa, Suélia S. R. F. de

    2014-12-10

    This paper presents a robustness analysis of an air heating plant with a multivariable closed-loop control law by using the polynomial chaos methodology (MPC). The plant consists of a PVC tube with a fan in the air input (that forces the air through the tube) and a mass flux sensor in the output. A heating resistance warms the air as it flows inside the tube, and a thermo-couple sensor measures the air temperature. The plant has thus two inputs (the fan's rotation intensity and heat generated by the resistance, both measured in percent of the maximum value) and two outputs (air temperature and air mass flux, also in percent of the maximal value). The mathematical model is obtained by System Identification techniques. The mass flux sensor, which is nonlinear, is linearized and the delays in the transfer functions are properly approximated by non-minimum phase transfer functions. The resulting model is transformed to a state-space model, which is used for control design purposes. The multivariable robust control design techniques used is the LQG/LTR, and the controllers are validated in simulation software and in the real plant. Finally, the MPC is applied by considering some of the system's parameters as random variables (one at a time, and the system's stochastic differential equations are solved by expanding the solution (a stochastic process) in an orthogonal basis of polynomial functions of the basic random variables. This method transforms the stochastic equations in a set of deterministic differential equations, which can be solved by traditional numerical methods (That is the MPC). Statistical data for the system (like expected values and variances) are then calculated. The effects of randomness in the parameters are evaluated in the open-loop and closed-loop pole's positions.

  18. Robustness analysis of an air heating plant and control law by using polynomial chaos

    NASA Astrophysics Data System (ADS)

    Colón, Diego; Ferreira, Murillo A. S.; Balthazar, José M.; Bueno, Átila M.; de S. R. F. Rosa, Suélia

    2014-12-01

    This paper presents a robustness analysis of an air heating plant with a multivariable closed-loop control law by using the polynomial chaos methodology (MPC). The plant consists of a PVC tube with a fan in the air input (that forces the air through the tube) and a mass flux sensor in the output. A heating resistance warms the air as it flows inside the tube, and a thermo-couple sensor measures the air temperature. The plant has thus two inputs (the fan's rotation intensity and heat generated by the resistance, both measured in percent of the maximum value) and two outputs (air temperature and air mass flux, also in percent of the maximal value). The mathematical model is obtained by System Identification techniques. The mass flux sensor, which is nonlinear, is linearized and the delays in the transfer functions are properly approximated by non-minimum phase transfer functions. The resulting model is transformed to a state-space model, which is used for control design purposes. The multivariable robust control design techniques used is the LQG/LTR, and the controllers are validated in simulation software and in the real plant. Finally, the MPC is applied by considering some of the system's parameters as random variables (one at a time, and the system's stochastic differential equations are solved by expanding the solution (a stochastic process) in an orthogonal basis of polynomial functions of the basic random variables. This method transforms the stochastic equations in a set of deterministic differential equations, which can be solved by traditional numerical methods (That is the MPC). Statistical data for the system (like expected values and variances) are then calculated. The effects of randomness in the parameters are evaluated in the open-loop and closed-loop pole's positions.

  19. Chaos in kicked ratchets.

    PubMed

    Zarlenga, D G; Larrondo, H A; Arizmendi, C M; Family, Fereydoon

    2015-03-01

    We present a minimal one-dimensional deterministic continuous dynamical system that exhibits chaotic behavior and complex transport properties. Our model is an overdamped rocking ratchet with finite dissipation, that is periodically kicked with a δ function driving force, without finite inertia terms or temporal or spatial stochastic forces. To our knowledge this is the simplest model reported in the literature for a ratchet, with this complex behavior. We develop an analytical approach that predicts many key features of the system, such as current reversals, as well as the presence of chaotic behavior and bifurcation. Our analytical approach allows us to study the transition from regular to chaotic motion as well as a tangent bifurcation associated with this transition. We show that our approach can be easily extended to other types of periodic driving forces. The square wave is shown as an example. PMID:25871166

  20. Computing with Chaos

    NASA Astrophysics Data System (ADS)

    Murali, K.; Sinah, Sudeshna; Ditto, William

    2004-03-01

    Recently there has been a new theoretical direction in harnessing the richness of spatially extended chaotic systems, namely the exploitation of coupled chaotic elements to do flexible computations [1]. The aim of this presentation is to demonstrate the use a single chaotic element to emulate different logic gates and perform different arithmetic tasks. Additionally we demonstrate that the elements can be controlled to switch easily between the different operational roles. Such a computing unit may then allow a more dynamic computer architecture and serve as ingredients of a general-purpose device more flexible than statically wired hardware. The theoretical scheme for flexible implementation of all these fundamental logical operations utilizing low dimensional chaos [1] will be reviewed along with a specific realization of the theory in a chaotic circuit [2]. Results will also be presented from experiments done on leech neurons. [1] Sinha, S., Munakata, T. and Ditto, W.L., Phys. Rev. E 65 036216 [2] "Experimental realization of the fundamental NOR Gate using a chaotic circuit," K. Murali, Sudeshna Sinha and William L. Ditto Phys. Rev. E 68, 016205 (2003).

  1. Preface to the Focus Issue: chaos detection methods and predictability.

    PubMed

    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. PMID:24985454

  2. Chaos in Periodic Discrete Systems

    NASA Astrophysics Data System (ADS)

    Shi, Yuming; Zhang, Lijuan; Yu, Panpan; Huang, Qiuling

    This paper focuses on chaos in periodic discrete systems, whose state space may vary with time. Some close relationships between some chaotic dynamical behaviors of a periodic discrete system and its autonomous induced system are given. Based on these relationships, several criteria of chaos are established and some sufficient conditions for no chaos are given for periodic discrete systems. Further, it is shown that a finite-dimensional linear periodic discrete system is not chaotic in the sense of Li-Yorke or Wiggins. In particular, an interesting problem of whether nonchaotic rules may generate a chaotic system is studied, with some examples provided, one of which surprisingly shows that a composition of globally asymptotically stable maps can be chaotic. In addition, some properties of sign pattern matrices of non-negative square matrices are given for convenience of the study.

  3. Deterministic scale-free networks

    NASA Astrophysics Data System (ADS)

    Barabási, Albert-László; Ravasz, Erzsébet; Vicsek, Tamás

    2001-10-01

    Scale-free networks are abundant in nature and society, describing such diverse systems as the world wide web, the web of human sexual contacts, or the chemical network of a cell. All models used to generate a scale-free topology are stochastic, that is they create networks in which the nodes appear to be randomly connected to each other. Here we propose a simple model that generates scale-free networks in a deterministic fashion. We solve exactly the model, showing that the tail of the degree distribution follows a power law.

  4. Modeling and Controlling Chaos in Breast Cancer: Toward Finding a Practical Cure—A first step

    NASA Astrophysics Data System (ADS)

    Abdollahzadeh, Somayeh; Sanayei, Ali

    2010-09-01

    The main aim of this work is finding a practical method which is based on a mathematical model to cure the breast cancer. This model with certain values of parameters could exhibit a chaotic behavior. Consequently, we achieve this goal by controlling chaos and find the best adjustable control parameter in order to control the malignancy.

  5. 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

  6. 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

  7. Two career chaos

    NASA Astrophysics Data System (ADS)

    Tauxe, L.

    2002-12-01

    When I finished graduate school I suppose I imagined myself as my dad. He worked hard, loved his job and family, made a good living. But I also saw myself as my mom - making a home, raising kids, cooking dinner, saving the world. I thought: I can handle being my mom and my dad. I can handle being a scientist and a mother. I can DO this.ÿ What I never imagined was the chaotic dynamic of the two career couple. The motions of bodies moving in response to the force of gravity cannot be predicted exactly if there are too many bodies. They dance in a jerky jumble, now faster, then slowly, bouncing, jostling, bumping and flying apart. Just so are the career trajectories of the two career couple. One rises up, the other, slower, pulls it down; overtaking, blocking preventing, now supporting, pulling along, now holding back - not moving, leap frogging, racing in opposite directions and snapping back together with a crack.ÿ The problem is non-linear. The outcome depends on feedback, whether positive or negative. The outcome cannot be predicted. Cannot be determined.ÿ Perhaps it cannot be done. Perhaps both husband and wife cannot be both mother and father. Too many mothers, too many fathers. Chaos.ÿ But I believe it can be done. Not like our mothers and fathers but a different way. And maybe our jerky paths will keep us sharp, make us work harder, and lead us through lives that at least cannot be described as dull.ÿ

  8. Dynamic chaos in the solution of the Gross-Pitaevskii equation for a periodic potential

    SciTech Connect

    Ishkhanyan, H. A.; Krainov, V. P.

    2011-09-15

    We analytically and numerically investigate the solution to the stationary Gross-Pitaevskii equation for a one-dimensional potential of the optical lattice in the case of repulsive nonlinearity. From the mathematical viewpoint, this problem is similar to the well-known problem of the classical mathematical Kapitza pendulum perturbed by a weak high-frequency force. At certain values of the parameters, dynamic chaos is produced in the considered problem. It is modeled analytically by a nonlinear diffusion equation.

  9. Probability densities for the sums of iterates of the sine-circle map in the vicinity of the quasiperiodic edge of chaos

    NASA Astrophysics Data System (ADS)

    Afsar, Ozgur; Tirnakli, Ugur

    2010-10-01

    We investigate the probability density of rescaled sum of iterates of sine-circle map within quasiperiodic route to chaos. When the dynamical system is strongly mixing (i.e., ergodic), standard central limit theorem (CLT) is expected to be valid, but at the edge of chaos where iterates have strong correlations, the standard CLT is not necessarily valid anymore. We discuss here the main characteristics of the probability densities for the sums of iterates of deterministic dynamical systems which exhibit quasiperiodic route to chaos. At the golden-mean onset of chaos for the sine-circle map, we numerically verify that the probability density appears to converge to a q -Gaussian with q<1 as the golden mean value is approached.

  10. Limited Imitation Contagion on Random Networks: Chaos, Universality, and Unpredictability

    NASA Astrophysics Data System (ADS)

    Dodds, Peter Sheridan; Harris, Kameron Decker; Danforth, Christopher M.

    2013-04-01

    We study a family of binary state, socially inspired contagion models which incorporate imitation limited by an aversion to complete conformity. We uncover rich behavior in our models whether operating with either probabilistic or deterministic individual response functions on both dynamic and fixed random networks. In particular, we find significant variation in the limiting behavior of a population’s infected fraction, ranging from steady state to chaotic. We show that period doubling arises as we increase the average node degree, and that the universality class of this well-known route to chaos depends on the interaction structure of random networks rather than the microscopic behavior of individual nodes. We find that increasing the fixedness of the system tends to stabilize the infected fraction, yet disjoint, multiple equilibria are possible depending solely on the choice of the initially infected node.

  11. Synchronicity from synchronized chaos

    SciTech Connect

    Duane, Gregory

    2015-04-01

    The synchronization of loosely-coupled chaotic oscillators, a phenomenon investigated intensively for the last two decades, may realize the philosophical concept of “synchronicity”—the commonplace notion that related events mysteriously occur at the same time. When extended to continuous media and/or large discrete arrays, and when general (non-identical) correspondences are considered between states, intermittent synchronous relationships indeed become ubiquitous. Meaningful synchronicity follows naturally if meaningful events are identified with coherent structures, defined by internal synchronization between remote degrees of freedom; a condition that has been posited as necessary for synchronizability with an external system. The important case of synchronization between mind and matter is realized if mind is analogized to a computer model, synchronizing with a sporadically observed system, as in meteorological data assimilation. Evidence for the ubiquity of synchronization is reviewed along with recent proposals that: (1) synchronization of different models of the same objective process may be an expeditious route to improved computational modeling and may also describe the functioning of conscious brains; and (2) the nonlocality in quantum phenomena implied by Bell’s theorem may be explained in a variety of deterministic (hidden variable) interpretations if the quantum world resides on a generalized synchronization “manifold”.

  12. Synchronicity from synchronized chaos

    DOE PAGESBeta

    Duane, Gregory

    2015-04-01

    The synchronization of loosely-coupled chaotic oscillators, a phenomenon investigated intensively for the last two decades, may realize the philosophical concept of “synchronicity”—the commonplace notion that related events mysteriously occur at the same time. When extended to continuous media and/or large discrete arrays, and when general (non-identical) correspondences are considered between states, intermittent synchronous relationships indeed become ubiquitous. Meaningful synchronicity follows naturally if meaningful events are identified with coherent structures, defined by internal synchronization between remote degrees of freedom; a condition that has been posited as necessary for synchronizability with an external system. The important case of synchronization between mind andmore » matter is realized if mind is analogized to a computer model, synchronizing with a sporadically observed system, as in meteorological data assimilation. Evidence for the ubiquity of synchronization is reviewed along with recent proposals that: (1) synchronization of different models of the same objective process may be an expeditious route to improved computational modeling and may also describe the functioning of conscious brains; and (2) the nonlocality in quantum phenomena implied by Bell’s theorem may be explained in a variety of deterministic (hidden variable) interpretations if the quantum world resides on a generalized synchronization “manifold”.« less

  13. Subspace inverse power method and polynomial chaos representation for the modal frequency responses of random mechanical systems

    NASA Astrophysics Data System (ADS)

    Pagnacco, E.; de Cursi, E. Souza; Sampaio, R.

    2016-04-01

    This study concerns the computation of frequency responses of linear stochastic mechanical systems through a modal analysis. A new strategy, based on transposing standards deterministic deflated and subspace inverse power methods into stochastic framework, is introduced via polynomial chaos representation. Applicability and effectiveness of the proposed schemes is demonstrated through three simple application examples and one realistic application example. It is shown that null and repeated-eigenvalue situations are addressed successfully.

  14. 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.

  15. 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.

  16. Entanglement induced by nonadiabatic chaos

    SciTech Connect

    Fujisaki, Hiroshi

    2004-07-01

    We investigate entanglement between electronic and nuclear degrees of freedom for a model nonadiabatic system. We find that entanglement (measured by the von Neumann entropy of the subsystem for the eigenstates) becomes nearly maximum when the system shows 'nonadiabatic chaos' behavior which was found in our previous work [Phys. Rev. E 63, 066221 (2001)], but the reverse is not necessarily the case.

  17. 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…

  18. Chao Formalism & Kondratenko Crossing Tests

    NASA Astrophysics Data System (ADS)

    Raymond, R. S.; Chao, A. W.; Krisch, A. D.; Leonova, M. A.; Morozov, V. S.; Sivers, D. W.; Wong, V. K.; Gebel, R.; Lehrach, A.; Lorentz, B.; Maier, R.; Prasuhn, D.; Schnase, A.; Stockhorst, H.; Hinterberger, F.; Ulbrich, K.; Kondratenko, A. M.

    2007-06-01

    We recently started testing Chao's proposed new matrix formalism for describing the spin dynamics due to a single spin resonance; this seems to be the first generalization of the Froissart-Stora equation since it was published in 1960. The Chao matrix formalism allows one to calculate analytically the polarization's behavior inside a resonance, which is not possible using the Froissart-Stora equation. We recently tested some Chao formalism predictions using a 1.85 GeV/c polarized deuteron beam stored in COSY. We swept an rf dipole's frequency through 200 Hz while varying the distance from the sweep's end frequency to an rf-induced spin resonance's central frequency. While the Froissart-Stora formula can make no prediction in this case, the data seem to support the Chao formalism. We also started investigating the new Kondratenko method to preserve beam polarization during a spin resonance crossing; the method uses 3 rapid changes of the crossing rate near the resonance. With a proper choice of crossing parameters, Kondratenko Crossing may better preserve the polarization than simple fast crossing. We tested Kondratenko's idea using 2.1 GeV/c polarized protons stored in COSY; the frequency of a ferrite rf dipole was swept though an rf-induced spin resonance using Kondratenko's crossing shape. We have not yet observed a significant advantage of Kondratenko Crossing over simple fast crossing. We plan to study it further by choosing better crossing parameters and a smaller momentum spread.

  19. 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!

  20. 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…

  1. 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)

  2. 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

  3. Continuing Through Iani Chaos

    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 continues the northward trend through the Iani Chaos region. Compare this image to Monday's and Tuesday's. This image was collected during the Southern Fall season.

    Image information: VIS instrument. Latitude -0.1 Longitude 342.6 East (17.4 West). 19 meter/pixel resolution.

    Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time.

    NASA's Jet Propulsion Laboratory manages the 2001

  4. Accessing Creativity: Jungian Night Sea Journeys, Wandering Minds, and Chaos.

    PubMed

    Rosen, Diane

    2016-01-01

    NDS theory has been meaningfully applied to the dynamics of creativity and psychology. These complex systems have much in common, including a broad definition of "product" as new order emerging from disorder, a new whole (etymologically, 'health') out of disintegration or destabilization. From a nonlinear dynamical systems perspective, this paper explores the far-from-equilibrium zone of creative incubation: first in the Jungian night sea journey, a primordial myth of psychological and creative transformation; then in the neuroscience of mind wandering, the well-spring of creative ideation within the larger neural matrix. Finally, chaos theory grounds the elusive subject of creativity, modeling chaotic generation of idea elements that tend toward strange attractors, combine unpredictably, and produce change by means of tension between opposites, particularly notes consciousness (light) and the poetic unconscious (darkness). Examples from my own artwork illustrate this dialectical process. Considered together, the unconscious mythic sea journey, the unknowing wandering mind, and the generative paradigm of deterministic chaos suggest conditions that facilitate creativity across disciplines, providing fresh indications that the darkness of the unknown or irrational is, paradoxically, the illuminative source and strength of creativity. PMID:26639923

  5. Global Optimal Trajectory in Chaos and NP-Hardness

    NASA Astrophysics Data System (ADS)

    Latorre, Vittorio; Gao, David Yang

    This paper presents an unconventional theory and method for solving general nonlinear dynamical systems. Instead of the direct iterative methods, the discretized nonlinear system is first formulated as a global optimization problem via the least squares method. A newly developed canonical duality theory shows that this nonconvex minimization problem can be solved deterministically in polynomial time if a global optimality condition is satisfied. The so-called pseudo-chaos produced by linear iterative methods are mainly due to the intrinsic numerical error accumulations. Otherwise, the global optimization problem could be NP-hard and the nonlinear system can be really chaotic. A conjecture is proposed, which reveals the connection between chaos in nonlinear dynamics and NP-hardness in computer science. The methodology and the conjecture are verified by applications to the well-known logistic equation, a forced memristive circuit and the Lorenz system. Computational results show that the canonical duality theory can be used to identify chaotic systems and to obtain realistic global optimal solutions in nonlinear dynamical systems. The method and results presented in this paper should bring some new insights into nonlinear dynamical systems and NP-hardness in computational complexity theory.

  6. 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.

  7. Demographic noise can reverse the direction of deterministic selection.

    PubMed

    Constable, George W A; Rogers, Tim; McKane, Alan J; Tarnita, Corina E

    2016-08-01

    Deterministic evolutionary theory robustly predicts that populations displaying altruistic behaviors will be driven to extinction by mutant cheats that absorb common benefits but do not themselves contribute. Here we show that when demographic stochasticity is accounted for, selection can in fact act in the reverse direction to that predicted deterministically, instead favoring cooperative behaviors that appreciably increase the carrying capacity of the population. Populations that exist in larger numbers experience a selective advantage by being more stochastically robust to invasions than smaller populations, and this advantage can persist even in the presence of reproductive costs. We investigate this general effect in the specific context of public goods production and find conditions for stochastic selection reversal leading to the success of public good producers. This insight, developed here analytically, is missed by the deterministic analysis as well as by standard game theoretic models that enforce a fixed population size. The effect is found to be amplified by space; in this scenario we find that selection reversal occurs within biologically reasonable parameter regimes for microbial populations. Beyond the public good problem, we formulate a general mathematical framework for models that may exhibit stochastic selection reversal. In this context, we describe a stochastic analog to [Formula: see text] theory, by which small populations can evolve to higher densities in the absence of disturbance. PMID:27450085

  8. Standard fluctuation-dissipation process from a deterministic mapping

    NASA Astrophysics Data System (ADS)

    Bianucci, Marco; Mannella, Riccardo; Fan, Ximing; Grigolini, Paolo; West, Bruce J.

    1993-03-01

    We illustrate a derivation of a standard fluctuation-dissipation process from a discrete deterministic dynamical model. This model is a three-dimensional mapping, driving the motion of three variables, w, ξ, and π. We show that for suitable values of the parameters of this mapping, the motion of the variable w is indistinguishable from that of a stochastic variable described by a Fokker-Planck equation with well-defined friction γ and diffusion D. This result can be explained as follows. The bidimensional system of the two variables ξ and π is a nonlinear, deterministic, and chaotic system, with the key property of resulting in a finite correlation time for the variable ξ and in a linear response of ξ to an external perturbation. Both properties are traced back to the fully chaotic nature of this system. When this subsystem is coupled to the variable w, via a very weak coupling guaranteeing a large-time-scale separation between the two systems, the variable w is proven to be driven by a standard fluctuation-dissipation process. We call the subsystem a booster whose chaotic nature triggers the standard fluctuation-dissipation process exhibited by the variable w. The diffusion process is a trivial consequence of the central-limit theorem, whose validity is assured by the finite time scale of the correlation function of ξ. The dissipation affecting the variable w is traced back to the linear response of the booster, which is evaluated adopting a geometrical procedure based on the properties of chaos rather than the conventional perturbation approach.

  9. Survivability of Deterministic Dynamical Systems

    PubMed Central

    Hellmann, Frank; Schultz, Paul; Grabow, Carsten; Heitzig, Jobst; Kurths, Jürgen

    2016-01-01

    The notion of a part of phase space containing desired (or allowed) states of a dynamical system is important in a wide range of complex systems research. It has been called the safe operating space, the viability kernel or the sunny region. In this paper we define the notion of survivability: Given a random initial condition, what is the likelihood that the transient behaviour of a deterministic system does not leave a region of desirable states. We demonstrate the utility of this novel stability measure by considering models from climate science, neuronal networks and power grids. We also show that a semi-analytic lower bound for the survivability of linear systems allows a numerically very efficient survivability analysis in realistic models of power grids. Our numerical and semi-analytic work underlines that the type of stability measured by survivability is not captured by common asymptotic stability measures. PMID:27405955

  10. Survivability of Deterministic Dynamical Systems

    NASA Astrophysics Data System (ADS)

    Hellmann, Frank; Schultz, Paul; Grabow, Carsten; Heitzig, Jobst; Kurths, Jürgen

    2016-07-01

    The notion of a part of phase space containing desired (or allowed) states of a dynamical system is important in a wide range of complex systems research. It has been called the safe operating space, the viability kernel or the sunny region. In this paper we define the notion of survivability: Given a random initial condition, what is the likelihood that the transient behaviour of a deterministic system does not leave a region of desirable states. We demonstrate the utility of this novel stability measure by considering models from climate science, neuronal networks and power grids. We also show that a semi-analytic lower bound for the survivability of linear systems allows a numerically very efficient survivability analysis in realistic models of power grids. Our numerical and semi-analytic work underlines that the type of stability measured by survivability is not captured by common asymptotic stability measures.

  11. Survivability of Deterministic Dynamical Systems.

    PubMed

    Hellmann, Frank; Schultz, Paul; Grabow, Carsten; Heitzig, Jobst; Kurths, Jürgen

    2016-01-01

    The notion of a part of phase space containing desired (or allowed) states of a dynamical system is important in a wide range of complex systems research. It has been called the safe operating space, the viability kernel or the sunny region. In this paper we define the notion of survivability: Given a random initial condition, what is the likelihood that the transient behaviour of a deterministic system does not leave a region of desirable states. We demonstrate the utility of this novel stability measure by considering models from climate science, neuronal networks and power grids. We also show that a semi-analytic lower bound for the survivability of linear systems allows a numerically very efficient survivability analysis in realistic models of power grids. Our numerical and semi-analytic work underlines that the type of stability measured by survivability is not captured by common asymptotic stability measures. PMID:27405955

  12. Chaos theory before Lorenz.

    PubMed

    Rosser, J Barkley

    2009-07-01

    We consider the precursors to the discovery of sensitive dependence on initial conditions by Edward Lorenz (1963) in his model of climatic fluid dynamics. This will focus on work in various disciplines that imply either such sensitivity, irregular endogenous dynamic patterns, or fractal nature of an attractor, as is also found in the attractor underlying the model Lorenz studied. Going from ancient hints in Anaxagoras through nineteenth century mathematics and physics, the main areas of such development will be argued to have been in celestial mechanics, oscillators, and economics. PMID:19527617

  13. Stability and chaos of Rulkov map-based neuron network with electrical synapse

    NASA Astrophysics Data System (ADS)

    Wang, Caixia; Cao, Hongjun

    2015-02-01

    In this paper, stability and chaos of a simple system consisting of two identical Rulkov map-based neurons with the bidirectional electrical synapse are investigated in detail. On the one hand, as a function of control parameters and electrical coupling strengthes, the conditions for stability of fixed points of this system are obtained by using the qualitative analysis. On the other hand, chaos in the sense of Marotto is proved by a strict mathematical way. These results could be useful for building-up large-scale neurons networks with specific dynamics and rich biophysical phenomena.

  14. Chaos for cardiac arrhythmias through a one-dimensional modulation equation for alternans

    PubMed Central

    Dai, Shu; Schaeffer, David G.

    2010-01-01

    Instabilities in cardiac dynamics have been widely investigated in recent years. One facet of this work has studied chaotic behavior, especially possible correlations with fatal arrhythmias. Previously chaotic behavior was observed in various models, specifically in the breakup of spiral and scroll waves. In this paper we study cardiac dynamics and find spatiotemporal chaotic behavior through the Echebarria–Karma modulation equation for alternans in one dimension. Although extreme parameter values are required to produce chaos in this model, it seems significant mathematically that chaos may occur by a different mechanism from previous observations. PMID:20590327

  15. Chaos Phenomena in a Current-Programmed Forward Converter Via Varying Load Resistance

    NASA Astrophysics Data System (ADS)

    Hsieh, Fei-Hu; Pan, Yi-Bin; Hsieh, Chun-Che

    This paper investigates the chaos phenomena in a current-programmed forward converter, then mathematical model is derived. IsSpice is used to construct simulation circuits of the converter whose operating under vary load resistance parameter. The output voltage, inductor current waveforms and vo - iL phase-plane portraits are observed. It can be seen that the system exhibits nonlinear dynamics form period-one operation through period-doubling to chaos phenomena as the load resistance are changed. Final, the experimental circuits are implemented and measured, the waveforms of output voltage, inductance current, phase-plane portraits which verified the accuracy of the circuit models.

