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.
Analysis of FBC deterministic chaos
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.
Master equation analysis of deterministic chemical chaos
NASA Astrophysics Data System (ADS)
Wang, Hongli; Li, Qianshu
1998-05-01
The underlying microscopic dynamics of deterministic chemical chaos was investigated in this paper. We analyzed the master equation for the Williamowski-Rössler model by direct stochastic simulation as well as in the generating function representation. Simulation within an ensemble revealed that in the chaotic regime the deterministic mass action kinetics is related neither to the ensemble mean nor to the most probable value within the ensemble. Cumulant expansion analysis of the master equation also showed that the molecular fluctuations do not admit bounded values but increase linearly in time infinitely, indicating the meaninglessness of the chaotic trajectories predicted by the phenomenological equations. These results proposed that the macroscopic description is no longer useful in the chaotic regime and a more microscopic description is necessary in this circumstance.
Deterministic representation of chaos in classical dynamics
NASA Technical Reports Server (NTRS)
Zak, M.
1985-01-01
Chaos in an Anosov-type mechanical system is eliminated by referring the governing equations to a specially selected rapidly oscillating (non-inertial) frame of reference in which the stabilization effect is caused by inertia forces. The result is generalized to any orbitally unstable mechanical system.
Deterministic chaos control in neural networks on various topologies
NASA Astrophysics Data System (ADS)
Neto, A. J. F.; Lima, F. W. S.
2017-01-01
Using numerical simulations, we study the control of deterministic chaos in neural networks on various topologies like Voronoi-Delaunay, Barabási-Albert, Small-World networks and Erdös-Rényi random graphs by "pinning" the state of a "special" neuron. We show that the chaotic activity of the networks or graphs, when control is on, can become constant or periodic.
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
Sharma, Vijay
2009-09-10
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.
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.
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).
NASA Astrophysics Data System (ADS)
Maggs, J. E.; Morales, G. J.
2011-10-01
The dynamics of transport at the edge of magnetized plasmas is deterministic chaos. The connection is made by a previous survey [M. A. Pedrosa , Phys. Rev. Lett. 82, 3621 (1999)PRLTAO0031-900710.1103/PhysRevLett.82.3621] of measurements of fluctuations that is shown to exhibit power spectra with exponential frequency dependence over a broad range, which is the signature of deterministic chaos. The exponential character arises from Lorentzian pulses. The results suggest that the generalization to complex times used in studies of deterministic chaos is a representation of Lorentzian pulses emerging from the chaotic dynamics.
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.
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.
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…
Pathological tremors: Deterministic chaos or nonlinear stochastic oscillators?
NASA Astrophysics Data System (ADS)
Timmer, Jens; Häußler, Siegfried; Lauk, Michael; Lücking, Carl
2000-02-01
Pathological tremors exhibit a nonlinear oscillation that is not strictly periodic. We investigate whether the deviation from periodicity is due to nonlinear deterministic chaotic dynamics or due to nonlinear stochastic dynamics. To do so, we apply methods from linear and nonlinear time series analysis to tremor time series. The results of the different methods suggest that the considered types of pathological tremors represent nonlinear stochastic second order processes.
The deterministic chaos and random noise in turbulent jet.
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.
The deterministic chaos and random noise in turbulent jet
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.
NASA Astrophysics Data System (ADS)
Nicolay, S.; Brodie of Brodie, E. B.; Touchon, M.; d'Aubenton-Carafa, Y.; Thermes, C.; Arneodo, A.
2004-10-01
We use the continuous wavelet transform to perform a space-scale analysis of the AT and GC skews (strand asymmetries) in human genomic sequences, which have been shown to correlate with gene transcription. This study reveals the existence of a characteristic scale ℓ c≃25±10 kb that separates a monofractal long-range correlated noisy regime at small scales (ℓ<ℓ c) from relaxational oscillatory behavior at large-scale (ℓ>ℓ c). We show that these large scale nonlinear oscillations enlighten an organization of the human genome into adjacent domains ( ≈400 kb) with preferential gene orientation. When using classical techniques from dynamical systems theory, we demonstrate that these relaxational oscillations display all the characteristic properties of the chaotic strange attractor behavior observed nearby homoclinic orbits of Shil'nikov type. We discuss the possibility that replication and gene regulation processes are governed by a low-dimensional dynamical system that displays deterministic chaos.
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.
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
Controlling chaos in ecology: from deterministic to individual-based models.