  16. Order-to-chaos transition in the hardness of random Boolean satisfiability problems

    NASA Astrophysics Data System (ADS)

    Varga, Melinda; Sumi, Robert; Ercsey-Ravasz, Maria; Toroczkai, Zoltan

    Transient chaos is a phenomenon characterizing the dynamics of phase space trajectories evolving towards an attractor in physical systems. We show that transient chaos also appears in the dynamics of certain algorithms searching for solutions of constraint satisfaction problems (e.g., Sudoku). We present a study of the emergence of hardness in Boolean satisfiability (k-SAT) using an analog deterministic algorithm. Problem hardness is defined through the escape rate κ, an invariant measure of transient chaos, and it expresses the rate at which the trajectory approaches a solution. We show that the hardness in random k-SAT ensembles has a wide variation approximable by a lognormal distribution. We also show that when increasing the density of constraints α, hardness appears through a second-order phase transition at αc in the random 3-SAT ensemble where dynamical trajectories become transiently chaotic, however, such transition does not occur for 2-SAT. This behavior also implies a novel type of transient chaos in which the escape rate has an exponential-algebraic dependence on the critical parameter. We demonstrate that the transition is generated by the appearance of non-solution basins in the solution space as the density of constraints is increased.

  17. 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.

  18. Analysis of heart rate variability signal during meditation using deterministic-chaotic quantifiers.

    PubMed

    Kamath, Chandrakar

    2013-10-01

    This study investigated the level of chaos and the existence of fractal patterns in the heart rate variability (HRV) signal prior to meditation and during meditation using two quantifiers adapted from non-linear dynamics and deterministic chaos theory: (1) component central tendency measures (CCTMs) and (2) Higuchi fractal dimension (HFD). CCTM quantifies degree of variability/chaos in the specified quadrant of the second-order difference plot for HRV time series, while HFD quantifies dimensional complexity of the HRV series. Both the quantifiers yielded excellent results in discriminating the different psychophysiological states. The study found (1) significantly higher first quadrant CCTM values and (2) significantly lower HFD values during meditation state compared to pre-meditation state. Both of these can be attributed to the respiratory-modulated oscillations shifting to the lower frequency region by parasympathetic tone during meditation. It is thought that these quantifiers are most promising in providing new insight into the evolution of complexity of underlying dynamics in different physiological states. PMID:24044586

  19. Effect of parametric variation on generation and enhancement of chaos in erbium-doped fiber-ring lasers

    NASA Astrophysics Data System (ADS)

    Ali, Syed Zafar; Islam, Muhammad Khawar; Zafrullah, Muhammad

    2010-10-01

    The simulation and numerical analysis of erbium-doped fiber-ring lasers for generation and enhancement of chaos is presented. The degree of chaos determines the level of security in chaotic optical communication systems. Various parameters such as pump power, modulation index, modulation frequency, decay rate, and cavity gain can be varied as a control in producing higher degree optical chaos. The effect of each pertinent model parameter is analyzed in time-expanded mode using a phase plot direct-observation method and time series analysis of the time domain wave form by calculating its Lyapunov exponents. The mathematical and numerical analysis of the generated chaos helps in generalizing the trend through variation of cavity parameters and driving conditions in achieving a relatively higher degree of chaos. These trends help in optimizing various parameters for generation of new sequences of optical chaos in realizing better security. To gain an insight into chaotic signatures, the width and height of individual pulses, relationship of their time periods, gain quenching, shape, formation of bunches, and humps of the chaotic wave forms are also analyzed. The study of individual and cumulative behavior of all the parameters in enhancing optical chaos leads toward a reliable development in designing secure communication systems.

  20. Increasing average period lengths by switching of robust chaos maps in finite precision

    NASA Astrophysics Data System (ADS)

    Nagaraj, N.; Shastry, M. C.; Vaidya, P. G.

    2008-12-01

    Grebogi, Ott and Yorke (Phys. Rev. A 38, 1988) have investigated the effect of finite precision on average period length of chaotic maps. They showed that the average length of periodic orbits (T) of a dynamical system scales as a function of computer precision (ɛ) and the correlation dimension (d) of the chaotic attractor: T ˜ɛ-d/2. In this work, we are concerned with increasing the average period length which is desirable for chaotic cryptography applications. Our experiments reveal that random and chaotic switching of deterministic chaotic dynamical systems yield higher average length of periodic orbits as compared to simple sequential switching or absence of switching. To illustrate the application of switching, a novel generalization of the Logistic map that exhibits Robust Chaos (absence of attracting periodic orbits) is first introduced. We then propose a pseudo-random number generator based on chaotic switching between Robust Chaos maps which is found to successfully pass stringent statistical tests of randomness.

  1. 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.

  2. 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

  3. Characteristic Spaces Emerging from Primitive Chaos

    NASA Astrophysics Data System (ADS)

    Ogasawara, Yoshihito; Oishi, Shin'ichi

    2014-01-01

    This paper describes the emergence of two characteristic notions, nondegenerate Peano continuum and Cantor set, by the exploration of the essence of the existence of primitive chaos from a topological viewpoint. The primitive chaos is closely related to vital problems in physics itself and leads to chaotic features under natural conditions. The nondegenerate Peano continuum represents an ordinarily observed space, and the existence of a single nondegenerate Peano continuum guarantees the existence of infinite varieties of the primitive chaos leading to the chaos. This result provides an explanation of the reason why we are surrounded by diverse chaotic behaviors. Also, the Cantor set is a general or universal notion different from the special set, the Cantor middle-third set, and the existence of a single Cantor set guarantees infinite varieties of the primitive chaos leading to the chaos. This analogy implies the potential of the Cantor set for the method of new recognizing physical phenomena.

  4. 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.

  5. 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…

  6. The evolution from weak to strong geomagnetic activity - An interpretation in terms of deterministic chaos

    NASA Technical Reports Server (NTRS)

    Baker, D. N.; Klimas, A. J.; Mcpherron, R. L.; Buechner, J.

    1990-01-01

    An analogue of the magnetosphere developed on the basis of Shaw's (1984) dripping faucet model was used to model the mechanisms of the magnetospheric response to energy transfer from the solar wind. It is demonstrated that geomagnetic activity results from nonlinearly coupled physical processes and that the strength and the nature of the coupling changes dramatically as the magnetosphere is driven harder and harder by increasing energy input. Based on initial results obtained from the model, is is suggested that a chaotic transition takes place in the analogue system as the loading rate is increased beyond a critical value. This model is able to explain many of the features in the results of linear prediction filtering techniques.

  7. Spatial variation of deterministic chaos in mean daily temperature and rainfall over Nigeria

    NASA Astrophysics Data System (ADS)

    Fuwape, I. A.; Ogunjo, S. T.; Oluyamo, S. S.; Rabiu, A. B.

    2016-07-01

    Daily rainfall and temperature data from 47 locations across Nigeria for the 36-year period 1979-2014 were treated to time series analysis technique to investigate some nonlinear trends in rainfall and temperature data. Some quantifiers such as Lyapunov exponents, correlation dimension, and entropy were obtained for the various locations. Positive Lyapunov exponents were obtained for the time series of mean daily rainfall for all locations in the southern part of Nigeria while negative Lyapunov exponents were obtained for all locations in the Northern part of Nigeria. The mean daily temperature had positive Lyapunov exponent values (0.35-1.6) for all the locations. Attempts were made in reconstructing the phase space of time series of rainfall and temperature.

  8. 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.

  9. 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.

  10. Magnetic field induced dynamical chaos

    SciTech Connect

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

    2013-12-15

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

  11. 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.

  12. Quantum chaos: An entropy approach

    NASA Astrophysics Data System (ADS)

    Sl/omczyński, Wojciech; Życzkowski, Karol

    1994-11-01

    A new definition of the entropy of a given dynamical system and of an instrument describing the measurement process is proposed within the operational approach to quantum mechanics. It generalizes other definitions of entropy, in both the classical and quantum cases. The Kolmogorov-Sinai (KS) entropy is obtained for a classical system and the sharp measurement instrument. For a quantum system and a coherent states instrument, a new quantity, coherent states entropy, is defined. It may be used to measure chaos in quantum mechanics. The following correspondence principle is proved: the upper limit of the coherent states entropy of a quantum map as ℏ→0 is less than or equal to the KS-entropy of the corresponding classical map. ``Chaos umpire sits, And by decision more imbroils the fray By which he reigns: next him high arbiter Chance governs all.'' John Milton, Paradise Lost, Book II

  13. 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.

  14. Master stability analysis in transient spatiotemporal chaos.

    PubMed

    Wackerbauer, Renate

    2007-11-01

    The asymptotic stability of spatiotemporal chaos is difficult to determine, since transient spatiotemporal chaos may be extremely long lived. A master stability analysis reveals that the asymptotic state of transient spatiotemporal chaos in the Gray-Scott system and in the Bär-Eiswirth system is characterized by negative transverse Lyapunov exponents on the attractor of the invariant synchronization manifold. The average lifetime of transient spatiotemporal chaos depends on the number of transverse directions that are unstable along a typical excitation cycle. PMID:18233739

  15. Price-Dynamics of Shares and Bohmian Mechanics: Deterministic or Stochastic Model?

    NASA Astrophysics Data System (ADS)

    Choustova, Olga

    2007-02-01

    We apply the mathematical formalism of Bohmian mechanics to describe dynamics of shares. The main distinguishing feature of the financial Bohmian model is the possibility to take into account market psychology by describing expectations of traders by the pilot wave. We also discuss some objections (coming from conventional financial mathematics of stochastic processes) against the deterministic Bohmian model. In particular, the objection that such a model contradicts to the efficient market hypothesis which is the cornerstone of the modern market ideology. Another objection is of pure mathematical nature: it is related to the quadratic variation of price trajectories. One possibility to reply to this critique is to consider the stochastic Bohm-Vigier model, instead of the deterministic one. We do this in the present note.

  16. 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.

  17. The World According to Malthus and Volterra: The Mathematical Theory of the Struggle for Existence.

    ERIC Educational Resources Information Center

    Bogdanov, Constantine

    1992-01-01

    Discusses the mathematical model presented by Vito Volterra to describe the dynamics of population density. Discusses the predator prey relationship, presents an computer simulated model from marine life involving sharks and mackerels, and discusses ecological chaos. (MDH)

  18. 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

  19. 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.}

  20. Chaos in daisyworld

    NASA Astrophysics Data System (ADS)

    Zeng, Xubin; Pielke, R. A.; Eykholt, R.

    1990-09-01

    Lovelock proposed a concept, referred to as Gaia, in which feedbacks from the biosphere minimize fluctuation in climatic conditions. A simple model, referred to as daisyworld, was later developed to illustrate the Gaia concept. Daisyworld is defined on a cloudless flat or cylindrical planet with negligible atmospheric greenhouse gases in which bare soil and daisies of different colors interact so as to maintain stable climatic conditions. In the current paper, this daisyworld model is used to study the interaction between biota and their environment in more detail. It is found that periodic, and even chaotic, states can exist when the parameter controlling the feedback between biota and environmental temperature is changed. The existence of periodic and chaotic solutions is verified by their power spectra, fractal dimensions, and Lyapunov exponents. These results show that stable climatic conditions are not always maintained in daisyworld, despite the presence of daisies which supply the required feedback. While daisyworld is a simple model, the mathematical analysis of this model raises questions about the validity of the Gaia hypothesis.

  1. 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.

  2. Topological chaos of the spatial prisoner's dilemma game on regular networks.

    PubMed

    Jin, Weifeng; Chen, Fangyue

    2016-02-21

    The spatial version of evolutionary prisoner's dilemma on infinitely large regular lattice with purely deterministic strategies and no memories among players is investigated in this paper. Based on the statistical inferences, it is pertinent to confirm that the frequency of cooperation for characterizing its macroscopic behaviors is very sensitive to the initial conditions, which is the most practically significant property of chaos. Its intrinsic complexity is then justified on firm ground from the theory of symbolic dynamics; that is, this game is topologically mixing and possesses positive topological entropy on its subsystems. It is demonstrated therefore that its frequency of cooperation could not be adopted by simply averaging over several steps after the game reaches the equilibrium state. Furthermore, the chaotically changing spatial patterns via empirical observations can be defined and justified in view of symbolic dynamics. It is worth mentioning that the procedure proposed in this work is also applicable to other deterministic spatial evolutionary games therein. PMID:26646768

  3. How Complex, Probable, and Predictable is Genetically Driven Red Queen Chaos?

    PubMed

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

    2015-12-01

    Coevolution between two antagonistic species has been widely studied theoretically for both ecologically- and genetically-driven Red Queen dynamics. A typical outcome of these systems is an oscillatory behavior causing an endless series of one species adaptation and others counter-adaptation. More recently, a mathematical model combining a three-species food chain system with an adaptive dynamics approach revealed genetically driven chaotic Red Queen coevolution. In the present article, we analyze this mathematical model mainly focusing on the impact of species rates of evolution (mutation rates) in the dynamics. Firstly, we analytically proof the boundedness of the trajectories of the chaotic attractor. The complexity of the coupling between the dynamical variables is quantified using observability indices. By using symbolic dynamics theory, we quantify the complexity of genetically driven Red Queen chaos computing the topological entropy of existing one-dimensional iterated maps using Markov partitions. Co-dimensional two bifurcation diagrams are also built from the period ordering of the orbits of the maps. Then, we study the predictability of the Red Queen chaos, found in narrow regions of mutation rates. To extend the previous analyses, we also computed the likeliness of finding chaos in a given region of the parameter space varying other model parameters simultaneously. Such analyses allowed us to compute a mean predictability measure for the system in the explored region of the parameter space. We found that genetically driven Red Queen chaos, although being restricted to small regions of the analyzed parameter space, might be highly unpredictable. PMID:26018821

  4. 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.

  5. 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…

  6. Strange Attractors: Chaos Theory and Composition Studies.

    ERIC Educational Resources Information Center

    Hesse, Doug

    Chaos theory provides a powerful lens for re-seeing a number of issues in composition studies ranging in scale from achieving a generative model for text production to articulating the very nature of the discipline. Chaos systems are nonlinear, have complex forms, manifest recursive symmetries between scale levels, have feedback mechanisms, and…

  7. Risk-based and deterministic regulation

    SciTech Connect

    Fischer, L.E.; Brown, N.W.

    1995-07-01

    Both risk-based and deterministic methods are used for regulating the nuclear industry to protect the public safety and health from undue risk. The deterministic method is one where performance standards are specified for each kind of nuclear system or facility. The deterministic performance standards address normal operations and design basis events which include transient and accident conditions. The risk-based method uses probabilistic risk assessment methods to supplement the deterministic one by (1) addressing all possible events (including those beyond the design basis events), (2) using a systematic, logical process for identifying and evaluating accidents, and (3) considering alternative means to reduce accident frequency and/or consequences. Although both deterministic and risk-based methods have been successfully applied, there is need for a better understanding of their applications and supportive roles. This paper describes the relationship between the two methods and how they are used to develop and assess regulations in the nuclear industry. Preliminary guidance is suggested for determining the need for using risk based methods to supplement deterministic ones. However, it is recommended that more detailed guidance and criteria be developed for this purpose.

  8. 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.

  9. Chaos in a Water Drop.

    NASA Astrophysics Data System (ADS)

    Schneider, Scott Dudley

    Nature is chaotic. It appears to be more disorderly and random than orderly and regular. The path of a leaf in a rocky stream can appear as complex as the smoke from a cigarette or the outline of a cloud. In trying to model the path of a leaf in a rocky stream, the dynamical equations become rapidly complicated. A branch of scientific analysis know as Chaos has sprung up in the last few decades with techniques that can be applied to most of the physical sciences in an attempt to describe or categorize the various non-linear phenomena found in Nature. The aim of this paper is to provide an introduction to the study of chaotic behavior, with an emphasis on the potential teaching possibilities contained in some of the analysis. An appropriate beginning would be motion that is regular and "easy" to understand--stable motion. Along the way, various graphical representations will be developed that enable a clear viewing of the motion of the system under study. Next, the Logistic model will be used to gain an understanding of the nature of chaos; it is very comprehensive in representing the characteristics of chaos that will be studied in other systems. Another system studied is the three-dimensional Rossler model. In the study of the "dripping faucet", a time series of the periods between drips of water is recorded. Various techniques (collected from the introductory systems) are applied in an attempt to model the mechanism behind the water drops, or at least to characterize the graphical "animals" that we find. The water drop "attractor" is found to be chaotic, exhibiting many of the chaotic characteristics seen in other models. It is hoped that this work can be used as a primer for those students beginning a journey into Chaos, or as a reference tool for those already familiar with the topics enclosed. Many areas in this work were touched lightly; there is a rich un-tapped complexity still waiting future study. The waters here have only begun to be charted.

  10. Optical textures: characterizing spatiotemporal chaos.

    PubMed

    Clerc, Marcel G; González-Cortés, Gregorio; Odent, Vincent; Wilson, Mario

    2016-07-11

    Macroscopic systems subjected to injection and dissipation of energy can exhibit complex spatiotemporal behaviors as result of dissipative self-organization. Here, we report a one- and two-dimensional pattern forming setup, which exhibits a transition from stationary patterns to spatiotemporal chaotic textures, based on a nematic liquid crystal layer with spatially modulated input beam and optical feedback. Using an adequate projection of spatiotemporal diagrams, we determine the largest Lyapunov exponent. Jointly, this exponent and Fourier transform allow us to distinguish between spatiotemporal chaos and amplitude turbulence concepts, which are usually merged. PMID:27410822

  11. PT-Symmetric Wave Chaos

    NASA Astrophysics Data System (ADS)

    West, Carl T.; Kottos, Tsampikos; Prosen, Tomaž

    2010-02-01

    We study a new class of chaotic systems with dynamical localization, where gain or loss mechanisms break the Hermiticity, while allowing for parity-time (PT) symmetry. For a value γPT of the gain or loss parameter the spectrum undergoes a spontaneous phase transition from real (exact phase) to complex values (broken phase). We develop a one parameter scaling theory for γPT, and show that chaos assists the exact PT phase. Our results have applications to the design of optical elements with PT symmetry.

  12. 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.

  13. 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.

  14. 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

  15. Improving ground-penetrating radar data in sedimentary rocks using deterministic deconvolution

    USGS Publications Warehouse

    Xia, J.; Franseen, E.K.; Miller, R.D.; Weis, T.V.; Byrnes, A.P.

    2003-01-01

    Resolution is key to confidently identifying unique geologic features using ground-penetrating radar (GPR) data. Source wavelet "ringing" (related to bandwidth) in a GPR section limits resolution because of wavelet interference, and can smear reflections in time and/or space. The resultant potential for misinterpretation limits the usefulness of GPR. Deconvolution offers the ability to compress the source wavelet and improve temporal resolution. Unlike statistical deconvolution, deterministic deconvolution is mathematically simple and stable while providing the highest possible resolution because it uses the source wavelet unique to the specific radar equipment. Source wavelets generated in, transmitted through and acquired from air allow successful application of deterministic approaches to wavelet suppression. We demonstrate the validity of using a source wavelet acquired in air as the operator for deterministic deconvolution in a field application using "400-MHz" antennas at a quarry site characterized by interbedded carbonates with shale partings. We collected GPR data on a bench adjacent to cleanly exposed quarry faces in which we placed conductive rods to provide conclusive groundtruth for this approach to deconvolution. The best deconvolution results, which are confirmed by the conductive rods for the 400-MHz antenna tests, were observed for wavelets acquired when the transmitter and receiver were separated by 0.3 m. Applying deterministic deconvolution to GPR data collected in sedimentary strata at our study site resulted in an improvement in resolution (50%) and improved spatial location (0.10-0.15 m) of geologic features compared to the same data processed without deterministic deconvolution. The effectiveness of deterministic deconvolution for increased resolution and spatial accuracy of specific geologic features is further demonstrated by comparing results of deconvolved data with nondeconvolved data acquired along a 30-m transect immediately adjacent

  16. Quantifying chaos for ecological stoichiometry

    NASA Astrophysics Data System (ADS)

    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.

  17. Half-Lives and Chaos

    NASA Astrophysics Data System (ADS)

    McHarris, Wm. C.

    1999-10-01

    The statistical nature of quantum mechanical transitions has often led to a comparison of half-lives of, say, nuclear transitions with the predictions of actuarial tables---although impossible to predict when an individual will transform, statistically one can obtain precise population predictions. For complex biological systems this is quite believable, but in ``simple" nuclear systems, the analogy is more questionable. Another way of looking at this is through feedback in non-linear systems. In many chaos games, e.g., varied, unpredictable starting points will always arrive at one or a few end points, but they take widely varying numbers of moves and routes to reach such end positions---this is the essence of chaotic attractors. Using the Uncertainty Principle to justify slightly varying initial states, one can play similar chaos games with quantum mechanical systems, and it is possible to arrive at the final destination(s) with predictable half-lives. Some simple examples of such transitions, as relating to nuclear transitions, will be presented.

  18. Invoking the muse: Dada's chaos.

    PubMed

    Rosen, Diane

    2014-07-01

    Dada, a self-proclaimed (anti)art (non)movement, took shape in 1916 among a group of writers and artists who rejected the traditions of a stagnating bourgeoisie. Instead, they adopted means of creative expression that embraced chaos, stoked instability and undermined logic, an outburst that overturned centuries of classical and Romantic aesthetics. Paradoxically, this insistence on disorder foreshadowed a new order in understanding creativity. Nearly one hundred years later, Nonlinear Dynamical Systems theory (NDS) gives renewed currency to Dada's visionary perspective on chance, chaos and creative cognition. This paper explores commonalities between NDS-theory and this early precursor of the nonlinear paradigm, suggesting that their conceptual synergy illuminates what it means to 'be creative' beyond the disciplinary boundaries of either. Key features are discussed within a 5P model of creativity based on Rhodes' 4P framework (Person, Process, Press, Product), to which I add Participant-Viewer for the interactivity of observer-observed. Grounded in my own art practice, several techniques are then put forward as non-methodical methods that invoke creative border zones, those regions where Dada's chance and design are wedded in a dialectical tension of opposites. PMID:24894264

  19. 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.

  20. Classification and unification of the microscopic deterministic traffic models.

    PubMed

    Yang, Bo; Monterola, Christopher

    2015-10-01

    We identify a universal mathematical structure in microscopic deterministic traffic models (with identical drivers), and thus we show that all such existing models in the literature, including both the two-phase and three-phase models, can be understood as special cases of a master model by expansion around a set of well-defined ground states. This allows any two traffic models to be properly compared and identified. The three-phase models are characterized by the vanishing of leading orders of expansion within a certain density range, and as an example the popular intelligent driver model is shown to be equivalent to a generalized optimal velocity (OV) model. We also explore the diverse solutions of the generalized OV model that can be important both for understanding human driving behaviors and algorithms for autonomous driverless vehicles. PMID:26565284

  1. Classification and unification of the microscopic deterministic traffic models

    NASA Astrophysics Data System (ADS)

    Yang, Bo; Monterola, Christopher

    2015-10-01

    We identify a universal mathematical structure in microscopic deterministic traffic models (with identical drivers), and thus we show that all such existing models in the literature, including both the two-phase and three-phase models, can be understood as special cases of a master model by expansion around a set of well-defined ground states. This allows any two traffic models to be properly compared and identified. The three-phase models are characterized by the vanishing of leading orders of expansion within a certain density range, and as an example the popular intelligent driver model is shown to be equivalent to a generalized optimal velocity (OV) model. We also explore the diverse solutions of the generalized OV model that can be important both for understanding human driving behaviors and algorithms for autonomous driverless vehicles.

  2. Experimental evidence of deterministic coherence resonance in coupled chaotic systems with frequency mismatch

    NASA Astrophysics Data System (ADS)

    García-Vellisca, M. A.; Pisarchik, A. N.; Jaimes-Reátegui, R.

    2016-07-01

    We present the experimental evidence of deterministic coherence resonance in unidirectionally coupled two and three Rössler electronic oscillators with mismatch between their natural frequencies. The regularity in both the amplitude and the phase of chaotic fluctuations is experimentally proven by the analyses of normalized standard deviations of the peak amplitude and interpeak interval and Lyapunov exponents. The resonant chaos suppression appears when the coupling strength is increased and the oscillators are in phase synchronization. In two coupled oscillators, the coherence enhancement is associated with negative third and fourth Lyapunov exponents, while the largest first and second exponents remain positive. Distinctly, in three oscillators coupled in a ring, all exponents become negative, giving rise to periodicity. Numerical simulations are in good agreement with the experiments.

  3. 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.

  4. 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

  5. Stochastic search with Poisson and deterministic resetting

    NASA Astrophysics Data System (ADS)

    Bhat, Uttam; De Bacco, Caterina; Redner, S.

    2016-08-01

    We investigate a stochastic search process in one, two, and three dimensions in which N diffusing searchers that all start at x 0 seek a target at the origin. Each of the searchers is also reset to its starting point, either with rate r, or deterministically, with a reset time T. In one dimension and for a small number of searchers, the search time and the search cost are minimized at a non-zero optimal reset rate (or time), while for sufficiently large N, resetting always hinders the search. In general, a single searcher leads to the minimum search cost in one, two, and three dimensions. When the resetting is deterministic, several unexpected feature arise for N searchers, including the search time being independent of T for 1/T\\to 0 and the search cost being independent of N over a suitable range of N. Moreover, deterministic resetting typically leads to a lower search cost than in Poisson resetting.

  6. Optimal partial deterministic quantum teleportation of qubits

    SciTech Connect

    Mista, Ladislav Jr.; Filip, Radim

    2005-02-01

    We propose a protocol implementing optimal partial deterministic quantum teleportation for qubits. This is a teleportation scheme realizing deterministically an optimal 1{yields}2 asymmetric universal cloning where one imperfect copy of the input state emerges at the sender's station while the other copy emerges at receiver's possibly distant station. The optimality means that the fidelities of the copies saturate the asymmetric cloning inequality. The performance of the protocol relies on the partial deterministic nondemolition Bell measurement that allows us to continuously control the flow of information among the outgoing qubits. We also demonstrate that the measurement is optimal two-qubit operation in the sense of the trade-off between the state disturbance and the information gain.

  7. Deterministic evolutionary game dynamics in finite populations.

    PubMed

    Altrock, Philipp M; Traulsen, Arne

    2009-07-01

    Evolutionary game dynamics describes the spreading of successful strategies in a population of reproducing individuals. Typically, the microscopic definition of strategy spreading is stochastic such that the dynamics becomes deterministic only in infinitely large populations. Here, we present a microscopic birth-death process that has a fully deterministic strong selection limit in well-mixed populations of any size. Additionally, under weak selection, from this process the frequency-dependent Moran process is recovered. This makes it a natural extension of the usual evolutionary dynamics under weak selection. We find simple expressions for the fixation probabilities and average fixation times of the process in evolutionary games with two players and two strategies. For cyclic games with two players and three strategies, we show that the resulting deterministic dynamics crucially depends on the initial condition in a nontrivial way. PMID:19658731

  8. Effect of Uncertainty on Deterministic Runway Scheduling

    NASA Technical Reports Server (NTRS)

    Gupta, Gautam; Malik, Waqar; Jung, Yoon C.