Solé, R V; Gamarra, J G; Ginovart, M; López, D
1999-11-01
The possibility of chaos control in biological systems has been stimulated by recent advances in the study of heart and brain tissue dynamics. More recently, some authors have conjectured that such a method might be applied to population dynamics and even play a nontrivial evolutionary role in ecology. In this paper we explore this idea by means of both mathematical and individual-based simulation models. Because of the intrinsic noise linked to individual behavior, controlling a noisy system becomes more difficult but, as shown here, it is a feasible task allowed to be experimentally tested.
Turcotte, D.L. )
1991-03-01
Fractal statistics are the only statistics that are scale invariant. Examples in tectonics include distributions of faults, displacements on faults, distributions and permeabilities of fractures, and distributions of folds. Many aspects of sedimentology are also fractal including distributions of sedimentary sequences, variations in permeability, and shapes of boundaries. Since the underlying processes are likely to be scale invariant, it is reasonable to conclude that the number-size statistics of oil fields will be fractal. Log-normal statistics are often applied; they are not scale invariant. Two explanations for fractal statistics can be given. They may be the result of scale-invariant stochastic processes. Random walk (Brownian noise) is one example. Topography generally resembles Brownian noise, a power-law spectrum with fractal dimension D = 1.5. Alternatively fractal statistics can be the result of deterministic chaos. Turbulent flows are examples of deterministic chaos, the governing equations are deterministic but the resulting flows are statistical. Tectonic displacements can be shown to be the result of deterministic chaos; it is likely that erosion is another example.
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.
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…
Deterministic chaos and noise in three in vitro hippocampal models of epilepsy.
Slutzky, M W; Cvitanović, P; Mogul, D J
2001-01-01
Recent reports have suggested that chaos control techniques may be useful for electrically manipulating epileptiform bursting behavior in neuronal ensembles. Because the dynamics of spontaneous in vitro bursting had not been well determined previously, analysis of this behavior in the rat hippocampus was performed. Epileptiform bursting was induced in transverse rat hippocampal slices using three experimental methods. Slices were bathed in artificial cerebrospinal fluid containing: (1) elevated potassium ([K+]o= 10.5 mM), (2) zero magnesium, or (3) the GABAA-receptor antagonists bicuculline (20 microM) and picrotoxin (250 microM). The existence of chaos and determinism was assessed using two different analytical techniques: unstable periodic orbit (UPO) analysis and a new technique for estimating Lyapunov exponents. Significance of these results was assessed by comparing the calculations for each experiment with corresponding randomized surrogate data. UPOs of multiple periods were highly prevalent in experiments from all three epilepsy models: 73% of all experiments contained at least one statistically significant period-1 or period-2 orbit. However, the expansion rate analysis did not provide any evidence of determinism in the data. This suggests that the system may be globally stochastic but contains local pockets of determinism. Thus, manipulation of bursting behavior using chaos control algorithms may yet hold promise for reverting or preventing epileptic seizures.
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.
Deterministic temporal chaos from a mid-infrared external cavity quantum cascade lasers
NASA Astrophysics Data System (ADS)
Grillot, Frédéric; Jumpertz, Louise; Schires, Kevin; Carras, Mathieu; Sciamanna, Marc
2016-02-01
Quantum cascade lasers (QCLs) are unipolar semiconductor lasers offering access to wavelengths from the mid-infrared (IR) to the terahertz domain and promising impact on various applications such as free-space communications, high-resolution spectroscopy, LIDAR remote sensing or optical countermeasures. Unlike bipolar semiconductor lasers, stimulated emission in QCLs is obtained via electronic transitions between discrete energy states inside the conduction band. Recent technological progress has led to QCLs operating in pulsed or continuous wave mode, at room temperature in single- or multi-mode operation, with high powers up to a few watts for mid-IR devices. This spectacular development raises multiple interrogations on the stability of QCLs as little is known on their dynamical properties. Very recently, experiments based on optical spectrum measurements have unveiled the existence of five distinct feedback regimes without, however, identifying the complex dynamics dwelling within the QCL. In this article we provide the first experimental evidence of a route to chaos in a QCL emitting at mid-IR wavelength. When applying optical feedback with an increasing strength, the QCL dynamics bifurcate to periodic dynamics at the external cavity frequency and later to chaos without an undamping of relaxation oscillations, hence contrasting with the well-known scenarios occurring in interband laser diodes.