    2012-01-01

    Active runway scheduling involves scheduling departures for takeoffs and arrivals for runway crossing subject to numerous constraints. This paper evaluates the effect of uncertainty on a deterministic runway scheduler. The evaluation is done against a first-come- first-serve scheme. In particular, the sequence from a deterministic scheduler is frozen and the times adjusted to satisfy all separation criteria; this approach is tested against FCFS. The comparison is done for both system performance (throughput and system delay) and predictability, and varying levels of congestion are considered. The modeling of uncertainty is done in two ways: as equal uncertainty in availability at the runway as for all aircraft, and as increasing uncertainty for later aircraft. Results indicate that the deterministic approach consistently performs better than first-come-first-serve in both system performance and predictability.

  9. Chaos-order transition in foraging behavior of ants.

    PubMed

    Li, Lixiang; Peng, Haipeng; Kurths, Jürgen; Yang, Yixian; Schellnhuber, Hans Joachim

    2014-06-10

    The study of the foraging behavior of group animals (especially ants) is of practical ecological importance, but it also contributes to the development of widely applicable optimization problem-solving techniques. Biologists have discovered that single ants exhibit low-dimensional deterministic-chaotic activities. However, the influences of the nest, ants' physical abilities, and ants' knowledge (or experience) on foraging behavior have received relatively little attention in studies of the collective behavior of ants. This paper provides new insights into basic mechanisms of effective foraging for social insects or group animals that have a home. We propose that the whole foraging process of ants is controlled by three successive strategies: hunting, homing, and path building. A mathematical model is developed to study this complex scheme. We show that the transition from chaotic to periodic regimes observed in our model results from an optimization scheme for group animals with a home. According to our investigation, the behavior of such insects is not represented by random but rather deterministic walks (as generated by deterministic dynamical systems, e.g., by maps) in a random environment: the animals use their intelligence and experience to guide them. The more knowledge an ant has, the higher its foraging efficiency is. When young insects join the collective to forage with old and middle-aged ants, it benefits the whole colony in the long run. The resulting strategy can even be optimal. PMID:24912159

  10. Deterministic mediated superdense coding with linear optics

    NASA Astrophysics Data System (ADS)

    Pavičić, Mladen

    2016-02-01

    We present a scheme of deterministic mediated superdense coding of entangled photon states employing only linear-optics elements. Ideally, we are able to deterministically transfer four messages by manipulating just one of the photons. Two degrees of freedom, polarization and spatial, are used. A new kind of source of heralded down-converted photon pairs conditioned on detection of another pair with an efficiency of 92% is proposed. Realistic probabilistic experimental verification of the scheme with such a source of preselected pairs is feasible with today's technology. We obtain the channel capacity of 1.78 bits for a full-fledged implementation.

  11. Deterministic aggregation kinetics of superparamagnetic colloidal particles

    NASA Astrophysics Data System (ADS)

    Reynolds, Colin P.; Klop, Kira E.; Lavergne, François A.; Morrow, Sarah M.; Aarts, Dirk G. A. L.; Dullens, Roel P. A.

    2015-12-01

    We study the irreversible aggregation kinetics of superparamagnetic colloidal particles in two dimensions in the presence of an in-plane magnetic field at low packing fractions. Optical microscopy and image analysis techniques are used to follow the aggregation process and in particular study the packing fraction and field dependence of the mean cluster size. We compare these to the theoretically predicted scalings for diffusion limited and deterministic aggregation. It is shown that the aggregation kinetics for our experimental system is consistent with a deterministic mechanism, which thus shows that the contribution of diffusion is negligible.

  12. Nine challenges for deterministic epidemic models

    PubMed Central

    Roberts, Mick; Andreasen, Viggo; Lloyd, Alun; Pellis, Lorenzo

    2016-01-01

    Deterministic models have a long history of being applied to the study of infectious disease epidemiology. We highlight and discuss nine challenges in this area. The first two concern the endemic equilibrium and its stability. We indicate the need for models that describe multi-strain infections, infections with time-varying infectivity, and those where super infection is possible. We then consider the need for advances in spatial epidemic models, and draw attention to the lack of models that explore the relationship between communicable and non-communicable diseases. The final two challenges concern the uses and limitations of deterministic models as approximations to stochastic systems. PMID:25843383

  13. Delay driven spatiotemporal chaos in single species population dynamics models.

    PubMed

    Jankovic, Masha; Petrovskii, Sergei; Banerjee, Malay

    2016-08-01

    Questions surrounding the prevalence of complex population dynamics form one of the central themes in ecology. Limit cycles and spatiotemporal chaos are examples that have been widely recognised theoretically, although their importance and applicability to natural populations remains debatable. The ecological processes underlying such dynamics are thought to be numerous, though there seems to be consent as to delayed density dependence being one of the main driving forces. Indeed, time delay is a common feature of many ecological systems and can significantly influence population dynamics. In general, time delays may arise from inter- and intra-specific trophic interactions or population structure, however in the context of single species populations they are linked to more intrinsic biological phenomena such as gestation or resource regeneration. In this paper, we consider theoretically the spatiotemporal dynamics of a single species population using two different mathematical formulations. Firstly, we revisit the diffusive logistic equation in which the per capita growth is a function of some specified delayed argument. We then modify the model by incorporating a spatial convolution which results in a biologically more viable integro-differential model. Using the combination of analytical and numerical techniques, we investigate the effect of time delay on pattern formation. In particular, we show that for sufficiently large values of time delay the system's dynamics are indicative to spatiotemporal chaos. The chaotic dynamics arising in the wake of a travelling population front can be preceded by either a plateau corresponding to dynamical stabilisation of the unstable equilibrium or by periodic oscillations. PMID:27154920

  14. Entanglement across a transition to quantum chaos

    SciTech Connect

    Mejia-Monasterio, Carlos; Benenti, Guliano; Casati, Giulio; Carlo, Gabriel G.

    2005-06-15

    We study the relation between entanglement and quantum chaos in one- and two-dimensional spin-1/2 lattice models, which exhibit mixing of the noninteracting eigenfunctions and transition from integrability to quantum chaos. Contrary to what occurs in a quantum phase transition, the onset of quantum chaos is not a property of the ground state but takes place for any typical many-spin quantum state. We study bipartite and pairwise entanglement measures--namely, the reduced von Neumann entropy and the concurrence--and discuss quantum entanglement sharing. Our results suggest that the behavior of the entanglement is related to the mixing of the eigenfunctions rather than to the transition to chaos.

  15. 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.

  16. Gaussian Multiplicative Chaos for Symmetric Isotropic Matrices

    NASA Astrophysics Data System (ADS)

    Chevillard, Laurent; Rhodes, Rémi; Vargas, Vincent

    2013-02-01

    Motivated by isotropic fully developed turbulence, we define a theory of symmetric matrix valued isotropic Gaussian multiplicative chaos. Our construction extends the scalar theory developed by J.P. Kahane in 1985.

  17. Temporal chaos in Boussinesq magnetoconvection

    SciTech Connect

    Bekki, Naoaki; Moriguchi, Hirofumi

    2007-01-15

    Two-dimensional Boussinesq magnetoconvection with idealized stress-free boundary conditions is numerically investigated in order to make clear the difference between chaos and turbulence. It is shown that the long-term behavior of magnetoconvection exhibits spatially coherent and temporally chaotic rolls in marked contrast to highly turbulent fluids. It is also shown that heat transport becomes larger anomalously when the polarity reversal of the magnetic field occurs intermittently in the case of temporally chaotic magnetoconvection. It is found that the Poincare return map of the relative maximum temperature fluctuation of partial differential equations as a function of the preceding maximum resembles the famous Lorenz plot in narrow rolls of magnetoconvection. The chaotic behavior of narrow rolls for individual parameter values robustly persists up to rolls about one fifth as wide as they are high near the codimension-two bifurcation point.

  18. Rotational chaos in dissipative systems

    NASA Astrophysics Data System (ADS)

    Casdagli, Martin

    1988-01-01

    An investigation is made into chaotic attractors arising from a quasiperiodic transition to chaos, using a quantity called the rotation interval. The rotation interval describes the short term rotation rates available to the attractor. We present algorithms to calculate it given an appropriate map, differential equation or time series. We find that the rotation interval has a very robust parameter dependence: its endpoints are almost always phase locked. Our numerical ideas are based on the theory of dissipative twist maps, which is reviewed. This theory is also used to prove a theorem about the non-existence of certain strange attractors in nearly conservative systems. Finally, an investigation is made into the relationship between the rotation interval and topological entropy, and the breakup of invariant circles.

  19. 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

  20. 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

  1. 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.

  2. Finite-dimensional models of diffusion chaos

    NASA Astrophysics Data System (ADS)

    Glyzin, S. D.; Kolesov, A. Yu.; Rozov, N. Kh.

    2010-05-01

    Some parabolic systems of the reaction-diffusion type exhibit the phenomenon of diffusion chaos. Specifically, when the diffusivities decrease proportionally, while the other parameters of a system remain fixed, the system exhibits a chaotic attractor whose dimension increases indefinitely. Various finite-dimensional models of diffusion chaos are considered that represent chains of coupled ordinary differential equations and similar chains of discrete mappings. A numerical analysis suggests that these chains with suitably chosen parameters exhibit chaotic attractors of arbitrarily high dimensions.

  3. Order-to-chaos transition in the hardness of random Boolean satisfiability problems

    NASA Astrophysics Data System (ADS)

    Varga, Melinda; Sumi, Róbert; Toroczkai, Zoltán; Ercsey-Ravasz, Mária

    2016-05-01

    Transient chaos is a ubiquitous phenomenon characterizing the dynamics of phase-space trajectories evolving towards a steady-state attractor in physical systems as diverse as fluids, chemical reactions, and condensed matter systems. Here we show that transient chaos also appears in the dynamics of certain efficient algorithms searching for solutions of constraint satisfaction problems that include scheduling, circuit design, routing, database problems, and even Sudoku. In particular, we present a study of the emergence of hardness in Boolean satisfiability (k -SAT), a canonical class of constraint satisfaction problems, by using an analog deterministic algorithm based on a system of ordinary differential equations. Problem hardness is defined through the escape rate κ , an invariant measure of transient chaos of the dynamical system corresponding to the analog algorithm, and it expresses the rate at which the trajectory approaches a solution. We show that for a given density of constraints and fixed number of Boolean variables N , the hardness of formulas in random k -SAT ensembles has a wide variation, approximable by a lognormal distribution. We also show that when increasing the density of constraints α , hardness appears through a second-order phase transition at αχ in the random 3-SAT ensemble where dynamical trajectories become transiently chaotic. A similar behavior is found in 4-SAT as well, however, such a transition does not occur for 2-SAT. This behavior also implies a novel type of transient chaos in which the escape rate has an exponential-algebraic dependence on the critical parameter κ ˜NB |α - αχ|1-γ with 0 <γ <1 . We demonstrate that the transition is generated by the appearance of metastable basins in the solution space as the density of constraints α is increased.

  4. Order-to-chaos transition in the hardness of random Boolean satisfiability problems.

    PubMed

    Varga, Melinda; Sumi, Róbert; Toroczkai, Zoltán; Ercsey-Ravasz, Mária

    2016-05-01

    Transient chaos is a ubiquitous phenomenon characterizing the dynamics of phase-space trajectories evolving towards a steady-state attractor in physical systems as diverse as fluids, chemical reactions, and condensed matter systems. Here we show that transient chaos also appears in the dynamics of certain efficient algorithms searching for solutions of constraint satisfaction problems that include scheduling, circuit design, routing, database problems, and even Sudoku. In particular, we present a study of the emergence of hardness in Boolean satisfiability (k-SAT), a canonical class of constraint satisfaction problems, by using an analog deterministic algorithm based on a system of ordinary differential equations. Problem hardness is defined through the escape rate κ, an invariant measure of transient chaos of the dynamical system corresponding to the analog algorithm, and it expresses the rate at which the trajectory approaches a solution. We show that for a given density of constraints and fixed number of Boolean variables N, the hardness of formulas in random k-SAT ensembles has a wide variation, approximable by a lognormal distribution. We also show that when increasing the density of constraints α, hardness appears through a second-order phase transition at α_{χ} in the random 3-SAT ensemble where dynamical trajectories become transiently chaotic. A similar behavior is found in 4-SAT as well, however, such a transition does not occur for 2-SAT. This behavior also implies a novel type of transient chaos in which the escape rate has an exponential-algebraic dependence on the critical parameter κ∼N^{B|α-α_{χ}|^{1-γ}} with 0<γ<1. We demonstrate that the transition is generated by the appearance of metastable basins in the solution space as the density of constraints α is increased. PMID:27300884

  5. A deterministic discrete ordinates transport proxy application

    Energy Science and Technology Software Center (ESTSC)

    2014-06-03

    Kripke is a simple 3D deterministic discrete ordinates (Sn) particle transport code that maintains the computational load and communications pattern of a real transport code. It is intended to be a research tool to explore different data layouts, new programming paradigms and computer architectures.

  6. STATISTICAL ANALYSIS OF A DETERMINISTIC STOCHASTIC ORBIT

    SciTech Connect

    Kaufman, Allan N.; Abarbanel, Henry D.I.; Grebogi, Celso

    1980-05-01

    If the solution of a deterministic equation is stochastic (in the sense of orbital instability), it can be subjected to a statistical analysis. This is illustrated for a coded orbit of the Chirikov mapping. Statistical dependence and the Markov assumption are tested. The Kolmogorov-Sinai entropy is related to the probability distribution for the orbit.

  7. Chaos control applied to cardiac rhythms represented by ECG signals

    NASA Astrophysics Data System (ADS)

    Borem Ferreira, Bianca; Amorim Savi, Marcelo; Souza de Paula, Aline

    2014-10-01

    The control of irregular or chaotic heartbeats is a key issue in cardiology. In this regard, chaos control techniques represent a good alternative since they suggest treatments different from those traditionally used. This paper deals with the application of the extended time-delayed feedback control method to stabilize pathological chaotic heart rhythms. Electrocardiogram (ECG) signals are employed to represent the cardiovascular behavior. A mathematical model is employed to generate ECG signals using three modified Van der Pol oscillators connected with time delay couplings. This model provides results that qualitatively capture the general behavior of the heart. Controlled ECG signals show the ability of the strategy either to control or to suppress the chaotic heart dynamics generating less-critical behaviors.

  8. Chaos in a spatially-developing plane mixing layer

    NASA Technical Reports Server (NTRS)

    Broze, J. G.; Hussain, Fazle; Buell, J. C.

    1988-01-01

    A spatially-developing plane mixing layer was analyzed for chaotic behavior. A direct numerical simulation of the Navier-Stokes equations in a 2-D domain infinite in y and having inflow-outflow boundary conditions in x was used for data. Spectra, correlation dimension and the largest Lyapunov exponent were computed as functions of downstream distance x. When forced at a single (fundamental) frequency with maximum amplitude, the flow is periodic at the inflow but becomes aperiodic with increasing x. The aperiodic behavior is caused by the presence of a noisy subharmonic caused by the feedback between the necessarily nonphysical inflow and outflow boundary conditions. In order to overshadow this noise the flow was also studied with the same fundamental forcing and added random forcing of amplitude upsilon prime sub R/delta U = 0.01 at the inlet. Results were qualitatively the same in both cases: for small x, spectral peaks were sharp and dimension was nearly 1, but as x increased a narrowband spectral peak grew, spectra decayed exponentially at high frequencies and dimension increased to greater than 3. Based on these results, the flow appears to exhibit deterministic chaos. However, at no location was the largest Lyapunov exponent found to be significantly greater than zero.

  9. Improving Deterministic Reserve Requirements for Security Constrained Unit Commitment and Scheduling Problems in Power Systems

    NASA Astrophysics Data System (ADS)

    Wang, Fengyu

    Traditional deterministic reserve requirements rely on ad-hoc, rule of thumb methods to determine adequate reserve in order to ensure a reliable unit commitment. Since congestion and uncertainties exist in the system, both the quantity and the location of reserves are essential to ensure system reliability and market efficiency. The modeling of operating reserves in the existing deterministic reserve requirements acquire the operating reserves on a zonal basis and do not fully capture the impact of congestion. The purpose of a reserve zone is to ensure that operating reserves are spread across the network. Operating reserves are shared inside each reserve zone, but intra-zonal congestion may block the deliverability of operating reserves within a zone. Thus, improving reserve policies such as reserve zones may improve the location and deliverability of reserve. As more non-dispatchable renewable resources are integrated into the grid, it will become increasingly difficult to predict the transfer capabilities and the network congestion. At the same time, renewable resources require operators to acquire more operating reserves. With existing deterministic reserve requirements unable to ensure optimal reserve locations, the importance of reserve location and reserve deliverability will increase. While stochastic programming can be used to determine reserve by explicitly modelling uncertainties, there are still scalability as well as pricing issues. Therefore, new methods to improve existing deterministic reserve requirements are desired. One key barrier of improving existing deterministic reserve requirements is its potential market impacts. A metric, quality of service, is proposed in this thesis to evaluate the price signal and market impacts of proposed hourly reserve zones. Three main goals of this thesis are: 1) to develop a theoretical and mathematical model to better locate reserve while maintaining the deterministic unit commitment and economic dispatch

  10. CaTs Lab (CHAOS and Thermal Sciences Laboratory)

    NASA Technical Reports Server (NTRS)

    Teate, Anthony A.

    2002-01-01

    The CHAOS and Thermal Sciences Laboratory (CaTs) at James Madison University evolved into a noteworthy effort to increase minority representation in the sciences and mathematics. Serving ten students and faculty directly, and nearly 50 students indirectly, CaTs, through recruitment efforts, workshops, mentoring programs, tutorial services and research and computational laboratories, fulfilled its intent to initiate an academically enriched research program aimed at strengthening the academic and self-actualization skills of undergraduate students with potential to pursue doctoral study in the sciences. The stated goal of the program was to increase by 5% the number of enrolled mathematics and science students into the program. Success far exceeded the program goals by producing 100% graduation rate of all supported recipients during its tenure, with 30% of the students subsequently in pursuit of graduate degrees. Student retention in the program exceeded 90% and faculty participation exceeded the three members involved in mentoring and tutoring, gaining multi-disciplinary support. Aggressive marketing of the program resulted in several paid summer internships and commitments from NASA and an ongoing relationship with CHROME, a nationally recognized organization which focuses on developing minority students in the sciences and mathematics. Success of the program was only limited by the limited fiscal resources at NASA which resulted in phasing out of the program.

  11. Mathematics Underground

    ERIC Educational Resources Information Center

    Luther, Kenneth H.

    2012-01-01

    Mathematical modeling of groundwater flow is a topic at the intersection of mathematics and geohydrology and is rarely encountered in undergraduate mathematics. However, this subject is full of interesting and meaningful examples of truly "applied" mathematics accessible to undergraduates, from the pre-calculus to advanced mathematics levels. This…

  12. Harvesting entropy and quantifying the transition from noise to chaos in a photon-counting feedback loop

    PubMed Central

    Hagerstrom, Aaron Morgan; Murphy, Thomas Edward; Roy, Rajarshi

    2015-01-01

    Many physical processes, including the intensity fluctuations of a chaotic laser, the detection of single photons, and the Brownian motion of a microscopic particle in a fluid are unpredictable, at least on long timescales. This unpredictability can be due to a variety of physical mechanisms, but it is quantified by an entropy rate. This rate, which describes how quickly a system produces new and random information, is fundamentally important in statistical mechanics and practically important for random number generation. We experimentally study entropy generation and the emergence of deterministic chaotic dynamics from discrete noise in a system that applies feedback to a weak optical signal at the single-photon level. We show that the dynamics transition from shot noise to chaos as the photon rate increases and that the entropy rate can reflect either the deterministic or noisy aspects of the system depending on the sampling rate and resolution. PMID:26175023

  13. Controlling influenza disease: Comparison between discrete time Markov chain and deterministic model

    NASA Astrophysics Data System (ADS)

    Novkaniza, F.; Ivana, Aldila, D.

    2016-04-01

    Mathematical model of respiratory diseases spread with Discrete Time Markov Chain (DTMC) and deterministic approach for constant total population size are analyzed and compared in this article. Intervention of medical treatment and use of medical mask included in to the model as a constant parameter to controlling influenza spreads. Equilibrium points and basic reproductive ratio as the endemic criteria and it level set depend on some variable are given analytically and numerically as a results from deterministic model analysis. Assuming total of human population is constant from deterministic model, number of infected people also analyzed with Discrete Time Markov Chain (DTMC) model. Since Δt → 0, we could assume that total number of infected people might change only from i to i + 1, i - 1, or i. Approximation probability of an outbreak with gambler's ruin problem will be presented. We find that no matter value of basic reproductive ℛ0, either its larger than one or smaller than one, number of infection will always tends to 0 for t → ∞. Some numerical simulation to compare between deterministic and DTMC approach is given to give a better interpretation and a better understanding about the models results.

  14. Deterministic dynamics in the minority game

    NASA Astrophysics Data System (ADS)

    Jefferies, P.; Hart, M. L.; Johnson, N. F.

    2002-01-01

    The minority game (MG) behaves as a stochastically disturbed deterministic system due to the coin toss invoked to resolve tied strategies. Averaging over this stochasticity yields a description of the MG's deterministic dynamics via mapping equations for the strategy score and global information. The strategy-score map contains both restoring-force and bias terms, whose magnitudes depend on the game's quenched disorder. Approximate analytical expressions are obtained and the effect of ``market impact'' is discussed. The global-information map represents a trajectory on a de Bruijn graph. For small quenched disorder, a Eulerian trail represents a stable attractor. It is shown analytically how antipersistence arises. The response to perturbations and different initial conditions is also discussed.

  15. The deterministic and statistical Burgers equation

    NASA Astrophysics Data System (ADS)

    Fournier, J.-D.; Frisch, U.

    Fourier-Lagrangian representations of the UV-region inviscid-limit solutions of the equations of Burgers (1939) are developed for deterministic and random initial conditions. The Fourier-mode amplitude behavior of the deterministic case is characterized by complex singularities with fast decrease, power-law preshocks with k indices of about -4/3, and shocks with k to the -1. In the random case, shocks are associated with a k to the -2 spectrum which overruns the smaller wavenumbers and appears immediately under Gaussian initial conditions. The use of the Hopf-Cole solution in the random case is illustrated in calculations of the law of energy decay by a modified Kida (1979) method. Graphs and diagrams of the results are provided.

  16. Regularly timed events amid chaos.

    PubMed

    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. PMID:26651759

  17. 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.

  18. Shape-Controlled Deterministic Assembly of Nanowires.

    PubMed

    Zhao, Yunlong; Yao, Jun; Xu, Lin; Mankin, Max N; Zhu, Yinbo; Wu, Hengan; Mai, Liqiang; Zhang, Qingjie; Lieber, Charles M

    2016-04-13

    Large-scale, deterministic assembly of nanowires and nanotubes with rationally controlled geometries could expand the potential applications of one-dimensional nanomaterials in bottom-up integrated nanodevice arrays and circuits. Control of the positions of straight nanowires and nanotubes has been achieved using several assembly methods, although simultaneous control of position and geometry has not been realized. Here, we demonstrate a new concept combining simultaneous assembly and guided shaping to achieve large-scale, high-precision shape controlled deterministic assembly of nanowires. We lithographically pattern U-shaped trenches and then shear transfer nanowires to the patterned substrate wafers, where the trenches serve to define the positions and shapes of transferred nanowires. Studies using semicircular trenches defined by electron-beam lithography yielded U-shaped nanowires with radii of curvature defined by inner surface of the trenches. Wafer-scale deterministic assembly produced U-shaped nanowires for >430,000 sites with a yield of ∼90%. In addition, mechanistic studies and simulations demonstrate that shaping results in primarily elastic deformation of the nanowires and show clearly the diameter-dependent limits achievable for accessible forces. Last, this approach was used to assemble U-shaped three-dimensional nanowire field-effect transistor bioprobe arrays containing 200 individually addressable nanodevices. By combining the strengths of wafer-scale top-down fabrication with diverse and tunable properties of one-dimensional building blocks in novel structural configurations, shape-controlled deterministic nanowire assembly is expected to enable new applications in many areas including nanobioelectronics and nanophotonics. PMID:26999059

  19. Ada programming guidelines for deterministic storage management

    NASA Technical Reports Server (NTRS)

    Auty, David

    1988-01-01

    Previous reports have established that a program can be written in the Ada language such that the program's storage management requirements are determinable prior to its execution. Specific guidelines for ensuring such deterministic usage of Ada dynamic storage requirements are described. Because requirements may vary from one application to another, guidelines are presented in a most-restrictive to least-restrictive fashion to allow the reader to match appropriate restrictions to the particular application area under investigation.

  20. 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

  1. 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

  2. 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.

  3. Deterministic Mean-Field Ensemble Kalman Filtering

    DOE PAGESBeta

    Law, Kody J. H.; Tembine, Hamidou; Tempone, Raul

    2016-05-03

    The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598--631] is extended to non-Gaussian state-space models. In this paper, a density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence κ between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d deterministic and standard EnKF. Numerical results support and extend the theory.« less

  4. Control design and robustness analysis of a ball and plate system by using polynomial chaos

    SciTech Connect

    Colón, Diego; Balthazar, José M.; Reis, Célia A. dos; Bueno, Átila M.; Diniz, Ivando S.; Rosa, Suelia de S. R. F.

    2014-12-10

    In this paper, we present a mathematical model of a ball and plate system, a control law and analyze its robustness properties by using the polynomial chaos method. The ball rolls without slipping. There is an auxiliary robot vision system that determines the bodies' positions and velocities, and is used for control purposes. The actuators are to orthogonal DC motors, that changes the plate's angles with the ground. The model is a extension of the ball and beam system and is highly nonlinear. The system is decoupled in two independent equations for coordinates x and y. Finally, the resulting nonlinear closed loop systems are analyzed by the polynomial chaos methodology, which considers that some system parameters are random variables, and generates statistical data that can be used in the robustness analysis.

  5. Control design and robustness analysis of a ball and plate system by using polynomial chaos

    NASA Astrophysics Data System (ADS)

    Colón, Diego; Balthazar, José M.; dos Reis, Célia A.; Bueno, Átila M.; Diniz, Ivando S.; de S. R. F. Rosa, Suelia

    2014-12-01

    In this paper, we present a mathematical model of a ball and plate system, a control law and analyze its robustness properties by using the polynomial chaos method. The ball rolls without slipping. There is an auxiliary robot vision system that determines the bodies' positions and velocities, and is used for control purposes. The actuators are to orthogonal DC motors, that changes the plate's angles with the ground. The model is a extension of the ball and beam system and is highly nonlinear. The system is decoupled in two independent equations for coordinates x and y. Finally, the resulting nonlinear closed loop systems are analyzed by the polynomial chaos methodology, which considers that some system parameters are random variables, and generates statistical data that can be used in the robustness analysis.

  6. 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

  7. Nicholas Steno's Chaos and the shaping of evolutionary thought in the Scientific Revolution

    NASA Astrophysics Data System (ADS)

    Rosenberg, Gary D.

    2006-09-01

    Nicholas Steno (1638 1686) compiled a notebook in 1659 when he was a student at the University of Copenhagen. Titled Chaos by Steno, it remains unstudied in English-speaking countries, despite having been translated in 1997. Chaos adds important insight into geology's place in the Scientific Revolution. It shows Steno disengaging from speculations about the cosmos based on the ruling paradigms of Aristotelian metaphysics and Cartesian misconceptions in favor of an empirical model based on the new mathematics of geometry applied to all of nature, from what we now would consider the atomic level, to the human body, and to the planet. Steno thereby earns heretofore unacknowledged credit for helping to establish the geometric definition of form that makes it possible to understand the evolution of the structure of organisms as well as of the planet.

  8. 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…

  9. 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…

  10. 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…

  11. Household Chaos--Links with Parenting and Child Behaviour

    ERIC Educational Resources Information Center

    Coldwell, Joanne; Pike, Alison; Dunn, Judy

    2006-01-01

    Background: The study aimed to confirm previous findings showing links between household chaos and parenting in addition to examining whether household chaos was predictive of children's behaviour over and above parenting. In addition, we investigated whether household chaos acts as a moderator between parenting and children's behaviour. Method:…

  12. Poincaré, celestial mechanics, dynamical-systems theory and ``chaos''

    NASA Astrophysics Data System (ADS)

    Holmes, Philip

    1990-09-01

    As demonstrated by the success of James Gleick's recent book [1987], there is considerable interest in the scientific community and among the general public in ``chaos'' and the ``new science'' which is supposed to accompany it. However, as usual, it is not easy to separate hyperbole from fact. In an attempt to do this, I will offer a precise definition of chaos in the context of differential equations: mathematical models which, since Newton, have played a vital role in scientific discovery. I will show how the classical problems of celestial mechanics led Poincaré to ask fundamental questions on the qualitative behavior of differential equations, and to realize that chaotic orbits would provide obstructions to the conventional methods of solving them. In a major paper which appeared almost exactly one hundred years ago, Poincaré studied mechanical systems with two degrees of freedom and identified an important class of solutions, now called transverse homoclinic orbits, the existence of which implies the system has no analytic integrals of motion other than the total (Hamiltonian) energy. I will explain these terms and outline the history of subsequent developments of these ideas by Birkhoff, Cartwright, Littlewood, Levinson and Smale, and describe how the ideas of Melnikov have made possible an ``analytical algorithm'' for the detection of chaos and proof of nonintegrability in wide classes of perturbed Hamiltonian systems. I will discuss the physical implications of the mathematical statements that these methods afford. In the process, I will point out that, while there is a precise vocabulary and grammar of chaos, developed largely by mathematicians and steaming from Poincaré's work, it is not always easy to use it in speaking of the real world.

  13. 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

  14. 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.

  15. Mathematics, Anyone?

    ERIC Educational Resources Information Center

    Reys, Robert; Reys, Rustin

    2011-01-01

    In their dual roles as mathematics teachers and tennis coaches, the authors have worked with tennis players who have never thought about how a knowledge of mathematics might help them become "better" tennis players. They have also worked with many mathematics students who have never considered how much mathematics is associated with tennis. This…

  16. Transition to chaos of thermocapillary convection

    NASA Astrophysics Data System (ADS)

    Li, Kai; Tang, Ze Mei; Aa, Yan; Hu, Wen-Rui

    Transition of fluid convection to chaos in dissipative dynamical systems is a subject of great interest for both its theoretical and practical aspects in the fluid mechanics. Extensive studies have shown that there are several routes of the buoyant natural convection to chaos depending on parameters of the dissipative dynamical systems such as the Rayleigh number, the Prandtl number and geometry aspect. Another important type of natural convection is thermocapillary convection driven by the surface-tension gradient prominent in fluid systems with interface in the microgravity condition or in small-scaled terrestrial configurations (The relative importance of the gravity effect to the capillary effect is scaled by the static Bond number, , and the dynamic Bond number, , the geometrical scale of the system in the terrestrial experiments, therefore, was significantly reduced to make the capillary effect dominant). The thermocapillary convection has become one of the fundamental subjects in the microgravity fluid physics and space fluid/heat management. However, most studies now available were focused on the onset of oscillatory thermocapillary convection, the initial regime of the route to chaos. A complete route to chaos in such a new sort of dissipative system is still an attractive open question, especially in the experimental study. In present study, the route to chaos of the thermocapillary convection has been investigated. Several routes to chaos, e.g. period oscillatory convection to quasi-period oscillatory convection with 2 to 3 major frequencies, a series of successive period doubling bifurcations and their combination, of the thermocapillary flow is reported through the temperature measurements and the corresponding real time analysis of frequency spectra accomplished by Fast-Fourier-Transformation (FFT) or numerically. The corresponding phase diagrams are also provided.

  17. 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. PMID:23556962

  18. Scaling of weighted spectral distribution in deterministic scale-free networks

    NASA Astrophysics Data System (ADS)

    Jiao, Bo; Nie, Yuan-ping; Shi, Jian-mai; Huang, Cheng-dong; Zhou, Ying; Du, Jing; Guo, Rong-hua; Tao, Ye-rong

    2016-06-01

    Scale-free networks are abundant in the real world. In this paper, we investigate the scaling properties of the weighted spectral distribution in several deterministic and stochastic models of evolving scale-free networks. First, we construct a new deterministic scale-free model whose node degrees have a unified format. Using graph structure features, we derive a precise formula for the spectral metric in this model. This formula verifies that the spectral metric grows sublinearly as network size (i.e., the number of nodes) grows. Additionally, the mathematical reasoning of the precise formula theoretically provides detailed explanations for this scaling property. Finally, we validate the scaling properties of the spectral metric using some stochastic models. The experimental results show that this scaling property can be retained regardless of local world, node deleting and assortativity adjustment.

  19. Stochastic Representation of Chaos using Terminal Attractors

    NASA Technical Reports Server (NTRS)

    Zak, Michail

    2005-01-01

    A nonlinear version of the Liouville equation based upon terminal attractors is proposed for describing post-instability motions of dynamical systems with exponential divergence of trajectories such as those leading to chaos and turbulence. As a result, the post-instability motions are represented by expectations, variances, and higher moments of the state variables as functions of time. The proposed approach can be applied to conservative chaos, and in particular, to n-bodies problem, as well as to dissipative systems, and in particular, to chaotic attractors and turbulence.

  20. Extensive chaos in the Nikolaevskii model

    NASA Astrophysics Data System (ADS)

    Xi, Hao-Wen; Toral, Raúl; Gunton, J. D.; Tribelsky, Michael I.

    2000-07-01

    We carry out a systematic study of a different type of chaos at onset (``soft-mode turbulence'') based on numerical integration of the simplest one-dimensional model. The chaos is characterized by a smooth interplay of different spatial scales, with defect generation being unimportant. The Lyapunov exponents are calculated for several system sizes for fixed values of the control parameter ɛ. The Lyapunov dimension and the Kolmogorov-Sinai entropy are calculated and both shown to exhibit extensive and microextensive scaling. The distribution functional is shown to satisfy Gaussian statistics at small wave numbers and small frequency.

  1. Extensive chaos in the nikolaevskii model

    PubMed

    Xi; Toral; Gunton; Tribelsky

    2000-07-01

    We carry out a systematic study of a different type of chaos at onset ("soft-mode turbulence") based on numerical integration of the simplest one-dimensional model. The chaos is characterized by a smooth interplay of different spatial scales, with defect generation being unimportant. The Lyapunov exponents are calculated for several system sizes for fixed values of the control parameter epsilon. The Lyapunov dimension and the Kolmogorov-Sinai entropy are calculated and both shown to exhibit extensive and microextensive scaling. The distribution functional is shown to satisfy Gaussian statistics at small wave numbers and small frequency. PMID:11088514

  2. Controlling chaos in an economic model

    NASA Astrophysics Data System (ADS)

    Chen, Liang; Chen, Guanrong

    2007-01-01

    A Cournot duopoly, with a bounded inverse demand function and different constant marginal production costs, can be modeled as a discrete-time dynamical system, which exhibits complex bifurcating and chaotic behaviors. Based on some essential features of the model, we show how bifurcation and chaos can be controlled via the delayed feedback control method. We then propose and evaluate an adaptive parameter-tuning algorithm for control. In addition, we discuss possible economic implications of the chaos control strategies described in the paper.

  3. 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.

  4. 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.

  5. 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.

  6. Experimental realization of chaos control by thresholding.

    PubMed

    Murali, K; Sinha, Sudeshna

    2003-07-01

    We report the experimental verification of thresholding as a versatile tool for efficient and flexible chaos control. The strategy here simply involves monitoring a single state variable and resetting it when it exceeds a threshold. We demonstrate the success of the technique in rapidly controlling different chaotic electrical circuits, including a hyperchaotic circuit, onto stable fixed points and limit cycles of different periods, by thresholding just one variable. The simplicity of this controller entailing no run-time computation, and the ease and rapidity of switching between different targets it offers, suggests a potent tool for chaos based applications. PMID:12935228

  7. 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. PMID:12284225

  8. Exact invariant measures: How the strength of measure settles the intensity of chaos.

    PubMed

    Venegeroles, Roberto

    2015-06-01

    The aim of this paper is to show how to extract dynamical behavior and ergodic properties from deterministic chaos with the assistance of exact invariant measures. On the one hand, we provide an approach to deal with the inverse problem of finding nonlinear interval maps from a given invariant measure. Then we show how to identify ergodic properties by means of transitions along the phase space via exact measures. On the other hand, we discuss quantitatively how infinite measures imply maps having subexponential Lyapunov instability (weakly chaotic), as opposed to finite measure ergodic maps, which are fully chaotic. In addition, we provide general solutions of maps for which infinite invariant measures are exactly known throughout the interval (a demand from this field). Finally, we give a simple proof that infinite measure implies universal Mittag-Leffler statistics of observables, rather than narrow distributions typically observed in finite measure ergodic maps. PMID:26172779

  9. Intrinsic noise and two-dimensional maps: quasicycles, quasiperiodicity, and chaos.

    PubMed

    Parra-Rojas, César; Challenger, Joseph D; Fanelli, Duccio; McKane, Alan J

    2014-09-01

    We develop a formalism to describe the discrete-time dynamics of systems containing an arbitrary number of interacting species. The individual-based model, which forms our starting point, is described by a Markov chain, which in the limit of large system sizes is shown to be very well-approximated by a Fokker-Planck-like equation, or equivalently by a set of stochastic difference equations. This formalism is applied to the specific case of two species: one predator species and its prey species. Quasicycles, stochastic cycles sustained and amplified by the demographic noise, previously found in continuous-time predator-prey models are shown to exist, and their behavior predicted from a linear noise analysis is shown to be in very good agreement with simulations. The effects of the noise on other attractors in the corresponding deterministic map, such as periodic cycles, quasiperiodicity, and chaos, are also investigated. PMID:25314423

  10. Persistent Chaos of Measles Epidemics in the Prevaccination United States Caused by a Small Change in Seasonal Transmission Patterns

    PubMed Central

    Dalziel, Benjamin D.; Bjørnstad, Ottar N.; van Panhuis, Willem G.; Burke, Donald S.; Metcalf, C. Jessica E.; Grenfell, Bryan T.

    2016-01-01

    Epidemics of infectious diseases often occur in predictable limit cycles. Theory suggests these cycles can be disrupted by high amplitude seasonal fluctuations in transmission rates, resulting in deterministic chaos. However, persistent deterministic chaos has never been observed, in part because sufficiently large oscillations in transmission rates are uncommon. Where they do occur, the resulting deep epidemic troughs break the chain of transmission, leading to epidemic extinction, even in large cities. Here we demonstrate a new path to locally persistent chaotic epidemics via subtle shifts in seasonal patterns of transmission, rather than through high-amplitude fluctuations in transmission rates. We base our analysis on a comparison of measles incidence in 80 major cities in the prevaccination era United States and United Kingdom. Unlike the regular limit cycles seen in the UK, measles cycles in US cities consistently exhibit spontaneous shifts in epidemic periodicity resulting in chaotic patterns. We show that these patterns were driven by small systematic differences between countries in the duration of the summer period of low transmission. This example demonstrates empirically that small perturbations in disease transmission patterns can fundamentally alter the regularity and spatiotemporal coherence of epidemics. PMID:26845437

  11. Persistent Chaos of Measles Epidemics in the Prevaccination United States Caused by a Small Change in Seasonal Transmission Patterns.

    PubMed

    Dalziel, Benjamin D; Bjørnstad, Ottar N; van Panhuis, Willem G; Burke, Donald S; Metcalf, C Jessica E; Grenfell, Bryan T

    2016-02-01

    Epidemics of infectious diseases often occur in predictable limit cycles. Theory suggests these cycles can be disrupted by high amplitude seasonal fluctuations in transmission rates, resulting in deterministic chaos. However, persistent deterministic chaos has never been observed, in part because sufficiently large oscillations in transmission rates are uncommon. Where they do occur, the resulting deep epidemic troughs break the chain of transmission, leading to epidemic extinction, even in large cities. Here we demonstrate a new path to locally persistent chaotic epidemics via subtle shifts in seasonal patterns of transmission, rather than through high-amplitude fluctuations in transmission rates. We base our analysis on a comparison of measles incidence in 80 major cities in the prevaccination era United States and United Kingdom. Unlike the regular limit cycles seen in the UK, measles cycles in US cities consistently exhibit spontaneous shifts in epidemic periodicity resulting in chaotic patterns. We show that these patterns were driven by small systematic differences between countries in the duration of the summer period of low transmission. This example demonstrates empirically that small perturbations in disease transmission patterns can fundamentally alter the regularity and spatiotemporal coherence of epidemics. PMID:26845437

  12. Minimal Deterministic Physicality Applied to Cosmology

    NASA Astrophysics Data System (ADS)

    Valentine, John S.

    This report summarizes ongoing research and development since our 2012 foundation paper, including the emergent effects of a deterministic mechanism for fermion interactions: (1) the coherence of black holes and particles using a quantum chaotic model; (2) wide-scale (anti)matter prevalence from exclusion and weak interaction during the fermion reconstitution process; and (3) red-shift due to variations of vacuum energy density. We provide a context for Standard Model fields, and show how gravitation can be accountably unified in the same mechanism, but not as a unified field.

  13. Deterministic Switching in Bismuth Ferrite Nanoislands.

    PubMed

    Morelli, Alessio; Johann, Florian; Burns, Stuart R; Douglas, Alan; Gregg, J Marty

    2016-08-10

    We report deterministic selection of polarization variant in bismuth BiFeO3 nanoislands via a two-step scanning probe microscopy procedure. The polarization orientation in a nanoisland is toggled to the desired variant after a reset operation by scanning a conductive atomic force probe in contact over the surface while a bias is applied. The final polarization variant is determined by the direction of the inhomogeneous in-plane trailing field associated with the moving probe tip. This work provides the framework for better control of switching in rhombohedral ferroelectrics and for a deeper understanding of exchange coupling in multiferroic nanoscale heterostructures toward the realization of magnetoelectric devices. PMID:27454612

  14. Deterministic convergence in iterative phase shifting

    SciTech Connect

    Luna, Esteban; Salas, Luis; Sohn, Erika; Ruiz, Elfego; Nunez, Juan M.; Herrera, Joel

    2009-03-10

    Previous implementations of the iterative phase shifting method, in which the phase of a test object is computed from measurements using a phase shifting interferometer with unknown positions of the reference, do not provide an accurate way of knowing when convergence has been attained. We present a new approach to this method that allows us to deterministically identify convergence. The method is tested with a home-built Fizeau interferometer that measures optical surfaces polished to {lambda}/100 using the Hydra tool. The intrinsic quality of the measurements is better than 0.5 nm. Other possible applications for this technique include fringe projection or any problem where phase shifting is involved.

  15. Deterministic quantum computation with one photonic qubit

    NASA Astrophysics Data System (ADS)

    Hor-Meyll, M.; Tasca, D. S.; Walborn, S. P.; Ribeiro, P. H. Souto; Santos, M. M.; Duzzioni, E. I.

    2015-07-01

    We show that deterministic quantum computing with one qubit (DQC1) can be experimentally implemented with a spatial light modulator, using the polarization and the transverse spatial degrees of freedom of light. The scheme allows the computation of the trace of a high-dimension matrix, being limited by the resolution of the modulator panel and the technical imperfections. In order to illustrate the method, we compute the normalized trace of unitary matrices and implement the Deutsch-Jozsa algorithm. The largest matrix that can be manipulated with our setup is 1080 ×1920 , which is able to represent a system with approximately 21 qubits.

  16. Deterministic and Stochastic Descriptions of Gene Expression Dynamics

    NASA Astrophysics Data System (ADS)

    Marathe, Rahul; Bierbaum, Veronika; Gomez, David; Klumpp, Stefan

    2012-09-01

    A key goal of systems biology is the predictive mathematical description of gene regulatory circuits. Different approaches are used such as deterministic and stochastic models, models that describe cell growth and division explicitly or implicitly etc. Here we consider simple systems of unregulated (constitutive) gene expression and compare different mathematical descriptions systematically to obtain insight into the errors that are introduced by various common approximations such as describing cell growth and division by an effective protein degradation term. In particular, we show that the population average of protein content of a cell exhibits a subtle dependence on the dynamics of growth and division, the specific model for volume growth and the age structure of the population. Nevertheless, the error made by models with implicit cell growth and division is quite small. Furthermore, we compare various models that are partially stochastic to investigate the impact of different sources of (intrinsic) noise. This comparison indicates that different sources of noise (protein synthesis, partitioning in cell division) contribute comparable amounts of noise if protein synthesis is not or only weakly bursty. If protein synthesis is very bursty, the burstiness is the dominant noise source, independent of other details of the model. Finally, we discuss two sources of extrinsic noise: cell-to-cell variations in protein content due to cells being at different stages in the division cycles, which we show to be small (for the protein concentration and, surprisingly, also for the protein copy number per cell) and fluctuations in the growth rate, which can have a significant impact.

  17. 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

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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…

  3. 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,…

  4. 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.

  5. 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

  6. 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

  7. Qualitative chaos in geomorphic systems, with an example from wetland response to sea level rise

    SciTech Connect

    Phillips, J.D. )

    1992-05-01

    The spatial and temporal complexity of earth surface processes and landforms and the presence of deterministic chaos in many fundamental physical processes provide reasons to suspect chaos in geomorphic systems. A method is presented to assess the likelihood of chaotic behavior in a geomorphic system. The method requires identification of the fundamental system components, their positive, negative, or negligible influences on each other, and the relative strength or magnitudes of these links. Based on this information, the method can classify geomorphic systems as stable and nonchaotic, unstable and potentially chaotic, or unstable and generally chaotic. Positive, self-enhancing feedback is a key diagnostic of the likelihood of chaotic behavior. A sample application of the method to the problem of coastal marsh response to sea level rise is provided, which shows the marsh to be unstable. If changes in vegetation cover are partly dependent on vegetation density, the system is generally chaotic if marsh vegetation exhibits self-enhancing feedback (for example, seed source effects) and potentially chaotic if vegetation exhibits self-limiting feedback (competitive effects). The attractors controlling the chaotic dynamics represent states of pronounced erosion/drowning or accretion/expansion.

  8. Spatial structure and chaos in insect population dynamics

    NASA Astrophysics Data System (ADS)

    Hassell, Michael P.; Comins, Hugh N.; Mayt, Robert M.

    1991-09-01

    MOST environments are spatially subdivided, or patchy, and there has been much interest in the relationship between the dynamics of populations at the local and regional (metapopulation) scales1. Here we study mathematical models for host-parasitoid interactions, where in each generation specified fractions (µN and µp, respectively) of the host and parasitoid subpopulations in each patch move to adjacent patches; in most previous work, the movement is not localized but is to any other patch2. These simple and biologically sensible models with limited diffusive dispersal exhibit a remarkable range of dynamic behaviour: the density of the host and parasitoid subpopulations in a two-dimensional array of patches may exhibit complex patterns of spiral waves or spatially chaotic variation, they may show static 'crystal lattice' patterns, or they may become extinct. This range of behaviour is obtained with the local dynamics being deterministically unstable, with a constant host reproductive rate and no density dependence in the movement patterns. The dynamics depend on the host reproductive rate, and on the values of the parameters µN and µp. The results are relatively insensitive to the details of the interactions; we get essentially the same results from the mathematically-explicit Nicholon-Bailey model of host-parasitoid interactions, and from a very general 'cellular automaton' model in which only qualitative rules are specified. We conclude that local movement in a patchy environment can help otherwise unstable host and parasitoid populations to persist together, but that the deterministically generated spatial patterns in population density can be exceedingly complex (and sometimes indistinguishable from random environmental fluctuations).

  9. Discrete Deterministic and Stochastic Petri Nets

    NASA Technical Reports Server (NTRS)

    Zijal, Robert; Ciardo, Gianfranco

    1996-01-01

    Petri nets augmented with timing specifications gained a wide acceptance in the area of performance and reliability evaluation of complex systems exhibiting concurrency, synchronization, and conflicts. The state space of time-extended Petri nets is mapped onto its basic underlying stochastic process, which can be shown to be Markovian under the assumption of exponentially distributed firing times. The integration of exponentially and non-exponentially distributed timing is still one of the major problems for the analysis and was first attacked for continuous time Petri nets at the cost of structural or analytical restrictions. We propose a discrete deterministic and stochastic Petri net (DDSPN) formalism with no imposed structural or analytical restrictions where transitions can fire either in zero time or according to arbitrary firing times that can be represented as the time to absorption in a finite absorbing discrete time Markov chain (DTMC). Exponentially distributed firing times are then approximated arbitrarily well by geometric distributions. Deterministic firing times are a special case of the geometric distribution. The underlying stochastic process of a DDSPN is then also a DTMC, from which the transient and stationary solution can be obtained by standard techniques. A comprehensive algorithm and some state space reduction techniques for the analysis of DDSPNs are presented comprising the automatic detection of conflicts and confusions, which removes a major obstacle for the analysis of discrete time models.

  10. Ballistic annihilation and deterministic surface growth

    NASA Astrophysics Data System (ADS)

    Belitsky, Vladimir; Ferrari, Pablo A.

    1995-08-01

    A model of deterministic surface growth studied by Krug and Spohn, a model of the annihilating reaction A+B→inert studied by Elskens and Frisch, a one-dimensional three-color cyclic cellular automaton studied by Fisch, and a particular automaton that has the number 184 in the classification of Wolfram can be studied via a cellular automaton with stochastic initial data called ballistic annihilation. This automaton is defined by the following rules: At time t=0, one particle is put at each integer point of ℝ. To each particle, a velocity is assigned in such a way that it may be either +1 or -1 with probabilities 1/2, independent of the velocities of the other particles. As time goes on, each particle moves along ℝ at the velocity assigned to it and annihilates when it collides with another particle. In the present paper we compute the distribution of this automaton for each time t ∈ ℕ. We then use this result to obtain the hydrodynamic limit for the surface profile from the model of deterministic surface growth mentioned above. We also show the relation of this limit process to the process which we call moving local minimum of Brownian motion. The latter is the process B {/x min}, x ∈ ℝ, defined by B {/x min}≔min{ B y ; x-1≤ y≤ x+1} for every x ∈ ℝ, where B x , x ∈ ℝ, is the standard Brownian motion with B 0=0.

  11. Moment equations for a piecewise deterministic PDE

    NASA Astrophysics Data System (ADS)

    Bressloff, Paul C.; Lawley, Sean D.

    2015-03-01

    We analyze a piecewise deterministic PDE consisting of the diffusion equation on a finite interval Ω with randomly switching boundary conditions and diffusion coefficient. We proceed by spatially discretizing the diffusion equation using finite differences and constructing the Chapman-Kolmogorov (CK) equation for the resulting finite-dimensional stochastic hybrid system. We show how the CK equation can be used to generate a hierarchy of equations for the r-th moments of the stochastic field, which take the form of r-dimensional parabolic PDEs on {{Ω }r} that couple to lower order moments at the boundaries. We explicitly solve the first and second order moment equations (r = 2). We then describe how the r-th moment of the stochastic PDE can be interpreted in terms of the splitting probability that r non-interacting Brownian particles all exit at the same boundary; although the particles are non-interacting, statistical correlations arise due to the fact that they all move in the same randomly switching environment. Hence the stochastic diffusion equation describes two levels of randomness: Brownian motion at the individual particle level and a randomly switching environment. Finally, in the limit of fast switching, we use a quasi-steady state approximation to reduce the piecewise deterministic PDE to an SPDE with multiplicative Gaussian noise in the bulk and a stochastically-driven boundary.

  12. Deterministic prediction of surface wind speed variations

    NASA Astrophysics Data System (ADS)

    Drisya, G. V.; Kiplangat, D. C.; Asokan, K.; Satheesh Kumar, K.

    2014-11-01

    Accurate prediction of wind speed is an important aspect of various tasks related to wind energy management such as wind turbine predictive control and wind power scheduling. The most typical characteristic of wind speed data is its persistent temporal variations. Most of the techniques reported in the literature for prediction of wind speed and power are based on statistical methods or probabilistic distribution of wind speed data. In this paper we demonstrate that deterministic forecasting methods can make accurate short-term predictions of wind speed using past data, at locations where the wind dynamics exhibit chaotic behaviour. The predictions are remarkably accurate up to 1 h with a normalised RMSE (root mean square error) of less than 0.02 and reasonably accurate up to 3 h with an error of less than 0.06. Repeated application of these methods at 234 different geographical locations for predicting wind speeds at 30-day intervals for 3 years reveals that the accuracy of prediction is more or less the same across all locations and time periods. Comparison of the results with f-ARIMA model predictions shows that the deterministic models with suitable parameters are capable of returning improved prediction accuracy and capturing the dynamical variations of the actual time series more faithfully. These methods are simple and computationally efficient and require only records of past data for making short-term wind speed forecasts within practically tolerable margin of errors.