Deterministic time-reversible thermostats: chaos, ergodicity, and the zeroth law of thermodynamics
NASA Astrophysics Data System (ADS)
Patra, Puneet Kumar; Sprott, Julien Clinton; Hoover, William Graham; Griswold Hoover, Carol
2015-09-01
The relative stability and ergodicity of deterministic time-reversible thermostats, both singly and in coupled pairs, are assessed through their Lyapunov spectra. Five types of thermostat are coupled to one another through a single Hooke's-law harmonic spring. The resulting dynamics shows that three specific thermostat types, Hoover-Holian, Ju-Bulgac, and Martyna-Klein-Tuckerman, have very similar Lyapunov spectra in their equilibrium four-dimensional phase spaces and when coupled in equilibrium or nonequilibrium pairs. All three of these oscillator-based thermostats are shown to be ergodic, with smooth analytic Gaussian distributions in their extended phase spaces (coordinate, momentum, and two control variables). Evidently these three ergodic and time-reversible thermostat types are particularly useful as statistical-mechanical thermometers and thermostats. Each of them generates Gibbs' universal canonical distribution internally as well as for systems to which they are coupled. Thus they obey the zeroth law of thermodynamics, as a good heat bath should. They also provide dissipative heat flow with relatively small nonlinearity when two or more such temperature baths interact and provide useful deterministic replacements for the stochastic Langevin equation.
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.
NASA Astrophysics Data System (ADS)
Lambrou, George I.; Chatziioannou, Aristotelis; Vlahopoulos, Spiros; Moschovi, Maria; Chrousos, George P.
Biological systems are dynamic and possess properties that depend on two key elements: initial conditions and the response of the system over time. Conceptualizing this on tumor models will influence conclusions drawn with regard to disease initiation and progression. Alterations in initial conditions dynamically reshape the properties of proliferating tumor cells. The present work aims to test the hypothesis of Wolfrom et al., that proliferation shows evidence for deterministic chaos in a manner such that subtle differences in the initial conditions give rise to non-linear response behavior of the system. Their hypothesis, tested on adherent Fao rat hepatoma cells, provides evidence that these cells manifest aperiodic oscillations in their proliferation rate. We have tested this hypothesis with some modifications to the proposed experimental setup. We have used the acute lymphoblastic leukemia cell line CCRF-CEM, as it provides an excellent substrate for modeling proliferation dynamics. Measurements were taken at time points varying from 24h to 48h, extending the assayed populations beyond that of previous published reports that dealt with the complex dynamic behavior of animal cell populations. We conducted flow cytometry studies to examine the apoptotic and necrotic rate of the system, as well as DNA content changes of the cells over time. The cells exhibited a proliferation rate of nonlinear nature, as this rate presented oscillatory behavior. The obtained data have been fit in known models of growth, such as logistic and Gompertzian growth.
Liao, Wenlin; Dai, Yifan; Xie, Xuhui; Zhou, Lin
2014-07-01
Ion beam figuring (IBF) is established for the final precision figuring of high-performance optical components, where the figuring accuracy is guaranteed by the stability of the removal function and the solution accuracy of the dwell time. In this deterministic method, the figuring process can be represented by a two-dimensional (2D) convolution operation of a constant removal function and the dwell time. However, we have found that the current 2D convolution operation cannot factually describe the IBF process of curved surfaces, which neglects the influences of the projection distortion and the workpiece geometry on the removal function. Consequently, the current 2D convolution algorithm would influence the solution accuracy for the dwell time and reduce the convergence of the figuring process. In this part, based on the material removal characteristics of IBF, a mathematical model of the removal function is developed theoretically and verified experimentally. Research results show that the removal function during IBF of a curved surface is actually a dynamic function in the 2D convolution algorithm. The mathematical modeling of the dynamic removal function provides theoretical foundations for our proposed new algorithm in the next part, and final verification experiments indicate that this algorithm can effectively improve the accuracy of the dwell time solution for the IBF of curved surfaces.
Decoherence, determinism and chaos revisited
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.
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.
Chaos, dynamical structure, and climate variability
Stewart, H.B.