  13. Deterministic Creation of Macroscopic Cat States

    PubMed Central

    Lombardo, Daniel; Twamley, Jason

    2015-01-01

    Despite current technological advances, observing quantum mechanical effects outside of the nanoscopic realm is extremely challenging. For this reason, the observation of such effects on larger scale systems is currently one of the most attractive goals in quantum science. Many experimental protocols have been proposed for both the creation and observation of quantum states on macroscopic scales, in particular, in the field of optomechanics. The majority of these proposals, however, rely on performing measurements, making them probabilistic. In this work we develop a completely deterministic method of macroscopic quantum state creation. We study the prototypical optomechanical Membrane In The Middle model and show that by controlling the membrane’s opacity, and through careful choice of the optical cavity initial state, we can deterministically create and grow the spatial extent of the membrane’s position into a large cat state. It is found that by using a Bose-Einstein condensate as a membrane high fidelity cat states with spatial separations of up to ∼300 nm can be achieved. PMID:26345157

  14. Deterministic forward scatter from surface gravity waves.

    PubMed

    Deane, Grant B; Preisig, James C; Tindle, Chris T; Lavery, Andone; Stokes, M Dale

    2012-12-01

    Deterministic structures in sound reflected by gravity waves, such as focused arrivals and Doppler shifts, have implications for underwater acoustics and sonar, and the performance of underwater acoustic communications systems. A stationary phase analysis of the Helmholtz-Kirchhoff scattering integral yields the trajectory of focused arrivals and their relationship to the curvature of the surface wave field. Deterministic effects along paths up to 70 water depths long are observed in shallow water measurements of surface-scattered sound at the Martha's Vineyard Coastal Observatory. The arrival time and amplitude of surface-scattered pulses are reconciled with model calculations using measurements of surface waves made with an upward-looking sonar mounted mid-way along the propagation path. The root mean square difference between the modeled and observed pulse arrival amplitude and delay, respectively, normalized by the maximum range of amplitudes and delays, is found to be 0.2 or less for the observation periods analyzed. Cross-correlation coefficients for modeled and observed pulse arrival delays varied from 0.83 to 0.16 depending on surface conditions. Cross-correlation coefficients for normalized pulse energy for the same conditions were small and varied from 0.16 to 0.06. In contrast, the modeled and observed pulse arrival delay and amplitude statistics were in good agreement. PMID:23231099

  15. Deterministic Creation of Macroscopic Cat States.

    PubMed

    Lombardo, Daniel; Twamley, Jason

    2015-01-01

    Despite current technological advances, observing quantum mechanical effects outside of the nanoscopic realm is extremely challenging. For this reason, the observation of such effects on larger scale systems is currently one of the most attractive goals in quantum science. Many experimental protocols have been proposed for both the creation and observation of quantum states on macroscopic scales, in particular, in the field of optomechanics. The majority of these proposals, however, rely on performing measurements, making them probabilistic. In this work we develop a completely deterministic method of macroscopic quantum state creation. We study the prototypical optomechanical Membrane In The Middle model and show that by controlling the membrane's opacity, and through careful choice of the optical cavity initial state, we can deterministically create and grow the spatial extent of the membrane's position into a large cat state. It is found that by using a Bose-Einstein condensate as a membrane high fidelity cat states with spatial separations of up to ∼300 nm can be achieved. PMID:26345157

  16. Theory of Secular Chaos and Mercury's Orbit

    NASA Astrophysics Data System (ADS)

    Lithwick, Yoram; Wu, Yanqin

    2011-09-01

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

  17. Mathematical Geology.

    ERIC Educational Resources Information Center

    Jones, Thomas A.

    1983-01-01

    Mathematical techniques used to solve geological problems are briefly discussed (including comments on use of geostatistics). Highlights of conferences/meetings and conference papers in mathematical geology are also provided. (JN)

  18. Mathematic Terminology.

    ERIC Educational Resources Information Center

    Hanh, Vu Duc, Ed.

    This document gives a listing of mathematical terminology in both the English and Vietnamese languages. Vocabulary used in algebra and geometry is included along with a translation of mathematical symbols. (DT)

  19. Mathematics disorder

    MedlinePlus

    ... this page: //medlineplus.gov/ency/article/001534.htm Mathematics disorder To use the sharing features on this page, please enable JavaScript. Mathematics disorder is a condition in which a child's ...

  20. Species fluctuations sustained by a cyclic succession at the edge of chaos

    PubMed Central

    Benincà, Elisa; Ballantine, Bill; Ellner, Stephen P.; Huisman, Jef

    2015-01-01

    Although mathematical models and laboratory experiments have shown that species interactions can generate chaos, field evidence of chaos in natural ecosystems is rare. We report on a pristine rocky intertidal community located in one of the world’s oldest marine reserves that has displayed a complex cyclic succession for more than 20 y. Bare rock was colonized by barnacles and crustose algae, they were overgrown by mussels, and the subsequent detachment of the mussels returned bare rock again. These processes generated irregular species fluctuations, such that the species coexisted over many generations without ever approaching a stable equilibrium state. Analysis of the species fluctuations revealed a dominant periodicity of about 2 y, a global Lyapunov exponent statistically indistinguishable from zero, and local Lyapunov exponents that alternated systematically between negative and positive values. This pattern indicates that the community moved back and forth between stabilizing and chaotic dynamics during the cyclic succession. The results are supported by a patch-occupancy model predicting similar patterns when the species interactions were exposed to seasonal variation. Our findings show that natural ecosystems can sustain continued changes in species abundances and that seasonal forcing may push these nonequilibrium dynamics to the edge of chaos. PMID:25902520

  1. Species fluctuations sustained by a cyclic succession at the edge of chaos.

    PubMed

    Benincà, Elisa; Ballantine, Bill; Ellner, Stephen P; Huisman, Jef

    2015-05-19

    Although mathematical models and laboratory experiments have shown that species interactions can generate chaos, field evidence of chaos in natural ecosystems is rare. We report on a pristine rocky intertidal community located in one of the world's oldest marine reserves that has displayed a complex cyclic succession for more than 20 y. Bare rock was colonized by barnacles and crustose algae, they were overgrown by mussels, and the subsequent detachment of the mussels returned bare rock again. These processes generated irregular species fluctuations, such that the species coexisted over many generations without ever approaching a stable equilibrium state. Analysis of the species fluctuations revealed a dominant periodicity of about 2 y, a global Lyapunov exponent statistically indistinguishable from zero, and local Lyapunov exponents that alternated systematically between negative and positive values. This pattern indicates that the community moved back and forth between stabilizing and chaotic dynamics during the cyclic succession. The results are supported by a patch-occupancy model predicting similar patterns when the species interactions were exposed to seasonal variation. Our findings show that natural ecosystems can sustain continued changes in species abundances and that seasonal forcing may push these nonequilibrium dynamics to the edge of chaos. PMID:25902520

  2. Local polynomial chaos expansion for linear differential equations with high dimensional random inputs

    SciTech Connect

    Chen, Yi; Jakeman, John; Gittelson, Claude; Xiu, Dongbin

    2015-01-08

    In this paper we present a localized polynomial chaos expansion for partial differential equations (PDE) with random inputs. In particular, we focus on time independent linear stochastic problems with high dimensional random inputs, where the traditional polynomial chaos methods, and most of the existing methods, incur prohibitively high simulation cost. Furthermore, the local polynomial chaos method employs a domain decomposition technique to approximate the stochastic solution locally. In each subdomain, a subdomain problem is solved independently and, more importantly, in a much lower dimensional random space. In a postprocesing stage, accurate samples of the original stochastic problems are obtained from the samples of the local solutions by enforcing the correct stochastic structure of the random inputs and the coupling conditions at the interfaces of the subdomains. Overall, the method is able to solve stochastic PDEs in very large dimensions by solving a collection of low dimensional local problems and can be highly efficient. In our paper we present the general mathematical framework of the methodology and use numerical examples to demonstrate the properties of the method.

  3. Rainforest Mathematics

    ERIC Educational Resources Information Center

    Kilpatrick, Jeremy

    2014-01-01

    This paper addresses the contested way that ethnomathematics has sometimes been received by mathematicians and others and what that disagreement might suggest about issues in mathematics education; namely, (a) the relation of ethnomathematics to academic mathematics; (b) recent efforts to reform secondary school mathematics so that it prepares…

  4. Ruling out chaos in comparable mass compact binary systems with one body spinning

    NASA Astrophysics Data System (ADS)

    Wu, Xin; Huang, Guoqing

    2015-09-01

    Levin (2006, Phys. Rev. D, 74, 124027) has given two contrary claims on the chaotic behaviour of a system in which only one body of comparable mass binaries spins and spin effects are restricted to the leading order spin-orbit couplings. Chaos in one set of second post-Newtonian (2PN) harmonic coordinate Lagrangian equations of motion was allowed via the fractal basin boundary method. However, in another set of 2PN Arnowitt-Deser-Misner (ADM) Hamiltonian equations of motion no chaos was confirmed with the aid of parametric solutions. Is there chaos for conservative PN Lagrangian and Hamiltonian approaches to the dynamics of comparable mass binaries when only one object spins? This is still an open question. A paper on canonical, conjugate spin variables (Wu and Xie, 2010, Phys. Rev. D, 81, 084045) has directly shown that these Hamiltonian approaches are integrable and non-chaotic regardless of PN orders and spin effects. In this sense, what we are required to answer is only the question of whether the Lagrangian approaches allow chaos. As recently confirmed by Wu et al. (2015, Phys. Rev. D, 91, 024042), in ADM coordinates, any one of these Lagrangian approaches at a certain order generally has an analytical mathematical equivalent Hamiltonian at an infinite order from an analytical point of view or at a certain high enough finite order from a numerical point of view. The Hamiltonian is completely canonical and has four integrals of the total energy and total angular momentum in an eight-dimensional phase space, and therefore it is typically integrable. We use this to show the absence of chaos in the Lagrangian. On the other hand, we use the method of fast Lyapunov exponents to revisit the 2PN harmonic coordinate Lagrangian dynamics with the leading-order spin-orbit coupling of one body spinning. It is found that the fractal method is not sufficient to support chaos in unstable merging binaries, even if the radiation reaction is turned off. In summary, neither the

  5. Deterministic, Nanoscale Fabrication of Mesoscale Objects

    SciTech Connect

    Jr., R M; Gilmer, J; Rubenchik, A; Shirk, M

    2004-12-08

    Neither LLNL nor any other organization has the capability to perform deterministic fabrication of mm-sized objects with arbitrary, {micro}m-sized, 3-D features and with 100-nm-scale accuracy and smoothness. This is particularly true for materials such as high explosives and low-density aerogels, as well as materials such as diamond and vanadium. The motivation for this project was to investigate the physics and chemistry that control the interactions of solid surfaces with laser beams and ion beams, with a view towards their applicability to the desired deterministic fabrication processes. As part of this LDRD project, one of our goals was to advance the state of the art for experimental work, but, in order to create ultimately a deterministic capability for such precision micromachining, another goal was to form a new modeling/simulation capability that could also extend the state of the art in this field. We have achieved both goals. In this project, we have, for the first time, combined a 1-D hydrocode (''HYADES'') with a 3-D molecular dynamics simulator (''MDCASK'') in our modeling studies. In FY02 and FY03, we investigated the ablation/surface-modification processes that occur on copper, gold, and nickel substrates with the use of sub-ps laser pulses. In FY04, we investigated laser ablation of carbon, including laser-enhanced chemical reaction on the carbon surface for both vitreous carbon and carbon aerogels. Both experimental and modeling results will be presented in the report that follows. The immediate impact of our investigation was a much better understanding of the chemical and physical processes that ensure when solid materials are exposed to femtosecond laser pulses. More broadly, we have better positioned LLNL to design a cluster tool for fabricating mesoscale objects utilizing laser pulses and ion-beams as well as more traditional machining/manufacturing techniques for applications such as components in NIF targets, remote sensors, including

  6. Stochastic versus deterministic variability in simple neuronal circuits: I. Monosynaptic spinal cord reflexes.

    PubMed Central

    Chang, T; Schiff, S J; Sauer, T; Gossard, J P; Burke, R E

    1994-01-01

    Long time series of monosynaptic Ia-afferent to alpha-motoneuron reflexes were recorded in the L7 or S1 ventral roots in the cat. Time series were collected before and after spinalization at T13 during constant amplitude stimulations of group Ia muscle afferents in the triceps surae muscle nerves. Using autocorrelation to analyze the linear correlation in the time series demonstrated oscillations in the decerebrate state (4/4) that were eliminated after spinalization (5/5). Three tests for determinism were applied to these series: 1) local flow, 2) local dispersion, and 3) nonlinear prediction. These algorithms were validated with time series generated from known deterministic equations. For each experimental and theoretical time series used, matched time-series of stochastic surrogate data were generated to serve as mathematical and statistical controls. Two of the time series collected in the decerebrate state (2/4) demonstrated evidence for deterministic structure. This structure could not be accounted for by the autocorrelation in the data, and was abolished following spinalization. None of the time series collected in the spinalized state (0/5) demonstrated evidence of determinism. Although monosynaptic reflex variability is generally stochastic in the spinalized state, this simple driven system may display deterministic behavior in the decerebrate state. Images FIGURE 1 PMID:7948680

  7. Central limit behavior of deterministic dynamical systems

    NASA Astrophysics Data System (ADS)

    Tirnakli, Ugur; Beck, Christian; Tsallis, Constantino

    2007-04-01

    We investigate the probability density of rescaled sums of iterates of deterministic dynamical systems, a problem relevant for many complex physical systems consisting of dependent random variables. A central limit theorem (CLT) is valid only if the dynamical system under consideration is sufficiently mixing. For the fully developed logistic map and a cubic map we analytically calculate the leading-order corrections to the CLT if only a finite number of iterates is added and rescaled, and find excellent agreement with numerical experiments. At the critical point of period doubling accumulation, a CLT is not valid anymore due to strong temporal correlations between the iterates. Nevertheless, we provide numerical evidence that in this case the probability density converges to a q -Gaussian, thus leading to a power-law generalization of the CLT. The above behavior is universal and independent of the order of the maximum of the map considered, i.e., relevant for large classes of critical dynamical systems.

  8. Deterministic multi-zone ice accretion modeling

    NASA Technical Reports Server (NTRS)

    Yamaguchi, K.; Hansman, R. J., Jr.; Kazmierczak, M.

    1991-01-01

    The study focuses on a deterministic model of the surface roughness transition behavior of glaze ice and analyzes the initial smooth/rough transition location, bead formation, and the propagation of the transition location. Based on a hypothesis that the smooth/rough transition location coincides with the laminar/turbulent boundary-layer transition location, a multizone model is implemented in the LEWICE code. In order to verify the effectiveness of the model, ice accretion predictions for simple cylinders calculated by the multizone LEWICE are compared to experimental ice shapes. The glaze ice shapes are found to be sensitive to the laminar surface roughness and bead thickness parameters controlling the transition location, while the ice shapes are found to be insensitive to the turbulent surface roughness.

  9. Deterministic multi-zone ice accretion modeling

    NASA Technical Reports Server (NTRS)

    Yamaguchi, K.; Hansman, R. John, Jr.; Kazmierczak, Michael

    1991-01-01

    The focus here is on a deterministic model of the surface roughness transition behavior of glaze ice. The initial smooth/rough transition location, bead formation, and the propagation of the transition location are analyzed. Based on the hypothesis that the smooth/rough transition location coincides with the laminar/turbulent boundary layer transition location, a multizone model is implemented in the LEWICE code. In order to verify the effectiveness of the model, ice accretion predictions for simple cylinders calculated by the multizone LEWICE are compared to experimental ice shapes. The glaze ice shapes are found to be sensitive to the laminar surface roughness and bead thickness parameters controlling the transition location, while the ice shapes are found to be insensitive to the turbulent surface roughness.

  10. Fast combinatorial optimization using generalized deterministic annealing

    NASA Astrophysics Data System (ADS)

    Acton, Scott T.; Ghosh, Joydeep; Bovik, Alan C.

    1993-08-01

    Generalized Deterministic Annealing (GDA) is a useful new tool for computing fast multi-state combinatorial optimization of difficult non-convex problems. By estimating the stationary distribution of simulated annealing (SA), GDA yields equivalent solutions to practical SA algorithms while providing a significant speed improvement. Using the standard GDA, the computational time of SA may be reduced by an order of magnitude, and, with a new implementation improvement, Windowed GDA, the time improvements reach two orders of magnitude with a trivial compromise in solution quality. The fast optimization of GDA has enabled expeditious computation of complex nonlinear image enhancement paradigms, such as the Piecewise Constant (PICO) regression examples used in this paper. To validate our analytical results, we apply GDA to the PICO regression problem and compare the results to other optimization methods. Several full image examples are provided that show successful PICO image enhancement using GDA in the presence of both Laplacian and Gaussian additive noise.

  11. Deterministic polishing from theory to practice

    NASA Astrophysics Data System (ADS)

    Hooper, Abigail R.; Hoffmann, Nathan N.; Sarkas, Harry W.; Escolas, John; Hobbs, Zachary

    2015-10-01

    Improving predictability in optical fabrication can go a long way towards increasing profit margins and maintaining a competitive edge in an economic environment where pressure is mounting for optical manufacturers to cut costs. A major source of hidden cost is rework - the share of production that does not meet specification in the first pass through the polishing equipment. Rework substantially adds to the part's processing and labor costs as well as bottlenecks in production lines and frustration for managers, operators and customers. The polishing process consists of several interacting variables including: glass type, polishing pads, machine type, RPM, downforce, slurry type, baume level and even the operators themselves. Adjusting the process to get every variable under control while operating in a robust space can not only provide a deterministic polishing process which improves profitability but also produces a higher quality optic.

  12. Targeted activation in deterministic and stochastic systems

    NASA Astrophysics Data System (ADS)

    Eisenhower, Bryan; Mezić, Igor

    2010-02-01

    Metastable escape is ubiquitous in many physical systems and is becoming a concern in engineering design as these designs (e.g., swarms of vehicles, coupled building energetics, nanoengineering, etc.) become more inspired by dynamics of biological, molecular and other natural systems. In light of this, we study a chain of coupled bistable oscillators which has two global conformations and we investigate how specialized or targeted disturbance is funneled in an inverse energy cascade and ultimately influences the transition process between the conformations. We derive a multiphase averaged approximation to these dynamics which illustrates the influence of actions in modal coordinates on the coarse behavior of this process. An activation condition that predicts how the disturbance influences the rate of transition is then derived. The prediction tools are derived for deterministic dynamics and we also present analogous behavior in the stochastic setting and show a divergence from Kramers activation behavior under targeted activation conditions.

  13. 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.

  14. Deterministic-random separation in nonstationary regime

    NASA Astrophysics Data System (ADS)

    Abboud, D.; Antoni, J.; Sieg-Zieba, S.; Eltabach, M.

    2016-02-01

    In rotating machinery vibration analysis, the synchronous average is perhaps the most widely used technique for extracting periodic components. Periodic components are typically related to gear vibrations, misalignments, unbalances, blade rotations, reciprocating forces, etc. Their separation from other random components is essential in vibration-based diagnosis in order to discriminate useful information from masking noise. However, synchronous averaging theoretically requires the machine to operate under stationary regime (i.e. the related vibration signals are cyclostationary) and is otherwise jeopardized by the presence of amplitude and phase modulations. A first object of this paper is to investigate the nature of the nonstationarity induced by the response of a linear time-invariant system subjected to speed varying excitation. For this purpose, the concept of a cyclo-non-stationary signal is introduced, which extends the class of cyclostationary signals to speed-varying regimes. Next, a "generalized synchronous average'' is designed to extract the deterministic part of a cyclo-non-stationary vibration signal-i.e. the analog of the periodic part of a cyclostationary signal. Two estimators of the GSA have been proposed. The first one returns the synchronous average of the signal at predefined discrete operating speeds. A brief statistical study of it is performed, aiming to provide the user with confidence intervals that reflect the "quality" of the estimator according to the SNR and the estimated speed. The second estimator returns a smoothed version of the former by enforcing continuity over the speed axis. It helps to reconstruct the deterministic component by tracking a specific trajectory dictated by the speed profile (assumed to be known a priori).The proposed method is validated first on synthetic signals and then on actual industrial signals. The usefulness of the approach is demonstrated on envelope-based diagnosis of bearings in variable

  15. Mathematical Modeling and Pure Mathematics

    ERIC Educational Resources Information Center

    Usiskin, Zalman

    2015-01-01

    Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…

  16. A novel 2D wavelength-time chaos code in optical CDMA system

    NASA Astrophysics Data System (ADS)

    Zhang, Qi; Xin, Xiangjun; Wang, Yongjun; Zhang, Lijia; Yu, Chongxiu; Meng, Nan; Wang, Houtian

    2012-11-01

    Two-dimensional wavelength-time chaos code is proposed and constructed for a synchronous optical code division multiple access system. The access performance is compared between one-dimensional chaos code, WDM/chaos code and the proposed code. Comparison shows that two-dimensional wavelength-time chaos code possesses larger capacity, better spectral efficiency and bit-error ratio than WDM/chaos combinations and one-dimensional chaos code.

  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. 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.

  19. Chaos in a Hydraulic Control Valve

    NASA Astrophysics Data System (ADS)

    Hayashi, S.; Hayase, T.; Kurahashi, T.

    1997-08-01

    In this paper we have studied the instability and chaos occurring in a pilot-type poppet valve circuit. The system consists of a poppet valve, an upstream plenum chamber, a supply pipeline and an orifice inserted between the pelnum and the pipeline. Although the poppet valve rests on the seat stably for a supply pressure lower than the cracking pressure, the circuit becomes unstable for an initial disturbance beyond a critical value and develops a self-excited vibration. In this unstable region, chaotic vibration appears at the period-doubling bifurcation. We have investigated the stability of the circuit and the chaotic phenomenon numerically, and elucidated it by power spectra, a bifurcation diagram and Lyapunov exponent calculations, showing that the phenomenon follows the Feigenbaum route to chaos.Copyright 1997 Academic Press Limited

  20. Chaos synchronization in networks of semiconductor superlattices

    NASA Astrophysics Data System (ADS)

    Li, Wen; Aviad, Yaara; Reidler, Igor; Song, Helun; Huang, Yuyang; Biermann, Klaus; Rosenbluh, Michael; Zhang, Yaohui; Grahn, Holger T.; Kanter, Ido

    2015-11-01

    Chaos synchronization has been demonstrated as a useful building block for various tasks in secure communications, including a source of all-electronic ultrafast physical random number generators based on room temperature spontaneous chaotic oscillations in a DC-biased weakly coupled GaAs/Al0.45Ga0.55As semiconductor superlattice (SSL). Here, we experimentally demonstrate the emergence of several types of chaos synchronization, e.g. leader-laggard, face-to-face and zero-lag synchronization in network motifs of coupled SSLs consisting of unidirectional and mutual coupling as well as self-feedback coupling. Each type of synchronization clearly reflects the symmetry of the topology of its network motif. The emergence of a chaotic SSL without external feedback and synchronization among different structured SSLs open up the possibility for advanced secure multi-user communication methods based on large networks of coupled SSLs.

  1. Comments on microcausality, chaos, and gravitational observables

    NASA Astrophysics Data System (ADS)

    Marolf, Donald

    2015-12-01

    Observables in gravitational systems must be non-local so as to be invariant under diffeomorphism gauge transformations. But at the classical level some such observables can nevertheless satisfy an exact form of microcausality. This property is conjectured to remain true at all orders in the semiclassical expansion, though with limitations at finite ℏ or {{\\ell }}{Planck}. We also discuss related issues concerning observables in black hole spacetimes and comment on the senses in which they do and do not experience the form of chaos identified by Shenker and Stanford. In particular, in contrast to the situation in a reflecting cavity, this chaos does not afflict observables naturally associated with Hawking radiation for evaporating black holes.

  2. Neutral line chaos and phase space structure

    NASA Technical Reports Server (NTRS)

    Burkhart, Grant R.; Speiser, Theodore W.; Martin, Richard F., Jr.; Dusenbery, Paul B.

    1991-01-01

    Phase space structure and chaos near a neutral line are studied with numerical surface-of-section (SOS) techniques and analytic methods. Results are presented for a linear neutral line model with zero crosstail electric field. It was found that particle motion can be divided into three regimes dependening on the value of the conserved canonical momentum, Py, and the conserved Hamiltonian, h. The phase space structure, using Poincare SOS plots, is highly sensitive to bn = Bn/B0 variations, but not to h variations. It is verified that the slow motion preserves the action, Jz, as evaluated by Sonnerup (1971), when the period of the fast motion is smaller than the time scale of the slow motion. Results show that the phase space structure and particle chaos depend sensitively upon Py and bn, but are independent of h.

  3. Deterministic and non-deterministic switching in chains of magnetic hysterons.

    PubMed

    Tanasa, R; Stancu, A

    2011-10-26

    This paper presents a fundamental analysis of a single-domain ferromagnetic particles chain hysteresis in perpendicular geometry as a prototype for ultra-high density memories. Due to magnetostatic long range interactions the system has a complex hysteresis but stable features can be found. The loop has a number of deterministic Barkhausen jumps and consequently a number of stable plateaus that could be used in multistate memories. The fundamental elements that sustain this behavior are shown and discussed. PMID:21969255

  4. Estimating ensemble average power delivered by a piezoelectric patch actuator to a non-deterministic subsystem

    NASA Astrophysics Data System (ADS)

    Muthalif, Asan G. A.; Wahid, Azni N.; Nor, Khairul A. M.

    2014-02-01

    Engineering systems such as aircraft, ships and automotive are considered built-up structures. Dynamically they are taught of as being fabricated from many components that are classified as 'deterministic subsystems' (DS) and 'non-deterministic subsystems' (Non-DS). Structures' response of the DS is deterministic in nature and analysed using deterministic modelling methods such as finite element (FE) method. The response of Non-DS is statistical in nature and estimated using statistical modelling technique such as statistical energy analysis (SEA). SEA method uses power balance equation, in which any external input to the subsystem must be represented in terms of power. Often, input force is taken as point force and ensemble average power delivered by point force is already well-established. However, the external input can also be applied in the form of moments exerted by a piezoelectric (PZT) patch actuator. In order to be able to apply SEA method for input moments, a mathematical representation for moment generated by PZT patch in the form of average power is needed, which is attempted in this paper. A simply-supported plate with attached PZT patch is taken as a benchmark model. Analytical solution to estimate average power is derived using mobility approach. Ensemble average of power given by the PZT patch actuator to the benchmark model when subjected to structural uncertainties is also simulated using Lagrangian method and FEA software. The analytical estimation is compared with the Lagrangian model and FE method for validation. The effects of size and location of the PZT actuators on the power delivered to the plate are later investigated.