1996-06-01
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 we 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. {copyright} {ital 1996 American Institute of Physics.}
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)
NASA Astrophysics Data System (ADS)
Blakely, Jonathan; Corron, Ned; Hayes, Scott; Pethel, Shawn
2007-03-01
Chaos is usually attributed only to nonlinear systems. Yet it was recently shown that chaotic waveforms can be synthesized by linear superposition of randomly polarized basis functions. The basis function contains a growing oscillation that terminates in a large pulse. We show that this function is easily realized when viewed backward in time as a pulse followed by ringing decay. Consequently, a linear filter driven by random pulses outputs a waveform that, when viewed backward in time, exhibits essential qualities of chaos, i.e. determinism and a positive Lyapunov exponent. This phenomenon suggests that chaos may be connected to physical theories whose framework is not that of a deterministic dynamical system. We demonstrate that synthesizing chaos requires a balance between the topological entropy of the random source and the dissipation in the filter. Surprisingly, using different encodings of the random source, the same filter can produce both Lorenz-like and R"ossler-like waveforms. The different encodings can be viewed as grammar restrictions on a more general encoding that produces a chaotic superset encompassing the Lorenz and R"ossler paradigms of nonlinear dynamics. Thus, the language of deterministic chaos provides a useful description for a class of signals not generated by a deterministic system.
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.
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...
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.
Chaos control of cardiac arrhythmias.
Garfinkel, A; Weiss, J N; Ditto, W L; Spano, M L
1995-01-01
Chaos theory has shown that many disordered and erratic phenomena are in fact deterministic, and can be understood causally and controlled. The prospect that cardiac arrhythmias might be instances of deterministic chaos is therefore intriguing. We used a recently developed method of chaos control to stabilize a ouabain-induced arrhythmia in rabbit ventricular tissue in vitro. Extension of these results to clinically significant arrhythmias such as fibrillation will require overcoming the additional obstacles of spatiotemporal complexity.
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
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.
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)
Ercsey-Ravasz, Mária; Toroczkai, Zoltán
2012-01-01
The mathematical structure of Sudoku puzzles is akin to hard constraint satisfaction problems lying at the basis of many applications, including protein folding and the ground-state problem of glassy spin systems. Via an exact mapping of Sudoku into a deterministic, continuous-time dynamical system, here we show that the difficulty of Sudoku translates into transient chaotic behavior exhibited by this system. We also show that the escape rate κ, an invariant of transient chaos, provides a scalar measure of the puzzle's hardness that correlates well with human difficulty ratings. Accordingly, η = −log10 κ can be used to define a “Richter”-type scale for puzzle hardness, with easy puzzles having 0 < η ≤ 1, medium ones 1 < η ≤ 2, hard with 2 < η ≤ 3 and ultra-hard with η > 3. To our best knowledge, there are no known puzzles with η > 4. PMID:23061008
Liao, Wenlin; Dai, Yifan; Xie, Xuhui; Zhou, Lin
2014-07-01
Ion beam figuring (IBF) is established for the final precision figuring of optical components. In this deterministic method, the figuring process is represented by a two-dimensional (2D) convolution operation of a constant removal function and the dwell time, where the figuring precision is guaranteed by the stability of the removal function as well as the solution accuracy of the dwell time. However, the current 2D convolution equation cannot factually reflect the IBF process of curved surfaces, which neglects the influence of the projection distortion and the workpiece geometry. Consequently, the current convolution algorithm for the IBF process would influence the solution accuracy for the dwell time and reduce the convergence of the figuring process. In this part, we propose an improved algorithm based on the mathematical modeling of the dynamic removal function in Part A, which provides a more accurate dwell time for IBF of a curved surface. Additionally, simulation analysis and figuring experiments are carried out to verify the feasibility of our proposed algorithm. The final experimental results indicate that the figuring precision and efficiency can be simultaneously improved by this method.
Introduction to the focus issue: fifty years of chaos: applied and theoretical.
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.
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
Does chaos theory have major implications for philosophy of medicine?
Holm, S
2002-12-01
In the literature it is sometimes claimed that chaos theory, non-linear dynamics, and the theory of fractals have major implications for philosophy of medicine, especially for our analysis of the concept of disease and the concept of causation. This paper gives a brief introduction to the concepts underlying chaos theory and non-linear dynamics. It is then shown that chaos theory has only very minimal implications for the analysis of the concept of disease and the concept of causation, mainly because the mathematics of chaotic processes entail that these processes are fully deterministic. The practical unpredictability of chaotic processes, caused by their extreme sensitivity to initial conditions, may raise practical problems in diagnosis, prognosis, and treatment, but it raises no major theoretical problems. The relation between chaos theory and the problem of free will is discussed, and it is shown that chaos theory may remove the problem of predictability of decisions, but does not solve the problem of free will. Chaos theory may thus be very important for our understanding of physiological processes, and specific disease entities, without having any major implications for philosophy of medicine.
Cognitive aspects of chaos in random networks.