  5. Controllable chaos in hybrid electro-optomechanical systems.

    PubMed

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

    2016-01-01

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

  6. Controllable chaos in hybrid electro-optomechanical systems

    NASA Astrophysics Data System (ADS)

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

    2016-03-01

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

  7. Chaos as a social determinant of child health: Reciprocal associations?

    PubMed

    Kamp Dush, Claire M; Schmeer, Kammi K; Taylor, Miles

    2013-10-01

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

  8. Controllable chaos in hybrid electro-optomechanical systems

    PubMed Central

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

    2016-01-01

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

  9. Characteristic Structures of Power Spectra in Periodic Chaos

    NASA Astrophysics Data System (ADS)

    Yoshida, T.; Tomita, K.

    1986-10-01

    The power spectra of periodic chaos are shown to have characteristic structures which are governed by the universal recursion relations. By periodic chaos we mean a chaos which emerges via period-doubling bifurcations, and the recursion relations are based on similarity structures in the process of band-splitting bifurcations of periodic chaos. To derive these relations, the asymmetric tent map is used, and the universal applicability of these relations to other classes of maps including the logistic map, where the rescaling factors are replaced by proper ones, is verified by numerical experiment. Some affirmative results for the H&{acutee}non maps are also given.

  10. Surrogate accelerated sampling of reservoir models with complex structures using sparse polynomial chaos expansion

    NASA Astrophysics Data System (ADS)

    Bazargan, Hamid; Christie, Mike; Elsheikh, Ahmed H.; Ahmadi, Mohammad

    2015-12-01

    Markov Chain Monte Carlo (MCMC) methods are often used to probe the posterior probability distribution in inverse problems. This allows for computation of estimates of uncertain system responses conditioned on given observational data by means of approximate integration. However, MCMC methods suffer from the computational complexities in the case of expensive models as in the case of subsurface flow models. Hence, it is of great interest to develop alterative efficient methods utilizing emulators, that are cheap to evaluate, in order to replace the full physics simulator. In the current work, we develop a technique based on sparse response surfaces to represent the flow response within a subsurface reservoir and thus enable efficient exploration of the posterior probability density function and the conditional expectations given the data. Polynomial Chaos Expansion (PCE) is a powerful tool to quantify uncertainty in dynamical systems when there is probabilistic uncertainty in the system parameters. In the context of subsurface flow model, it has been shown to be more accurate and efficient compared with traditional experimental design (ED). PCEs have a significant advantage over other response surfaces as the convergence to the true probability distribution when the order of the PCE is increased can be proved for the random variables with finite variances. However, the major drawback of PCE is related to the curse of dimensionality as the number of terms to be estimated grows drastically with the number of the input random variables. This renders the computational cost of classical PCE schemes unaffordable for reservoir simulation purposes when the deterministic finite element model is expensive to evaluate. To address this issue, we propose the reduced-terms polynomial chaos representation which uses an impact factor to only retain the most relevant terms of the PCE decomposition. Accordingly, the reduced-terms polynomial chaos proxy can be used as the pseudo

  11. 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.

  12. 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.

  13. Gravity waves, chaos, and spinning compact binaries

    PubMed

    Levin

    2000-04-17

    Spinning compact binaries are shown to be chaotic in the post-Newtonian expansion of the two-body system. Chaos by definition is the extreme sensitivity to initial conditions and a consequent inability to predict the outcome of the evolution. As a result, the spinning pair will have unpredictable gravitational waveforms during coalescence. This poses a challenge to future gravity wave observatories which rely on a match between the data and a theoretical template. PMID:11019134

  14. Theoretical Mathematics

    NASA Astrophysics Data System (ADS)

    Stöltzner, Michael

    Answering to the double-faced influence of string theory on mathematical practice and rigour, the mathematical physicists Arthur Jaffe and Frank Quinn have contemplated the idea that there exists a `theoretical' mathematics (alongside `theoretical' physics) whose basic structures and results still require independent corroboration by mathematical proof. In this paper, I shall take the Jaffe-Quinn debate mainly as a problem of mathematical ontology and analyse it against the backdrop of two philosophical views that are appreciative towards informal mathematical development and conjectural results: Lakatos's methodology of proofs and refutations and John von Neumann's opportunistic reading of Hilbert's axiomatic method. The comparison of both approaches shows that mitigating Lakatos's falsificationism makes his insights about mathematical quasi-ontology more relevant to 20th century mathematics in which new structures are introduced by axiomatisation and not necessarily motivated by informal ancestors. The final section discusses the consequences of string theorists' claim to finality for the theory's mathematical make-up. I argue that ontological reductionism as advocated by particle physicists and the quest for mathematically deeper axioms do not necessarily lead to identical results.

  15. 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

  16. Chaos Cryptography with Dynamical Systems

    NASA Astrophysics Data System (ADS)

    Anderson, Robert; Morse, Jack; Schimmrigk, Rolf

    2001-11-01

    Cryptography is a subject that draws strength from an amazing variety of different mathematical fields, including such deep results as the Weil-Dwork-Deligne theorem on the zeta function. Physical theories have recently entered the subject as well, an example being the subject of quantum cryptography, motivated in part by Shor's insight into the vulnerability of prime number factorization based crypto systems. In this contribution we describe a cryptographic algorithm which is based on the dynamics of a class of physical models that exhibit chaotic behavior. More precisely, we consider dissipative systems which are described by nonlinear three-dimensional systems of differential equations with strange attractor surfaces of non-integer Lyapunov dimension. The time evolution of such systems in part of the moduli space shows unpredictable behavior, which suggests that they might be useful as pseudorandom number generators. We will show that this is indeed the case and illustrate our procedure mainly with the Lorenz attractor, though we also briefly mention the Rössler system. We use this class of nonlinear models to construct an extremely fast stream cipher with a large keyspace, which we test with Marsaglia's battery of DieHard tests.

  17. Continuum models for gas in disturbed galaxies. III. Bifurcations and chaos in a deterministic model for bursts of star formation

    SciTech Connect

    Struck-Marcell, C.; Scalo, J.M.

    1987-05-01

    A study of the nonlinear behavior of model equations describing the Oort model for interstellar cloud evolution and star formation is presented. One-zone cloud fluid equations for the Oort model are given, and it is shown how, as the time-delay parameter T(d) is increased, the system bifurcates to limit-cycle behavior accompanied by star formation bursts and, with further increase in T(d), suffers further bifurcations leading to chaotic behavior. A linear stability analysis, including time delay, is used to demonstrate that the behavior of the Oort model does not depend sensitively on the other parameters involved. It is also shown that the onset of bifurcation to a limit cycle can be predicted analytically. The major predictions of the calculations are compared with available relevant observations of star formation activity in galaxies, especially tidally interacting galaxies. 112 references.

  18. Designing a stochastic genetic switch by coupling chaos and bistability

    SciTech Connect

    Zhao, Xiang; Ouyang, Qi; Wang, Hongli

    2015-11-15

    In stem cell differentiation, a pluripotent stem cell becomes progressively specialized and generates specific cell types through a series of epigenetic processes. How cells can precisely determine their fate in a fluctuating environment is a currently unsolved problem. In this paper, we suggest an abstract gene regulatory network to describe mathematically the differentiation phenomenon featuring stochasticity, divergent cell fates, and robustness. The network consists of three functional motifs: an upstream chaotic motif, a buffering motif of incoherent feed forward loop capable of generating a pulse, and a downstream motif which is bistable. The dynamic behavior is typically a transient chaos with fractal basin boundaries. The trajectories take transiently chaotic journeys before divergently settling down to the bistable states. The ratio of the probability that the high state is achieved to the probability that the low state is reached can maintain a constant in a population of cells with varied molecular fluctuations. The ratio can be turned up or down when proper parameters are adjusted. The model suggests a possible mechanism for the robustness against fluctuations that is prominently featured in pluripotent cell differentiations and developmental phenomena.

  19. Chaos in integrate-and-fire dynamical systems

    NASA Astrophysics Data System (ADS)

    Coombes, S.

    2000-02-01

    Integrate-and-fire (IF) mechanisms are often studied within the context of neural dynamics. From a mathematical perspective they represent a minimal yet biologically realistic model of a spiking neuron. The non-smooth nature of the dynamics leads to extremely rich spike train behavior capable of explaining a variety of biological phenomenon including phase-locked states, mode-locking, bursting and pattern formation. The conditions under which chaotic spike trains may be generated in synaptically interacting networks of neural oscillators is an important open question. Using techniques originally introduced for the study of impact oscillators we develop the notion of a Liapunov exponent for IF systems. In the strong coupling regime a network may undergo a discrete Turing-Hopf bifurcation of the firing times from a synchronous state to a state with periodic or quasiperiodic variations of the interspike intervals on closed orbits. Away from the bifurcation point these invariant circles may break up. We establish numerically that in this case the largest IF Liapunov exponent becomes positive. Hence, one route to chaos in networks of synaptically coupled IF neurons is via the breakup of invariant circles.

  20. Designing a stochastic genetic switch by coupling chaos and bistability

    NASA Astrophysics Data System (ADS)

    Zhao, Xiang; Ouyang, Qi; Wang, Hongli

    2015-11-01

    In stem cell differentiation, a pluripotent stem cell becomes progressively specialized and generates specific cell types through a series of epigenetic processes. How cells can precisely determine their fate in a fluctuating environment is a currently unsolved problem. In this paper, we suggest an abstract gene regulatory network to describe mathematically the differentiation phenomenon featuring stochasticity, divergent cell fates, and robustness. The network consists of three functional motifs: an upstream chaotic motif, a buffering motif of incoherent feed forward loop capable of generating a pulse, and a downstream motif which is bistable. The dynamic behavior is typically a transient chaos with fractal basin boundaries. The trajectories take transiently chaotic journeys before divergently settling down to the bistable states. The ratio of the probability that the high state is achieved to the probability that the low state is reached can maintain a constant in a population of cells with varied molecular fluctuations. The ratio can be turned up or down when proper parameters are adjusted. The model suggests a possible mechanism for the robustness against fluctuations that is prominently featured in pluripotent cell differentiations and developmental phenomena.

  1. Deterministic and stochastic bifurcations in the Hindmarsh-Rose neuronal model

    NASA Astrophysics Data System (ADS)

    Dtchetgnia Djeundam, S. R.; Yamapi, R.; Kofane, T. C.; Aziz-Alaoui, M. A.

    2013-09-01

    We analyze the bifurcations occurring in the 3D Hindmarsh-Rose neuronal model with and without random signal. When under a sufficient stimulus, the neuron activity takes place; we observe various types of bifurcations that lead to chaotic transitions. Beside the equilibrium solutions and their stability, we also investigate the deterministic bifurcation. It appears that the neuronal activity consists of chaotic transitions between two periodic phases called bursting and spiking solutions. The stochastic bifurcation, defined as a sudden change in character of a stochastic attractor when the bifurcation parameter of the system passes through a critical value, or under certain condition as the collision of a stochastic attractor with a stochastic saddle, occurs when a random Gaussian signal is added. Our study reveals two kinds of stochastic bifurcation: the phenomenological bifurcation (P-bifurcations) and the dynamical bifurcation (D-bifurcations). The asymptotical method is used to analyze phenomenological bifurcation. We find that the neuronal activity of spiking and bursting chaos remains for finite values of the noise intensity.

  2. Simple Deterministically Constructed Recurrent Neural Networks

    NASA Astrophysics Data System (ADS)

    Rodan, Ali; Tiňo, Peter

    A large number of models for time series processing, forecasting or modeling follows a state-space formulation. Models in the specific class of state-space approaches, referred to as Reservoir Computing, fix their state-transition function. The state space with the associated state transition structure forms a reservoir, which is supposed to be sufficiently complex so as to capture a large number of features of the input stream that can be potentially exploited by the reservoir-to-output readout mapping. The largely "black box" character of reservoirs prevents us from performing a deeper theoretical investigation of the dynamical properties of successful reservoirs. Reservoir construction is largely driven by a series of (more-or-less) ad-hoc randomized model building stages, with both the researchers and practitioners having to rely on a series of trials and errors. We show that a very simple deterministically constructed reservoir with simple cycle topology gives performances comparable to those of the Echo State Network (ESN) on a number of time series benchmarks. Moreover, we argue that the memory capacity of such a model can be made arbitrarily close to the proved theoretical limit.

  3. Deterministic particle transport in a ratchet flow

    NASA Astrophysics Data System (ADS)

    Beltrame, Philippe; Makhoul, Mounia; Joelson, Maminirina

    2016-01-01

    This study is motivated by the issue of the pumping of particle through a periodic modulated channel. We focus on a simplified deterministic model of small inertia particles within the Stokes flow framework that we call "ratchet flow." A path-following method is employed in the parameter space in order to retrace the scenario which from bounded periodic solutions leads to particle transport. Depending on whether the magnitude of the particle drag is moderate or large, two main transport mechanisms are identified in which the role of the parity symmetry of the flow differs. For large drag, transport is induced by flow asymmetry, while for moderate drag, since the full transport solution bifurcation structure already exists for symmetric settings, flow asymmetry only makes the transport effective. We analyzed the scenarios of current reversals for each mechanism as well as the role of synchronization. In particular we show that, for large drag, the particle drift is similar to phase slip in a synchronization problem.

  4. Experimental Mathematics and Mathematical Physics

    SciTech Connect

    Bailey, David H.; Borwein, Jonathan M.; Broadhurst, David; Zudilin, Wadim

    2009-06-26

    One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recognize the resulting numerical values. Recently these techniques have been applied with great success to problems in mathematical physics. Notable among these applications are the identification of some key multi-dimensional integrals that arise in Ising theory, quantum field theory and in magnetic spin theory.

  5. Stochastic and Deterministic Assembly Processes in Subsurface Microbial Communities

    SciTech Connect

    Stegen, James C.; Lin, Xueju; Konopka, Allan; Fredrickson, Jim K.

    2012-03-29

    A major goal of microbial community ecology is to understand the forces that structure community composition. Deterministic selection by specific environmental factors is sometimes important, but in other cases stochastic or ecologically neutral processes dominate. Lacking is a unified conceptual framework aiming to understand why deterministic processes dominate in some contexts but not others. Here we work towards such a framework. By testing predictions derived from general ecological theory we aim to uncover factors that govern the relative influences of deterministic and stochastic processes. We couple spatiotemporal data on subsurface microbial communities and environmental parameters with metrics and null models of within and between community phylogenetic composition. Testing for phylogenetic signal in organismal niches showed that more closely related taxa have more similar habitat associations. Community phylogenetic analyses further showed that ecologically similar taxa coexist to a greater degree than expected by chance. Environmental filtering thus deterministically governs subsurface microbial community composition. More importantly, the influence of deterministic environmental filtering relative to stochastic factors was maximized at both ends of an environmental variation gradient. A stronger role of stochastic factors was, however, supported through analyses of phylogenetic temporal turnover. While phylogenetic turnover was on average faster than expected, most pairwise comparisons were not themselves significantly non-random. The relative influence of deterministic environmental filtering over community dynamics was elevated, however, in the most temporally and spatially variable environments. Our results point to general rules governing the relative influences of stochastic and deterministic processes across micro- and macro-organisms.

  6. Mathematics Education.

    ERIC Educational Resources Information Center

    Langbort, Carol, Ed.; Curtis, Deborah, Ed.

    2000-01-01

    The focus of this special issue is mathematics education. All articles were written by graduates of the new masters Degree program in which students earn a Master of Arts degree in Education with a concentration in Mathematics Education at San Francisco State University. Articles include: (1) "Developing Teacher-Leaders in a Masters Degree Program…

  7. Technical Mathematics.

    ERIC Educational Resources Information Center

    Flannery, Carol A.

    This manuscript provides information and problems for teaching mathematics to vocational education students. Problems reflect applications of mathematical concepts to specific technical areas. The materials are organized into six chapters. Chapter 1 covers basic arithmetic, including fractions, decimals, ratio and proportions, percentages, and…

  8. Innovative Mathematics.

    ERIC Educational Resources Information Center

    Siskiyou County Superintendent of Schools, Yreka, CA.

    The purpose of this project was to raise the mathematics skills of 100 mathematically retarded students in grades one through eight by one year through the development of an inservice strategy prepared by four teacher specialists. Also used in the study was a control group of 100 students chosen from the median range of stanines on pretest scores…

  9. Mathematics Scrapbook

    ERIC Educational Resources Information Center

    Prochazka, Helen

    2004-01-01

    One section of this "scrapbook" section describes Pythagoras' belief in the connections between music and mathematics -- that everything in the universe was a series of harmonies and regulated by music. Another section explains why Phythagoras felt it important for women to be encouraged to learn mathematics. At least 28 women were involved in his…

  10. Home Chaos: Sociodemographic, Parenting, Interactional, and Child Correlates

    ERIC Educational Resources Information Center

    Dumas, Jean E.; Nissley, Jenelle; Nordstrom, Alicia; Smith, Emilie Phillips; Prinz, Ronald J.; Levine, Douglas W.

    2005-01-01

    We conducted 2 studies to (a) establish the usefulness of the construct of home chaos, (b) investigate its correlates, and (c) determine the validity of the Confusion, Hubbub, and Order Scale (CHAOS) used to measure the construct in each study. Study 1 relied on a sample of European American preschoolers and their mothers and Study 2 on a sample…

  11. 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…

  12. 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…

  13. C. Y. Chao, Pair Creation and Pair Annihilation

    NASA Astrophysics Data System (ADS)

    Li, Bing An; Yang, C. N.

    C. Y. Chao's contribution to physicists' acceptance of QED in 1933-1934 through his experiments of 1930 is analyzed. It is pointed out that Blackett and Occhialini's key suggestion of 1933 about hole theory was based on identifying Chao's "additional scattered rays" (1930) as due to pair annihilation.

  14. C. Y. Chao, Pair Creation and Pair Annihilation

    NASA Astrophysics Data System (ADS)

    Li, Bing An; Yang, C. N.

    2013-05-01

    C. Y. Chao's contribution to physicists' acceptance of QED in 1933-1934 through his experiments of 1930 is analyzed. It is pointed out that Blackett and Occhialini's key suggestion of 1933 about hole theory was based on identifying Chao's "additional scattered rays" (1930) as due to pair annihilation.

  15. 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…

  16. 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…

  17. 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…

  18. Chaos/Complexity Science and Second Language Acquisition.

    ERIC Educational Resources Information Center

    Larsen-Freeman, Diane

    1997-01-01

    Discusses the similarities between the science of chaos/complexity and second language acquisition (SLA). Notes that chaos/complexity scientists focus on how disorder yields to order and on how complexity arises in nature. Points out that the study of dynamic, complex nonlinear systems is meaningful in SLA as well. (78 references) (Author/CK)

  19. Chaos formation by sublimation of volatile-rich substrate: Evidence from Galaxias Chaos, Mars

    NASA Astrophysics Data System (ADS)

    Pedersen, G. B. M.; Head, J. W.

    2011-01-01

    Galaxias Chaos deviates significantly from other chaotic regions due to the lack of associated outflow channels, lack of big elevation differences between the chaos and the surrounding terrain and due to gradual trough formation. A sequence of troughs in different stages is observed, and examples of closed troughs within blocks suggest that the trough formation is governed by a local stress field rather than a regional stress field. Moreover, geomorphic evidence suggests that Galaxias Chaos is capped by Elysium lavas, which superpose an unstable subsurface layer that causes chaotic tilting of blocks and trough formation. Based on regional mapping we suggest a formation model, where Vastitas Borealis Formation embedded between Elysium lavas is the unstable subsurface material, because gradual volatile loss causes shrinkage and differential substrate movement. This process undermines the lava cap, depressions form and gradually troughs develop producing a jigsaw puzzle of blocks due to trough coalescence. Observations of chaos west of Elysium Rise indicate that this process might have been widespread along the contact between Vastitas Borealis Formation and Elysium lavas. However, the chaotic regions have probably been superposed by Elysium/Utopia flows to the NW of Elysium Rise, and partly submerged with younger lavas to the west.

  20. BOOK REVIEW: Nonlinear Dynamics: Integrability, Chaos and Patterns

    NASA Astrophysics Data System (ADS)

    Grammaticos, B.

    2004-02-01

    When the editorial office of Journal of Physics A: Mathematical and General of the Institute of Physics Publishing asked me to review a book on nonlinear dynamics I experienced an undeniable apprehension. Indeed, the domain is a rapidly expanding one and writing a book aiming at a certain degree of completeness looks like an almost impossible task. My uneasiness abated somewhat when I saw the names of the authors, two well-known specialists of the nonlinear domain, but it was only when I held the book in my hands that I felt really reassured. The book is not just a review of the recent (and less so) findings on nonlinear systems. It is also a textbook. The authors set out to provide a detailed, step by step, introduction to the domain of nonlinearity and its various subdomains: chaos, integrability and pattern formation (although this last topic is treated with far less detail than the other two). The public they have in mind is obviously that of university students, graduate or undergraduate, who are interested in nonlinear phenomena. I suspect that a non-negligible portion of readers will be people who have to teach topics which figure among those included in the book: they will find this monograph an excellent companion to their course. The book is written in a pedagogical way, with a profusion of examples, detailed explanations and clear diagrams. The point of view is that of a physicist, which to my eyes is a major advantage. The mathematical formulation remains simple and perfectly intelligible. Thus the reader is not bogged down by fancy mathematical formalism, which would have discouraged the less experienced ones. A host of exercises accompanies every chapter. This will give the novice the occasion to develop his/her problem-solving skills and acquire competence in the use of nonlinear techniques. Some exercises are quite straightforward, like `verify the relation 14.81'. Others are less so, such as `prepare a write-up on a) frequency-locking and b) devil

  1. Nanotransfer and nanoreplication using deterministically grown sacrificial nanotemplates

    DOEpatents

    Melechko, Anatoli V.; McKnight, Timothy E. , Guillorn, Michael A.; Ilic, Bojan; Merkulov, Vladimir I.; Doktycz, Mitchel J.; Lowndes, Douglas H.; Simpson, Michael L.

    2011-05-17

    Methods, manufactures, machines and compositions are described for nanotransfer and nanoreplication using deterministically grown sacrificial nanotemplates. A method includes depositing a catalyst particle on a surface of a substrate to define a deterministically located position; growing an aligned elongated nanostructure on the substrate, an end of the aligned elongated nanostructure coupled to the substrate at the deterministically located position; coating the aligned elongated nanostructure with a conduit material; removing a portion of the conduit material to expose the catalyst particle; removing the catalyst particle; and removing the elongated nanostructure to define a nanoconduit.

  2. Surface plasmon field enhancements in deterministic aperiodic structures.

    PubMed

    Shugayev, Roman

    2010-11-22

    In this paper we analyze optical properties and plasmonic field enhancements in large aperiodic nanostructures. We introduce extension of Generalized Ohm's Law approach to estimate electromagnetic properties of Fibonacci, Rudin-Shapiro, cluster-cluster aggregate and random deterministic clusters. Our results suggest that deterministic aperiodic structures produce field enhancements comparable to random morphologies while offering better understanding of field localizations and improved substrate design controllability. Generalized Ohm's law results for deterministic aperiodic structures are in good agreement with simulations obtained using discrete dipole method. PMID:21164839

  3. Bond chaos in spin glasses revealed through thermal boundary conditions

    NASA Astrophysics Data System (ADS)

    Wang, Wenlong; Machta, Jonathan; Katzgraber, Helmut G.

    2016-06-01

    Spin glasses have competing interactions that lead to a rough energy landscape which is highly susceptible to small perturbations. These chaotic effects strongly affect numerical simulations and, as such, gaining a deeper understanding of chaos in spin glasses is of much importance. The use of thermal boundary conditions is an effective approach to study chaotic phenomena. Here we generalize population annealing Monte Carlo, combined with thermal boundary conditions, to study bond chaos due to small perturbations in the spin-spin couplings of the three-dimensional Edwards-Anderson Ising spin glass. We show that bond and temperature-induced chaos share the same scaling exponents and that bond chaos is stronger than temperature chaos.

  4. 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

  5. Deterministic, Nanoscale Fabrication of Mesoscale Objects

    SciTech Connect

    Jr., R M; Shirk, M; Gilmer, G; Rubenchik, A

    2004-09-24

    Neither LLNL nor any other organization has the capability to perform deterministic fabrication of mm-sized objects with arbitrary, {micro}m-sized, 3-dimensional features with 20-nm-scale accuracy and smoothness. This is particularly true for materials such as high explosives and low-density aerogels. For deterministic fabrication of high energy-density physics (HEDP) targets, it will be necessary both to fabricate features in a wide variety of materials as well as to understand and simulate the fabrication process. We continue to investigate, both in experiment and in modeling, the ablation/surface-modification processes that occur with the use of laser pulses that are near the ablation threshold fluence. During the first two years, we studied ablation of metals, and we used sub-ps laser pulses, because pulses shorter than the electron-phonon relaxation time offered the most precise control of the energy that can be deposited into a metal surface. The use of sub-ps laser pulses also allowed a decoupling of the energy-deposition process from the ensuing movement/ablation of the atoms from the solid, which simplified the modeling. We investigated the ablation of material from copper, gold, and nickel substrates. We combined the power of the 1-D hydrocode ''HYADES'' with the state-of-the-art, 3-D molecular dynamics simulations ''MDCASK'' in our studies. For FY04, we have stretched ourselves to investigate laser ablation of carbon, including chemically-assisted processes. We undertook this research, because the energy deposition that is required to perform direct sublimation of carbon is much higher than that to stimulate the reaction 2C + O{sub 2} => 2CO. Thus, extremely fragile carbon aerogels might survive the chemically-assisted process more readily than ablation via direct laser sublimation. We had planned to start by studying vitreous carbon and move onto carbon aerogels. We were able to obtain flat, high-quality vitreous carbon, which was easy to work on

  6. Deterministic Function Computation with Chemical Reaction Networks*

    PubMed Central

    Chen, Ho-Lin; Doty, David; Soloveichik, David

    2013-01-01

    Chemical reaction networks (CRNs) formally model chemistry in a well-mixed solution. CRNs are widely used to describe information processing occurring in natural cellular regulatory networks, and with upcoming advances in synthetic biology, CRNs are a promising language for the design of artificial molecular control circuitry. Nonetheless, despite the widespread use of CRNs in the natural sciences, the range of computational behaviors exhibited by CRNs is not well understood. CRNs have been shown to be efficiently Turing-universal (i.e., able to simulate arbitrary algorithms) when allowing for a small probability of error. CRNs that are guaranteed to converge on a correct answer, on the other hand, have been shown to decide only the semilinear predicates (a multi-dimensional generalization of “eventually periodic” sets). We introduce the notion of function, rather than predicate, computation by representing the output of a function f : ℕk → ℕl by a count of some molecular species, i.e., if the CRN starts with x1, …, xk molecules of some “input” species X1, …, Xk, the CRN is guaranteed to converge to having f(x1, …, xk) molecules of the “output” species Y1, …, Yl. We show that a function f : ℕk → ℕl is deterministically computed by a CRN if and only if its graph {(x, y) ∈ ℕk × ℕl ∣ f(x) = y} is a semilinear set. Finally, we show that each semilinear function f (a function whose graph is a semilinear set) can be computed by a CRN on input x in expected time O(polylog ∥x∥1). PMID:25383068

  7. Reproducible and deterministic production of aspheres

    NASA Astrophysics Data System (ADS)

    Leitz, Ernst Michael; Stroh, Carsten; Schwalb, Fabian

    2015-10-01

    Aspheric lenses are ground in a single point cutting mode. Subsequently different iterative polishing methods are applied followed by aberration measurements on external metrology instruments. For an economical production, metrology and correction steps need to be reduced. More deterministic grinding and polishing is mandatory. Single point grinding is a path-controlled process. The quality of a ground asphere is mainly influenced by the accuracy of the machine. Machine improvements must focus on path accuracy and thermal expansion. Optimized design, materials and thermal management reduce thermal expansion. The path accuracy can be improved using ISO 230-2 standardized measurements. Repeated interferometric measurements over the total travel of all CNC axes in both directions are recorded. Position deviations evaluated in correction tables improve the path accuracy and that of the ground surface. Aspheric polishing using a sub-aperture flexible polishing tool is a dwell time controlled process. For plano and spherical polishing the amount of material removal during polishing is proportional to pressure, relative velocity and time (Preston). For the use of flexible tools on aspheres or freeform surfaces additional non-linear components are necessary. Satisloh ADAPT calculates a predicted removal function from lens geometry, tool geometry and process parameters with FEM. Additionally the tooĺs local removal characteristics is determined in a simple test. By oscillating the tool on a plano or spherical sample of the same lens material, a trench is created. Its 3-D profile is measured to calibrate the removal simulation. Remaining aberrations of the desired lens shape can be predicted, reducing iteration and metrology steps.

  8. Deterministic versus stochastic trends: Detection and challenges

    NASA Astrophysics Data System (ADS)

    Fatichi, S.; Barbosa, S. M.; Caporali, E.; Silva, M. E.

    2009-09-01

    The detection of a trend in a time series and the evaluation of its magnitude and statistical significance is an important task in geophysical research. This importance is amplified in climate change contexts, since trends are often used to characterize long-term climate variability and to quantify the magnitude and the statistical significance of changes in climate time series, both at global and local scales. Recent studies have demonstrated that the stochastic behavior of a time series can change the statistical significance of a trend, especially if the time series exhibits long-range dependence. The present study examines the trends in time series of daily average temperature recorded in 26 stations in the Tuscany region (Italy). In this study a new framework for trend detection is proposed. First two parametric statistical tests, the Phillips-Perron test and the Kwiatkowski-Phillips-Schmidt-Shin test, are applied in order to test for trend stationary and difference stationary behavior in the temperature time series. Then long-range dependence is assessed using different approaches, including wavelet analysis, heuristic methods and by fitting fractionally integrated autoregressive moving average models. The trend detection results are further compared with the results obtained using nonparametric trend detection methods: Mann-Kendall, Cox-Stuart and Spearman's ρ tests. This study confirms an increase in uncertainty when pronounced stochastic behaviors are present in the data. Nevertheless, for approximately one third of the analyzed records, the stochastic behavior itself cannot explain the long-term features of the time series, and a deterministic positive trend is the most likely explanation.

  9. Understanding Vertical Jump Potentiation: A Deterministic Model.

    PubMed

    Suchomel, Timothy J; Lamont, Hugh S; Moir, Gavin L

    2016-06-01

    This review article discusses previous postactivation potentiation (PAP) literature and provides a deterministic model for vertical jump (i.e., squat jump, countermovement jump, and drop/depth jump) potentiation. There are a number of factors that must be considered when designing an effective strength-power potentiation complex (SPPC) focused on vertical jump potentiation. Sport scientists and practitioners must consider the characteristics of the subject being tested and the design of the SPPC itself. Subject characteristics that must be considered when designing an SPPC focused on vertical jump potentiation include the individual's relative strength, sex, muscle characteristics, neuromuscular characteristics, current fatigue state, and training background. Aspects of the SPPC that must be considered for vertical jump potentiation include the potentiating exercise, level and rate of muscle activation, volume load completed, the ballistic or non-ballistic nature of the potentiating exercise, and the rest interval(s) used following the potentiating exercise. Sport scientists and practitioners should design and seek SPPCs that are practical in nature regarding the equipment needed and the rest interval required for a potentiated performance. If practitioners would like to incorporate PAP as a training tool, they must take the athlete training time restrictions into account as a number of previous SPPCs have been shown to require long rest periods before potentiation can be realized. Thus, practitioners should seek SPPCs that may be effectively implemented in training and that do not require excessive rest intervals that may take away from valuable training time. Practitioners may decrease the necessary time needed to realize potentiation by improving their subject's relative strength. PMID:26712510

  10. Deterministic phase retrieval employing spherical illumination

    NASA Astrophysics Data System (ADS)

    Martínez-Carranza, J.; Falaggis, K.; Kozacki, T.

    2015-05-01

    Deterministic Phase Retrieval techniques (DPRTs) employ a series of paraxial beam intensities in order to recover the phase of a complex field. These paraxial intensities are usually generated in systems that employ plane-wave illumination. This type of illumination allows a direct processing of the captured intensities with DPRTs for recovering the phase. Furthermore, it has been shown that intensities for DPRTs can be acquired from systems that use spherical illumination as well. However, this type of illumination presents a major setback for DPRTs: the captured intensities change their size for each position of the detector on the propagation axis. In order to apply the DPRTs, reescalation of the captured intensities has to be applied. This condition can increase the error sensitivity of the final phase result if it is not carried out properly. In this work, we introduce a novel system based on a Phase Light Modulator (PLM) for capturing the intensities when employing spherical illumination. The proposed optical system enables us to capture the diffraction pattern of under, in, and over-focus intensities. The employment of the PLM allows capturing the corresponding intensities without displacing the detector. Moreover, with the proposed optical system we can control accurately the magnification of the captured intensities. Thus, the stack of captured intensities can be used in DPRTs, overcoming the problems related with the resizing of the images. In order to prove our claims, the corresponding numerical experiments will be carried out. These simulations will show that the retrieved phases with spherical illumination are accurate and can be compared with those that employ plane wave illumination. We demonstrate that with the employment of the PLM, the proposed optical system has several advantages as: the optical system is compact, the beam size on the detector plane is controlled accurately, and the errors coming from mechanical motion can be suppressed easily.

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

    PubMed

    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

  12. 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

  13. Deconstructing spatiotemporal chaos using local symbolic dynamics.

    PubMed

    Pethel, Shawn D; Corron, Ned J; Bollt, Erik

    2007-11-23

    We find that the global symbolic dynamics of a diffusively coupled map lattice is well approximated by a very small local model for weak to moderate coupling strengths. A local symbolic model is a truncation of the full symbolic model to one that considers only a single element and a few neighbors. Using interval analysis, we give rigorous results for a range of coupling strengths and different local model widths. Examples are presented of extracting a local symbolic model from data and of controlling spatiotemporal chaos. PMID:18233220

  14. Chaos in classical D0-brane mechanics

    NASA Astrophysics Data System (ADS)

    Gur-Ari, Guy; Hanada, Masanori; Shenker, Stephen H.

    2016-02-01

    We study chaos in the classical limit of the matrix quantum mechanical system describing D0-brane dynamics. We determine a precise value of the largest Lyapunov exponent, and, with less precision, calculate the entire spectrum of Lyapunov exponents. We verify that these approach a smooth limit as N → ∞. We show that a classical analog of scrambling occurs with fast scrambling scaling, t ∗ ˜ log S. These results confirm the k-locality property of matrix mechanics discussed by Sekino and Susskind.

  15. Chaos in the BMN matrix model

    NASA Astrophysics Data System (ADS)

    Asano, Yuhma; Kawai, Daisuke; Yoshida, Kentaroh

    2015-06-01

    We study classical chaotic motions in the Berenstein-Maldacena-Nastase (BMN) matrix model. For this purpose, it is convenient to focus upon a reduced system composed of two-coupled anharmonic oscillators by supposing an ansatz. We examine three ansätze: 1) two pulsating fuzzy spheres, 2) a single Coulomb-type potential, and 3) integrable fuzzy spheres. For the first two cases, we show the existence of chaos by computing Poincaré sections and a Lyapunov spectrum. The third case leads to an integrable system. As a result, the BMN matrix model is not integrable in the sense of Liouville, though there may be some integrable subsectors.

  16. 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. PMID:24483542

  17. 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.

  18. Delayed self-synchronization in homoclinic chaos

    NASA Astrophysics Data System (ADS)

    Arecchi, F. T.; Meucci, R.; Allaria, E.; di Garbo, A.; Tsimring, L. S.

    2002-04-01

    The chaotic spike train of a homoclinic dynamical system is self-synchronized by applying a time-delayed correction proportional to the laser output intensity. Due to the sensitive nature of the homoclinic chaos to external perturbations, stabilization of very long-periodic orbits is possible. On these orbits, the dynamics appears chaotic over a finite time, but then it repeats with a recurrence time that is slightly longer than the delay time. The effect, called delayed self-synchronization, displays analogies with neurodynamic events that occur in the buildup of long-term memories.

  19. Topological organization of (low-dimensional) chaos

    SciTech Connect

    Tufillaro, N.B.

    1992-12-01

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

  20. Topological organization of (low-dimensional) chaos

    SciTech Connect

    Tufillaro, N.B.

    1992-01-01

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

  1. A Method to Separate Stochastic and Deterministic Information from Electrocardiograms

    NASA Astrophysics Data System (ADS)

    Gutiérrez, R. M.; Sandoval, L. A.

    2005-01-01

    In this work we present a new idea to develop a method to separate stochastic and deterministic information contained in an electrocardiogram, ECG, which may provide new sources of information with diagnostic purposes. We assume that the ECG has information corresponding to many different processes related with the cardiac activity as well as contamination from different sources related with the measurement procedure and the nature of the observed system itself. The method starts with the application of an improved archetypal analysis to separate the mentioned stochastic and deterministic information. From the stochastic point of view we analyze Renyi entropies, and with respect to the deterministic perspective we calculate the autocorrelation function and the corresponding correlation time. We show that healthy and pathologic information may be stochastic and/or deterministic, can be identified by different measures and located in different parts of the ECG.

  2. Integral-transport-based deterministic brachytherapy dose calculations

    NASA Astrophysics Data System (ADS)

    Zhou, Chuanyu; Inanc, Feyzi

    2003-01-01

    We developed a transport-equation-based deterministic algorithm for computing three-dimensional brachytherapy dose distributions. The deterministic algorithm has been based on the integral transport equation. The algorithm provided us with the capability of computing dose distributions for multiple isotropic point and/or volumetric sources in a homogenous/heterogeneous medium. The algorithm results have been benchmarked against the results from the literature and MCNP results for isotropic point sources and volumetric sources.

  3. HyDRa: control of parameters for deterministic polishing.

    PubMed

    Ruiz, E; Salas, L; Sohn, E; Luna, E; Herrera, J; Quiros, F

    2013-08-26

    Deterministic hydrodynamic polishing with HyDRa requires a precise control of polishing parameters, such as propelling air pressure, slurry density, slurry flux and tool height. We describe the HyDRa polishing system and prove how precise, deterministic polishing can be achieved in terms of the control of these parameters. The polishing results of an 84 cm hyperbolic mirror are presented to illustrate how the stability of these parameters is important to obtain high-quality surfaces. PMID:24105579

  4. Experimental Chaos - Proceedings of the 3rd Conference

    NASA Astrophysics Data System (ADS)

    Harrison, Robert G.; Lu, Weiping; Ditto, William; Pecora, Lou; Spano, Mark; Vohra, Sandeep

    1996-10-01

    The Table of Contents for the full book PDF is as follows: * Preface * Spatiotemporal Chaos and Patterns * Scale Segregation via Formation of Domains in a Nonlinear Optical System * Laser Dynamics as Hydrodynamics * Spatiotemporal Dynamics of Human Epileptic Seizures * Experimental Transition to Chaos in a Quasi 1D Chain of Oscillators * Measuring Coupling in Spatiotemporal Dynamical Systems * Chaos in Vortex Breakdown * Dynamical Analysis * Radial Basis Function Modelling and Prediction of Time Series * Nonlinear Phenomena in Polyrhythmic Hand Movements * Using Models to Diagnose, Test and Control Chaotic Systems * New Real-Time Analysis of Time Series Data with Physical Wavelets * Control and Synchronization * Measuring and Controlling Chaotic Dynamics in a Slugging Fluidized Bed * Control of Chaos in a Laser with Feedback * Synchronization and Chaotic Diode Resonators * Control of Chaos by Continuous-time Feedback with Delay * A Framework for Communication using Chaos Sychronization * Control of Chaos in Switching Circuits * Astrophysics, Meteorology and Oceanography * Solar-Wind-Magnetospheric Dynamics via Satellite Data * Nonlinear Dynamics of the Solar Atmosphere * Fractal Dimension of Scalar and Vector Variables from Turbulence Measurements in the Atmospheric Surface Layer * Mechanics * Escape and Overturning: Subtle Transient Behavior in Nonlinear Mechanical Models * Organising Centres in the Dynamics of Parametrically Excited Double Pendulums * Intermittent Behaviour in a Heating System Driven by Phase Transitions * Hydrodynamics * Size Segregation in Couette Flow of Granular Material * Routes to Chaos in Rotational Taylor-Couette Flow * Experimental Study of the Laminar-Turbulent Transition in an Open Flow System * Chemistry * Order and Chaos in Excitable Media under External Forcing * A Chemical Wave Propagation with Accelerating Speed Accompanied by Hydrodynamic Flow * Optics * Instabilities in Semiconductor Lasers with Optical Injection * Spatio

  5. Structural deterministic safety factors selection criteria and verification

    NASA Technical Reports Server (NTRS)

    Verderaime, V.

    1992-01-01

    Though current deterministic safety factors are arbitrarily and unaccountably specified, its ratio is rooted in resistive and applied stress probability distributions. This study approached the deterministic method from a probabilistic concept leading to a more systematic and coherent philosophy and criterion for designing more uniform and reliable high-performance structures. The deterministic method was noted to consist of three safety factors: a standard deviation multiplier of the applied stress distribution; a K-factor for the A- or B-basis material ultimate stress; and the conventional safety factor to ensure that the applied stress does not operate in the inelastic zone of metallic materials. The conventional safety factor is specifically defined as the ratio of ultimate-to-yield stresses. A deterministic safety index of the combined safety factors was derived from which the corresponding reliability proved the deterministic method is not reliability sensitive. The bases for selecting safety factors are presented and verification requirements are discussed. The suggested deterministic approach is applicable to all NASA, DOD, and commercial high-performance structures under static stresses.

  6. Mathematical Geology.

    ERIC Educational Resources Information Center

    McCammon, Richard B.

    1979-01-01

    The year 1978 marked a continued trend toward practical applications in mathematical geology. Developments included work in interactive computer graphics, factor analysis, the vanishing tons problem, universal kriging, and resource estimating. (BB)

  7. Mathematics disorder

    MedlinePlus

    The child may have problems in school, including behavior problems and loss of self-esteem. Some children with mathematics disorder become anxious or afraid when given math problems, making the problem even worse.

  8. Mathematics Detective.

    ERIC Educational Resources Information Center

    Johnson, Jerry

    1997-01-01

    Presents 12 questions related to a given real-life situation about a man shaving and the number of hairs in his beard in order to help students see the connection between mathematics and the world around them. (ASK)

  9. Mathematical Games

    ERIC Educational Resources Information Center

    Gardner, Martin

    1978-01-01

    Describes the life and work of Charles Peirce, U.S. mathematician and philosopher. His accomplishments include contributions to logic, the foundations of mathematics and scientific method, and decision theory and probability theory. (MA)

  10. 'Chaos is come again': Nothingness in Shakespeare's metadramatic time and space

    NASA Astrophysics Data System (ADS)

    Oswald, John David

    The extraordinary advances of twentieth-century science, which overlay, and in some cases overturn, the Newtonian precepts upon which physics was founded, have captured a share of the popular imagination. Quantum mechanics, relativity theory, and chaos theory are the stuff of science fact and science fiction, of technological innovation and artistic invention. Intricate ``fractal'' images adorn poster art, and science fiction fantasy (long a niche market for popular fiction) is the genre of the blockbuster film and the television franchise. Astronomers and physicists are writing pop-science bestsellers for the layman, making theory accessible to those who cannot do the math. This work focuses on Shakespearean notions of time and space in selected metadramatic passages from three plays that feature embattled monarchs: Richard II, King Lear, and The Winter's Tale. Shakespeare's employment of metaphors that are also ``cardinal metaphors'' of science is examined to determine how his dramatic works fare under a post-deterministic paradigm. A chaos-theory model is advanced for theatrical performance, and analogies are drawn from scientific theory to discuss dramatic language and action (e.g., ``nothingness'' in different contexts is compared variously with black holes, dark matter, vacuum genesis in a spatial void roiling with virtual particles, the empty space within matter, etc.). Of primary importance are the notions of quantum observership (the impossibility of separating observation from participation in scientific experimentation) and complementarity (Bohr's theory to account for the dual behavior of radiation as both waves and particles). Shakespeare's persistent metadramatic emphasis is seen as an effort to draw his audience (observers) into conscious participation in the imaginative act of bringing his plays into being. Complementarity relates to the promotion of multiple perspectives in all three plays and to the dramaturgical structure of The Winter's Tale.

  11. 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.

  12. Order and chaos in soft condensed matter

    NASA Astrophysics Data System (ADS)

    Sood, A. K.; Ganapathy, Rajesh

    2006-07-01

    Soft matter, like colloidal suspensions and surfactant gels, exhibit strong response to modest external perturbations. This paper reviews our recent experiments on the nonlinear flow behaviour of surfactant worm-like micellar gels. A rich dynamic behaviour exhibiting regular, quasi-periodic, intermittency and chaos is observed. In particular, we have shown experimentally that the route to chaos is via Type-II intermittency in shear thinning worm-like micellar solution of cetyltrimethylammonium tosylate where the strength of flow-concentration coupling is tuned by the addition of sodium chloride. A Poincaré first return map of the time series and the probability distribution of laminar length between burst events show that our data are consistent with Type-II intermittency. The existence of a `Butterfly' intensity pattern in small angle light scattering (SALS) measurements performed simultaneously with the rheological measurements confirms the coupling of flow to concentration fluctuations in the system under study. The scattered depolarised intensity in SALS, sensitive to orientational order fluctuations, shows the same time-dependence (like intermittency) as that of shear stress.

  13. The dream's navel between chaos and thought.

    PubMed

    Scalzone, F; Zontini, G

    2001-04-01

    The authors begin by drawing attention to the problem of the transition from the biological to the psychic, noting that Freud himself, with his background in the neurosciences, grappled with it throughout his career. Certain recent paradigms more commonly applied to the natural sciences, such as in particular chaos and complexity theory, can in their view prove fruitful in psychoanalysis too, and it is shown how these notions are inherent in some of Freud's conceptions. The unconscious is stated to operate like a neural network, performing the kind of parallel processing used in the computing of highly complex situations, whereas the conscious mind is sequential. Dreams, in the authors' opinion, are organisers of the mind, imparting order to the turbulence of the underlying wishes and unconscious fantasies and structuring them through the dream work. Through dreams, the structured linearity of conscious thought can emerge out of the non-linear chaos of the drives. The dream's navel can be seen as the chaotic link, or interface, between the unconscious wish, which constitutes an attractor, and the conscious thought. The attractor may be visualised as having an hourglass or clepsydra shape, the narrow section being the dream's navel, and, being the same at any scale of observation, has the property of fractality. PMID:11341062

  14. 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.

  15. A Comparison of Deterministic and Stochastic Modeling Approaches for Biochemical Reaction Systems: On Fixed Points, Means, and Modes

    PubMed Central

    Hahl, Sayuri K.; Kremling, Andreas

    2016-01-01

    In the mathematical modeling of biochemical reactions, a convenient standard approach is to use ordinary differential equations (ODEs) that follow the law of mass action. However, this deterministic ansatz is based on simplifications; in particular, it neglects noise, which is inherent to biological processes. In contrast, the stochasticity of reactions is captured in detail by the discrete chemical master equation (CME). Therefore, the CME is frequently applied to mesoscopic systems, where copy numbers of involved components are small and random fluctuations are thus significant. Here, we compare those two common modeling approaches, aiming at identifying parallels and discrepancies between deterministic variables and possible stochastic counterparts like the mean or modes of the state space probability distribution. To that end, a mathematically flexible reaction scheme of autoregulatory gene expression is translated into the corresponding ODE and CME formulations. We show that in the thermodynamic limit, deterministic stable fixed points usually correspond well to the modes in the stationary probability distribution. However, this connection might be disrupted in small systems. The discrepancies are characterized and systematically traced back to the magnitude of the stoichiometric coefficients and to the presence of nonlinear reactions. These factors are found to synergistically promote large and highly asymmetric fluctuations. As a consequence, bistable but unimodal, and monostable but bimodal systems can emerge. This clearly challenges the role of ODE modeling in the description of cellular signaling and regulation, where some of the involved components usually occur in low copy numbers. Nevertheless, systems whose bimodality originates from deterministic bistability are found to sustain a more robust separation of the two states compared to bimodal, but monostable systems. In regulatory circuits that require precise coordination, ODE modeling is thus still

  16. Selection of polynomial chaos bases via Bayesian model uncertainty methods with applications to sparse approximation of PDEs with stochastic inputs

    SciTech Connect

    Karagiannis, Georgios Lin, Guang

    2014-02-15

    Generalized polynomial chaos (gPC) expansions allow us to represent the solution of a stochastic system using a series of polynomial chaos basis functions. The number of gPC terms increases dramatically as the dimension of the random input variables increases. When the number of the gPC terms is larger than that of the available samples, a scenario that often occurs when the corresponding deterministic solver is computationally expensive, evaluation of the gPC expansion can be inaccurate due to over-fitting. We propose a fully Bayesian approach that allows for global recovery of the stochastic solutions, in both spatial and random domains, by coupling Bayesian model uncertainty and regularization regression methods. It allows the evaluation of the PC coefficients on a grid of spatial points, via (1) the Bayesian model average (BMA) or (2) the median probability model, and their construction as spatial functions on the spatial domain via spline interpolation. The former accounts for the model uncertainty and provides Bayes-optimal predictions; while the latter provides a sparse representation of the stochastic solutions by evaluating the expansion on a subset of dominating gPC bases. Moreover, the proposed methods quantify the importance of the gPC bases in the probabilistic sense through inclusion probabilities. We design a Markov chain Monte Carlo (MCMC) sampler that evaluates all the unknown quantities without the need of ad-hoc techniques. The proposed methods are suitable for, but not restricted to, problems whose stochastic solutions are sparse in the stochastic space with respect to the gPC bases while the deterministic solver involved is expensive. We demonstrate the accuracy and performance of the proposed methods and make comparisons with other approaches on solving elliptic SPDEs with 1-, 14- and 40-random dimensions.

  17. A New Approach for Controlling Chaos in Lorenz System

    NASA Astrophysics Data System (ADS)

    Sanayei, Ali

    2009-09-01

    Is there a need for chaos? In order to answer to this important question, first, we should answer to "what chaos is?" Does "chaos" mean anarchy and confusion, or it means "randomness"? In order to answer to the second question, one may briefly consider that "chaos" means "far from the equilibrium." It is true that in a random behavior, we have "far from the equilibrium" phenomenon, but in the chaotic behavior, however, the trajectory goes far from the equilibrium, but it moves in a bounded basin. Therefore, chaos differs from randomness. In order to answer to the first question, we distinguish two states from each other. Chaos could be dangerous in many states, e.g. for an aircraft in the sky. Therefore, we should control it and return the system from the chaotic mood. But, in some states it is useful. Suppose that we have a periode-2 behavior system. If we intend to change its period, what should we do? One of the best techniques in order to change a system behavior is reaching the system into the chaotic mood for a short time, and then, by controlling chaos which is based on the feedback law, we could return the system into the desired period. Further, the control of chaos is also a way to manipulate the natural systems that are already chaotic. In this paper, we can imagine each mentioned states for chaos. Our goal is the control of a very famous system in the chaotic mood, in order to stabilize it and change its behavior into the desired behavior. We will achieved to this goal using OGY method which is based on the discrete dynamical system concept, and find the stabilized state by a new approach which is based on the generalized Routh-Hurwitz criterion.

  18. Topological supersymmetry breaking: The definition and stochastic generalization of chaos and the limit of applicability of statistics

    NASA Astrophysics Data System (ADS)

    Ovchinnikov, Igor V.; Schwartz, Robert N.; Wang, Kang L.

    2016-03-01

    The concept of deterministic dynamical chaos has a long history and is well established by now. Nevertheless, its field theoretic essence and its stochastic generalization have been revealed only very recently. Within the newly found supersymmetric theory of stochastics (STS), all stochastic differential equations (SDEs) possess topological or de Rahm supersymmetry and stochastic chaos is the phenomenon of its spontaneous breakdown. Even though the STS is free of approximations and thus is technically solid, it is still missing a firm interpretational basis in order to be physically sound. Here, we make a few important steps toward the construction of the interpretational foundation for the STS. In particular, we discuss that one way to understand why the ground states of chaotic SDEs are conditional (not total) probability distributions, is that some of the variables have infinite memory of initial conditions and thus are not “thermalized”, i.e., cannot be described by the initial-conditions-independent probability distributions. As a result, the definitive assumption of physical statistics that the ground state is a steady-state total probability distribution is not valid for chaotic SDEs.

  19. Ergodicity of Truncated Stochastic Navier Stokes with Deterministic Forcing and Dispersion

    NASA Astrophysics Data System (ADS)

    Majda, Andrew J.; Tong, Xin T.

    2016-05-01

    Turbulence in idealized geophysical flows is a very rich and important topic. The anisotropic effects of explicit deterministic forcing, dispersive effects from rotation due to the β -plane and F-plane, and topography together with random forcing all combine to produce a remarkable number of realistic phenomena. These effects have been studied through careful numerical experiments in the truncated geophysical models. These important results include transitions between coherent jets and vortices, and direct and inverse turbulence cascades as parameters are varied, and it is a contemporary challenge to explain these diverse statistical predictions. Here we contribute to these issues by proving with full mathematical rigor that for any values of the deterministic forcing, the β - and F-plane effects and topography, with minimal stochastic forcing, there is geometric ergodicity for any finite Galerkin truncation. This means that there is a unique smooth invariant measure which attracts all statistical initial data at an exponential rate. In particular, this rigorous statistical theory guarantees that there are no bifurcations to multiple stable and unstable statistical steady states as geophysical parameters are varied in contrast to claims in the applied literature. The proof utilizes a new statistical Lyapunov function to account for enstrophy exchanges between the statistical mean and the variance fluctuations due to the deterministic forcing. It also requires careful proofs of hypoellipticity with geophysical effects and uses geometric control theory to establish reachability. To illustrate the necessity of these conditions, a two-dimensional example is developed which has the square of the Euclidean norm as the Lyapunov function and is hypoelliptic with nonzero noise forcing, yet fails to be reachable or ergodic.

  20. A new surrogate modeling technique combining Kriging and polynomial chaos expansions – Application to uncertainty analysis in computational dosimetry

    SciTech Connect

    Kersaudy, Pierric; Sudret, Bruno; Varsier, Nadège; Picon, Odile; Wiart, Joe

    2015-04-01

    In numerical dosimetry, the recent advances in high performance computing led to a strong reduction of the required computational time to assess the specific absorption rate (SAR) characterizing the human exposure to electromagnetic waves. However, this procedure remains time-consuming and a single simulation can request several hours. As a consequence, the influence of uncertain input parameters on the SAR cannot be analyzed using crude Monte Carlo simulation. The solution presented here to perform such an analysis is surrogate modeling. This paper proposes a novel approach to build such a surrogate model from a design of experiments. Considering a sparse representation of the polynomial chaos expansions using least-angle regression as a selection algorithm to retain the most influential polynomials, this paper proposes to use the selected polynomials as regression functions for the universal Kriging model. The leave-one-out cross validation is used to select the optimal number of polynomials in the deterministic part of the Kriging model. The proposed approach, called LARS-Kriging-PC modeling, is applied to three benchmark examples and then to a full-scale metamodeling problem involving the exposure of a numerical fetus model to a femtocell device. The performances of the LARS-Kriging-PC are compared to an ordinary Kriging model and to a classical sparse polynomial chaos expansion. The LARS-Kriging-PC appears to have better performances than the two other approaches. A significant accuracy improvement is observed compared to the ordinary Kriging or to the sparse polynomial chaos depending on the studied case. This approach seems to be an optimal solution between the two other classical approaches. A global sensitivity analysis is finally performed on the LARS-Kriging-PC model of the fetus exposure problem.

  1. A new surrogate modeling technique combining Kriging and polynomial chaos expansions - Application to uncertainty analysis in computational dosimetry

    NASA Astrophysics Data System (ADS)

    Kersaudy, Pierric; Sudret, Bruno; Varsier, Nadège; Picon, Odile; Wiart, Joe

    2015-04-01

    In numerical dosimetry, the recent advances in high performance computing led to a strong reduction of the required computational time to assess the specific absorption rate (SAR) characterizing the human exposure to electromagnetic waves. However, this procedure remains time-consuming and a single simulation can request several hours. As a consequence, the influence of uncertain input parameters on the SAR cannot be analyzed using crude Monte Carlo simulation. The solution presented here to perform such an analysis is surrogate modeling. This paper proposes a novel approach to build such a surrogate model from a design of experiments. Considering a sparse representation of the polynomial chaos expansions using least-angle regression as a selection algorithm to retain the most influential polynomials, this paper proposes to use the selected polynomials as regression functions for the universal Kriging model. The leave-one-out cross validation is used to select the optimal number of polynomials in the deterministic part of the Kriging model. The proposed approach, called LARS-Kriging-PC modeling, is applied to three benchmark examples and then to a full-scale metamodeling problem involving the exposure of a numerical fetus model to a femtocell device. The performances of the LARS-Kriging-PC are compared to an ordinary Kriging model and to a classical sparse polynomial chaos expansion. The LARS-Kriging-PC appears to have better performances than the two other approaches. A significant accuracy improvement is observed compared to the ordinary Kriging or to the sparse polynomial chaos depending on the studied case. This approach seems to be an optimal solution between the two other classical approaches. A global sensitivity analysis is finally performed on the LARS-Kriging-PC model of the fetus exposure problem.

  2. 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.

  3. Mathematical vistas

    SciTech Connect

    Malkevitch, J. ); McCarthy, D. )

    1990-01-01

    The papers in this volume represent talks given at the monthly meetings of the Mathematics Section of the New York Academy of Sciences. They reflect the operating philosophy of the Section in its efforts to make a meaningful contribution to the mathematical life of a community that is exceedingly rich in cultural resources and intellectual opportunities. Each week during the academic year a dazzling abundance of mathematical seminars and colloquia is available in the New York metropolitan area. Most of these offer highly technical treatments intended for specialists. At the New York Academy we try to provide a forum of a different sort, where interesting ideas are presented in a congenial atmosphere to a broad mathematical audience. Many of the Section talks contain substantial specialized material, but we ask our speakers to include a strong expository component aimed at working mathematicians presumed to have no expert knowledge of the topic at hand. We urge speakers to try to provide the motivating interest they themselves would like to find in an introduction to a field other than their own. The same advice has been given to the authors of the present papers, with the goal of producing a collection that will be both accessible and stimulating to mathematical minds at large. We have tried to provide variety in the mathematical vistas offered; both pure and applied mathematics are well represented. Since the papers are presented alphabetically by author, some guidance seems appropriate as to what sorts of topics are treated, and where. There are three papers in analysis: those by Engber, Narici and Beckenstein, and Todd. Engber's deals with complex analysis on compact Riemann surfaces; Narici and Beckenstein provide an introduction to analysis on non-Archimendean fields; Todd surveys an area of contemporary functional analysis.

  4. Mathematical Perspectives

    SciTech Connect

    Glimm, J.

    2009-10-14

    Progress for the past decade or so has been extraordinary. The solution of Fermat's Last Theorem [11] and of the Poincare Conjecture [1] have resolved two of the most outstanding challenges to mathematics. For both cases, deep and advanced theories and whole subfields of mathematics came into play and were developed further as part of the solutions. And still the future is wide open. Six of the original seven problems from the Clay Foundation challenge remain open, the 23 DARPA challenge problems are open. Entire new branches of mathematics have been developed, including financial mathematics and the connection between geometry and string theory, proposed to solve the problems of quantized gravity. New solutions of the Einstein equations, inspired by shock wave theory, suggest a cosmology model which fits accelerating expansion of the universe possibly eliminating assumptions of 'dark matter'. Intellectual challenges and opportunities for mathematics are greater than ever. The role of mathematics in society continues to grow; with this growth comes new opportunities and some growing pains; each will be analyzed here. We see a broadening of the intellectual and professional opportunities and responsibilities for mathematicians. These trends are also occuring across all of science. The response can be at the level of the professional societies, which can work to deepen their interactions, not only within the mathematical sciences, but also with other scientific societies. At a deeper level, the choices to be made will come from individual mathematicians. Here, of course, the individual choices will be varied, and we argue for respect and support for this diversity of responses. In such a manner, we hope to preserve the best of the present while welcoming the best of the new.

  5. [New horizons in medicine. Chaos and its laws].

    PubMed

    Guarini, G

    1993-04-01

    We have synthesized the fundamentals that modern technology offers in all areas of research, especially in the field of biomedicine. The theory of systems, cybernetics, synergetics, boolean algebra, communication science (according to modern laws of signal transmission and translation), the solution of non-linear equations by computer science, applied principles of reduction in biological survey, fractal analysis as a representation of dynamic, chaotic, non-linear systems, defined attractors as conditioning elements of biologic function, are just a few of the many instruments that modern science offers as a revolutionary approach to research programming. Borrowing the laws of mathematics, we have defined the fundamental characteristics of linear and non-linear homeostatic systems along with the concept of predictable behavior of a system as a function of its complex structure. Lastly, we have documented, based on personal research and recent findings in biomathematics, and despite current and strong opposition, how the functional death of any dynamic system is identified by the system's absolute state of equilibrium. The operative errors at times caused by different stimuli acting on specific organs and apparatus, are interpreted not as an index of altered function but as an expression of a chaotic response of the deterministic type and therefore an indication of the system's adaptability to the specific functional requirements in that precise moment. PMID:8488333

  6. Chaos and Chaos Synchronization of a Symmetric Gyro with Linear-Plus Damping

    NASA Astrophysics Data System (ADS)

    CHEN, H.-K.

    2002-08-01

    The dynamic behavior of a symmetric gyro with linear-plus-cubic damping, which is subjected to a harmonic excitation, is studied in this paper. The Liapunov direct method has been used to obtain the sufficient conditions of the stability of the equilibrium points of the system. By applying numerical results, time history, phase diagrams, Poincaré maps, Liapunov exponents and Liapunov dimensions are presented to observe periodic and chaotic motions. Besides, several control methods, the delayed feedback control, the addition of constant motor torque, the addition of period force, and adaptive control algorithm (ACA), have been used to control chaos effectively. Finally, attention is shifted to the synchronization of chaos in the two identical chaotic motions of symmetric gyros. The results show that one can make two identical chaotic systems to synchronize through applying four different kinds of one-way coupling. Furthermore, the synchronization time is also examined.

  7. Survival thresholds and mortality rates in adaptive dynamics: conciliating deterministic and stochastic simulations.

    PubMed

    Perthame, Benoît; Gauduchon, Mathias

    2010-09-01

    Deterministic population models for adaptive dynamics are derived mathematically from individual-centred stochastic models in the limit of large populations. However, it is common that numerical simulations of both models fit poorly and give rather different behaviours in terms of evolution speeds and branching patterns. Stochastic simulations involve extinction phenomenon operating through demographic stochasticity, when the number of individual 'units' is small. Focusing on the class of integro-differential adaptive models, we include a similar notion in the deterministic formulations, a survival threshold, which allows phenotypical traits in the population to vanish when represented by few 'individuals'. Based on numerical simulations, we show that the survival threshold changes drastically the solution; (i) the evolution speed is much slower, (ii) the branching patterns are reduced continuously and (iii) these patterns are comparable to those obtained with stochastic simulations. The rescaled models can also be analysed theoretically. One can recover the concentration phenomena on well-separated Dirac masses through the constrained Hamilton-Jacobi equation in the limit of small mutations and large observation times. PMID:19734200

  8. Comparison of deterministic and stochastic methods for time-dependent Wigner simulations

    NASA Astrophysics Data System (ADS)

    Shao, Sihong; Sellier, Jean Michel

    2015-11-01

    Recently a Monte Carlo method based on signed particles for time-dependent simulations of the Wigner equation has been proposed. While it has been thoroughly validated against physical benchmarks, no technical study about its numerical accuracy has been performed. To this end, this paper presents the first step towards the construction of firm mathematical foundations for the signed particle Wigner Monte Carlo method. An initial investigation is performed by means of comparisons with a cell average spectral element method, which is a highly accurate deterministic method and utilized to provide reference solutions. Several different numerical tests involving the time-dependent evolution of a quantum wave-packet are performed and discussed in deep details. In particular, this allows us to depict a set of crucial criteria for the signed particle Wigner Monte Carlo method to achieve a satisfactory accuracy.

  9. Controlling chaos in a defined trajectory using adaptive fuzzy logic algorithm

    NASA Astrophysics Data System (ADS)

    Sadeghi, Maryam; Menhaj, Bagher

    2012-09-01

    Chaos is a nonlinear behavior of chaotic system with the extreme sensitivity to the initial conditions. Chaos control is so complicated that solutions never converge to a specific numbers and vary chaotically from one amount to the other next. A tiny perturbation in a chaotic system may result in chaotic, periodic, or stationary behavior. Modern controllers are introduced for controlling the chaotic behavior. In this research an adaptive Fuzzy Logic Controller (AFLC) is proposed to control the chaotic system with two equilibrium points. This method is introduced as an adaptive progressed fashion with the full ability to control the nonlinear systems even in the undertrained conditions. Using AFLC designers are released to determine the precise mathematical model of system and satisfy the vast adaption that is needed for a rapid variation which may be caused in the dynamic of nonlinear system. Rules and system parameters are generated through the AFLC and expert knowledge is downright only in the initialization stage. So if the knowledge was not assuring the dynamic of system it could be changed through the adaption procedure of parameters values. AFLC methodology is an advanced control fashion in control yielding to both robustness and smooth motion in nonlinear system control.

  10. 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.

  11. Mathematical Methods for Geophysics and Space Physics

    NASA Astrophysics Data System (ADS)

    Newman, William I.

    2016-05-01

    Graduate students in the natural sciences - including not only geophysics and space physics but also atmospheric and planetary physics, ocean sciences, and astronomy - need a broad-based mathematical toolbox to facilitate their research. In addition, they need to survey a wider array of mathematical methods that, while outside their particular areas of expertise, are important in related ones. While it is unrealistic to expect them to develop an encyclopedic knowledge of all the methods that are out there, they need to know how and where to obtain reliable and effective insights into these broader areas. Here at last is a graduate textbook that provides these students with the mathematical skills they need to succeed in today's highly interdisciplinary research environment. This authoritative and accessible book covers everything from the elements of vector and tensor analysis to ordinary differential equations, special functions, and chaos and fractals. Other topics include integral transforms, complex analysis, and inverse theory; partial differential equations of mathematical geophysics; probability, statistics, and computational methods; and much more. Proven in the classroom, Mathematical Methods for Geophysics and Space Physics features numerous exercises throughout as well as suggestions for further reading. * Provides an authoritative and accessible introduction to the subject * Covers vector and tensor analysis, ordinary differential equations, integrals and approximations, Fourier transforms, diffusion and dispersion, sound waves and perturbation theory, randomness in data, and a host of other topics * Features numerous exercises throughout * Ideal for students and researchers alike * An online illustration package is available to professors

  12. Transient Spatiotemporal Chaos in a Synaptically Coupled Neural Network

    NASA Astrophysics Data System (ADS)

    Lafranceschina, Jacopo; Wackerbauer, Renate

    2014-03-01

    Spatiotemporal chaos is transient in a diffusively coupled Morris-Lecar neural network. This study shows that the addition of synaptic coupling in the ring network reduces the average lifetime of spatiotemporal chaos for small to intermediate coupling strength and almost all numbers of synapses. For large coupling strength, 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 Lyaponov exponent and degree of phase coherence as the number of synaptic links increases. The presence of transient spatiotemporal chaos in a network of coupled neurons and the associated chaotic saddle provides a possibility for switching between metastable states observed in information processing and brain function. This research is supported by the University of Alaska Fairbanks.

  13. Numerical and experimental exploration of phase control of chaos.

    PubMed

    Zambrano, Samuel; Allaria, Enrico; Brugioni, Stefano; Leyva, Immaculada; Meucci, Riccardo; Sanjuán, Miguel A F; Arecchi, Fortunato T

    2006-03-01

    A well-known method to suppress chaos in a periodically forced chaotic system is to add a harmonic perturbation. The phase control of chaos scheme uses the phase difference between a small added harmonic perturbation and the main driving to suppress chaos, leading the system to different periodic orbits. Using the Duffing oscillator as a paradigm, we present here an in-depth study of this technique. A thorough numerical exploration has been made focused in the important role played by the phase, from which new interesting patterns in parameter space have appeared. On the other hand, our novel experimental implementation of phase control in an electronic circuit confirms both the well-known features of this method and the new ones detected numerically. All this may help in future implementations of phase control of chaos, which is globally confirmed here to be robust and easy to implement experimentally. PMID:16599742

  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

    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).].

  16. Strategic leadership: a view from quantum and chaos theories.

    PubMed

    McDaniel, R R

    1997-01-01

    Viewing health care from the perspective of chaos and quantum theories offers new insights into management techniques for effective and efficient delivery of health care services. This article introduces these concepts and gives specific prescriptions for managerial action. PMID:9058085

  17. 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.

  18. Digital key for chaos communication performing time delay concealment.

    PubMed

    Nguimdo, Romain Modeste; Colet, Pere; Larger, Laurent; Pesquera, Luís

    2011-07-15

    We introduce a scheme that integrates a digital key in a phase-chaos electro-optical delay system for optical chaos communications. A pseudorandom binary sequence (PRBS) is mixed within the chaotic dynamics in a way that a mutual concealment is performed; e.g., the time delay is hidden by the binary sequence, and the PRBS is also masked by the chaos. In addition to bridging the gap between algorithmic symmetric key cryptography and chaos-based analog encoding, the proposed approach is intended to benefit from the complex algebra mixing between a (pseudorandom) Boolean variable, and another continuous time (chaotic) variable. The scheme also provides a large flexibility allowing for easy reconfigurations to communicate securely at a high bit rate between different systems. PMID:21838363

  19. Digital Key for Chaos Communication Performing Time Delay Concealment

    NASA Astrophysics Data System (ADS)

    Nguimdo, Romain Modeste; Colet, Pere; Larger, Laurent; Pesquera, Luís

    2011-07-01

    We introduce a scheme that integrates a digital key in a phase-chaos electro-optical delay system for optical chaos communications. A pseudorandom binary sequence (PRBS) is mixed within the chaotic dynamics in a way that a mutual concealment is performed; e.g., the time delay is hidden by the binary sequence, and the PRBS is also masked by the chaos. In addition to bridging the gap between algorithmic symmetric key cryptography and chaos-based analog encoding, the proposed approach is intended to benefit from the complex algebra mixing between a (pseudorandom) Boolean variable, and another continuous time (chaotic) variable. The scheme also provides a large flexibility allowing for easy reconfigurations to communicate securely at a high bit rate between different systems.

  20. 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

  1. 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. PMID:22060475

  2. 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.

  3. Secure communication based on spatiotemporal chaos

    NASA Astrophysics Data System (ADS)

    Ren, Hai-Peng; Bai, Chao

    2015-08-01

    In this paper, we propose a novel approach to secure communication based on spatiotemporal chaos. At the transmitter end, the state variables of the coupled map lattice system are divided into two groups: one is used as the key to encrypt the plaintext in the N-shift encryption function, and the other is used to mix with the output of the N-shift function to further confuse the information to transmit. At the receiver end, the receiver lattices are driven by the received signal to synchronize with the transmitter lattices and an inverse procedure of the encoding is conducted to decode the information. Numerical simulation and experiment based on the TI TMS320C6713 Digital Signal Processor (DSP) show the feasibility and the validity of the proposed scheme. Project supported by the National Natural Science Foundation of China (Grant No. 61172070) and the Funds from the Science and Technology Innovation Team of Shaanxi Province, China (Grant No. 2013CKT-04).

  4. 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. PMID:17084962

  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. 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.

  7. 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.

  8. High precision framework for chaos many-body engine

    NASA Astrophysics Data System (ADS)

    Grossu, I. V.; Besliu, C.; Felea, D.; Jipa, Al.

    2014-04-01

    In this paper we present a C# 4.0 high precision framework for simulation of relativistic many-body systems. In order to benefit from the, previously developed, chaos analysis instruments, all new modules were integrated with Chaos Many-Body Engine (Grossu et al. 2010, 2013). As a direct application, we used 46 digits precision for analyzing the "Butterfly Effect" of the gravitational force in a specific relativistic nuclear collision toy-model.

  9. The chaos paradigm: developments and applications in engineering and science

    SciTech Connect

    Katz, R.A. )

    1994-01-01

    These proceedings are a compilation of technical topics presented at the Office of Naval Research (ONR)/Naval Undersea Warfare Center (NUWS) Technical Conference on Nonlinear Dynamics and Full-spectrum processing. The topics discussed consisted of synchronization and control of chaos, mechanical sources of chaos, turbulences, and advanced signal processing methods. There were eighteen papers presented at the conference and none is abstracted for the Energy Science and Technology database. (AIP)

  10. 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

  11. DETERMINISTIC TRANSPORT METHODS AND CODES AT LOS ALAMOS

    SciTech Connect

    J. E. MOREL

    1999-06-01

    The purposes of this paper are to: Present a brief history of deterministic transport methods development at Los Alamos National Laboratory from the 1950's to the present; Discuss the current status and capabilities of deterministic transport codes at Los Alamos; and Discuss future transport needs and possible future research directions. Our discussion of methods research necessarily includes only a small fraction of the total research actually done. The works that have been included represent a very subjective choice on the part of the author that was strongly influenced by his personal knowledge and experience. The remainder of this paper is organized in four sections: the first relates to deterministic methods research performed at Los Alamos, the second relates to production codes developed at Los Alamos, the third relates to the current status of transport codes at Los Alamos, and the fourth relates to future research directions at Los Alamos.

  12. Estimating the epidemic threshold on networks by deterministic connections

    SciTech Connect

    Li, Kezan Zhu, Guanghu; Fu, Xinchu; Small, Michael

    2014-12-15

    For many epidemic networks some connections between nodes are treated as deterministic, while the remainder are random and have different connection probabilities. By applying spectral analysis to several constructed models, we find that one can estimate the epidemic thresholds of these networks by investigating information from only the deterministic connections. Nonetheless, in these models, generic nonuniform stochastic connections and heterogeneous community structure are also considered. The estimation of epidemic thresholds is achieved via inequalities with upper and lower bounds, which are found to be in very good agreement with numerical simulations. Since these deterministic connections are easier to detect than those stochastic connections, this work provides a feasible and effective method to estimate the epidemic thresholds in real epidemic networks.

  13. Deterministic transformations of multipartite entangled states with tensor rank 2

    SciTech Connect

    Turgut, S.; Guel, Y.; Pak, N. K.

    2010-01-15

    Transformations involving only local operations assisted with classical communication are investigated for multipartite entangled pure states having tensor rank 2. All necessary and sufficient conditions for the possibility of deterministically converting truly multipartite, rank-2 states into each other are given. Furthermore, a chain of local operations that successfully achieves the transformation has been identified for all allowed transformations. The identified chains have two nice features: (1) each party needs to carry out at most one local operation and (2) all of these local operations are also deterministic transformations by themselves. Finally, it is found that there are disjoint classes of states, all of which can be identified by a single real parameter, which remain invariant under deterministic transformations.

  14. Mathematical Visualization

    ERIC Educational Resources Information Center

    Rogness, Jonathan

    2011-01-01

    Advances in computer graphics have provided mathematicians with the ability to create stunning visualizations, both to gain insight and to help demonstrate the beauty of mathematics to others. As educators these tools can be particularly important as we search for ways to work with students raised with constant visual stimulation, from video games…

  15. Learning Mathematics.

    ERIC Educational Resources Information Center

    Lapointe, Archie E.; And Others

    In 1990-91, 20 countries (Brazil, Canada, China, England, France, Hungary, Ireland, Israel, Italy, Jordan, Korea, Mozambique, Portugal, Scotland, Slovenia, Soviet Union, Spain, Switzerland, Taiwan, and the United States) surveyed the mathematics and science performance of 13-year-old students (and 14 countries also assessed 9-year-olds in the same…

  16. Underground Mathematics

    ERIC Educational Resources Information Center

    Hadlock, Charles R

    2013-01-01

    The movement of groundwater in underground aquifers is an ideal physical example of many important themes in mathematical modeling, ranging from general principles (like Occam's Razor) to specific techniques (such as geometry, linear equations, and the calculus). This article gives a self-contained introduction to groundwater modeling with…

  17. Relevant Mathematics.

    ERIC Educational Resources Information Center

    Catterton, Gene; And Others

    This material was developed to be used with the non college-bound student in the senior high school. It provides the student with everyday problems and experiences in which practical mathematical applications are made. The package includes worksheets pertaining to letterhead invoices, sales slips, payroll sheets, inventory sheets, carpentry and…

  18. A breakthrough in neuroscience needs a "Nebulous Cartesian System" Oscillations, quantum dynamics and chaos in the brain and vegetative system.

    PubMed

    Başar, Erol; Güntekin, Bahar

    2007-04-01

    The Cartesian System is a fundamental conceptual and analytical framework related and interwoven with the concept and applications of Newtonian Dynamics. In order to analyze quantum processes physicist moved to a Probabilistic Cartesian System in which the causality principle became a probabilistic one. This means the trajectories of particles (obeying quantum rules) can be described only with the concept of cloudy wave packets. The approach to the brain-body-mind problem requires more than the prerequisite of modern physics and quantum dynamics. In the analysis of the brain-body-mind construct we have to include uncertain causalities and consequently multiple uncertain causalities. These multiple causalities originate from (1) nonlinear properties of the vegetative system (e.g. irregularities in biochemical transmitters, cardiac output, turbulences in the vascular system, respiratory apnea, nonlinear oscillatory interactions in peristalsis); (2) nonlinear behavior of the neuronal electricity (e.g. chaotic behavior measured by EEG), (3) genetic modulations, and (4) additional to these physiological entities nonlinear properties of physical processes in the body. The brain shows deterministic chaos with a correlation dimension of approx. D(2)=6, the smooth muscles approx. D(2)=3. According to these facts we propose a hyper-probabilistic approach or a hyper-probabilistic Cartesian System to describe and analyze the processes in the brain-body-mind system. If we add aspects as our sentiments, emotions and creativity to this construct, better said to this already hyper-probabilistic construct, this "New Cartesian System" is more than hyper-probabilistic, it is a nebulous system, we can predict the future only in a nebulous way; however, despite this chain of reasoning we can still provide predictions on brain-body-mind incorporations. We tentatively assume that the processes or mechanisms of the brain-body-mind system can be analyzed and predicted similar to the

  19. Locating the transition from periodic oscillations to spatiotemporal chaos in the wake of invasion

    PubMed Central

    Sherratt, Jonathan A.; Smith, Matthew J.; Rademacher, Jens D. M.

    2009-01-01

    In systems with cyclic dynamics, invasions often generate periodic spatiotemporal oscillations, which undergo a subsequent transition to chaos. The periodic oscillations have the form of a wavetrain and occur in a band of constant width. In applications, a key question is whether one expects spatiotemporal data to be dominated by regular or irregular oscillations or to involve a significant proportion of both. This depends on the width of the wavetrain band. Here, we present mathematical theory that enables the direct calculation of this width. Our method synthesizes recent developments in stability theory and computation. It is developed for only 1 equation system, but because this is a normal form close to a Hopf bifurcation, the results can be applied directly to a wide range of models. We illustrate this by considering a classic example from ecology: wavetrains in the wake of the invasion of a prey population by predators. PMID:19553205

  20. Mixed-mode oscillations and chaos in return maps of an oscillatory chemical reaction

    NASA Astrophysics Data System (ADS)

    Blagojević, S. N.; Čupić, Ž.; Ivanović-Šašić, A.; Kolar-Anić, Lj.

    2015-12-01

    The return maps, as an element of mathematical phenomenology appropriate for general examinations of complex dynamic states of the oscillatory systems were used to detect and explain the evolution of mixed-mode oscillations and chaos in a six-dimensional nonlinear reaction system of the Bray-Liebhafsky (BL) reaction, a well-studied nonlinear chemical reaction system that exhibits complex dynamic behavior. For this purpose principally different Poincaré sections were applied and different transition scenarios between periodic and aperiodic states were examined by numerical simulations. It is shown that emergence of new periodic patterns can be detected by return maps already within chaotic windows. Besides, we also show that the higher dimensionality of manifold gives the impression of having several layers of manifolds.