Aiello, Gaetano L
2012-01-01
A special case of deterministic chaos that is independent of the architecture of the connections has been observed in a computer model of a purely excitatory neuronal network. Chaos onsets when the level of connectivity is critically low. The results indicate a typical period-doubling route to chaos as the connectivity decreases. A cognitive interpretation of such type of chaos, based on information theory and phase-transitions, is proposed.
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.
[Chaos and fractals. Are these of interest to medical science?].
Hauge, A
1993-12-10
Biological systems are governed by nonlinear dynamics and often appear to be random, because the available information, though accurate, is usually incomplete. It is important to be aware of the fact that nonlinear deterministic systems can behave unpredictably in the long term. Traditional reductionism is unable to provide an adequate understanding of such systems. A more global description and explanation of forms, features and functions is required. Chaos theory and fractal geometry are of value in this respect. This article is an introduction to this relatively new field of science and mathematics.
Chaos and chaotic dynamics in economics.
Faggini, Marisa
2009-07-01
Proponents of chaos theory attempted to articulate a new, more realistic, scientific world-view contradictory to the fundamental notions of the Newtonian view of science. Nonlinearity and chaos give the opportunity of a reconciliation of economics with a more realistic representation of its phenomena. Chaos theory represents a means for enhancing both the methodological and theoretical foundations for exploring the complexity of economic phenomena. This paper offers an overview of the applications of chaos theory in economics highlighting that recognizing the existence of deterministic chaos in economics is important from both a theoretical and practical point of view.
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…
Deterministic Chaos in Tropical Atmospheric Dynamics.
NASA Astrophysics Data System (ADS)
Waelbroeck, H.
1995-07-01
An 11-year dataset from the tropical weather station of Tlaxcala, Mexico, is examined. It is found that mutual information drops quickly with the delay, to a positive value that relaxes to zero with a timescale of 20 days. The mutual dependence of the observables is also examined and it is concluded that the dataset gives the equivalent of eight variables per day, known to a precision of 2%. It is determined that the effective dimension of the attractor is Deff 11.7 at the scale 3.5% < R/Rmax < 8%. Evidence is found that the effective dimension increases as R/Rmax 0, supporting a conjecture by Lorenz that the climate system may consist of a large number of weakly coupled subsystems, some of which have low-dimensional attractors. A local reconstruction of the dynamics in phase space is performed; the short-term predictability is modest and agrees with theoretical estimates. Useful skill in predictions of 10-day rainfall accumulation anomalies reflects the persistence of weather patterns, which follow the 20-day decay rate of the mutual information.
Chaos, patterns, coherent structures, and turbulence: Reflections on nonlinear science.
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.
Fluid turbulence - Deterministic or statistical
NASA Astrophysics Data System (ADS)
Cheng, Sin-I.
The deterministic view of turbulence suggests that the classical theory of fluid turbulence may be treating the wrong entity. The paper explores the physical implications of such an abstract mathematical result, and provides a constructive computational demonstration of the deterministic and the wave nature of fluid turbulence. The associated pressure disturbance for restoring solenoidal velocity is the primary agent, and its reflection from solid surface(s) the dominant mechanism of turbulence production. Statistical properties and their modeling must address to the statistics of the uncertainties of initial boundary data of the ensemble.
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.
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…
Titration of chaos with added noise
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
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.
Linear vs nonlinear and infinite vs finite: An interpretation of chaos
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.
[Radiotherapy and chaos theory: the tit bird and the butterfly...].
Denis, F; Letellier, C
2012-09-01
Although the same simple laws govern cancer outcome (cell division repeated again and again), each tumour has a different outcome before as well as after irradiation therapy. The linear-quadratic radiosensitivity model allows an assessment of tumor sensitivity to radiotherapy. This model presents some limitations in clinical practice because it does not take into account the interactions between tumour cells and non-tumoral bystander cells (such as endothelial cells, fibroblasts, immune cells...) that modulate radiosensitivity and tumor growth dynamics. These interactions can lead to non-linear and complex tumor growth which appears to be random but that is not since there is not so many tumors spontaneously regressing. In this paper we propose to develop a deterministic approach for tumour growth dynamics using chaos theory. Various characteristics of cancer dynamics and tumor radiosensitivity can be explained using mathematical models of competing cell species.
Comparison of the Nature of Chaos in Experimental [EEG] Data and Theoretical [ANN] Data
NASA Astrophysics Data System (ADS)
Das, Atin; Das, Pritha
2003-08-01
In this paper, nonlinear dynamical tools like largest Lyapunov exponents (LE), fractal dimension, correlation dimension, pointwise correlation dimension will be employed to analyze electroencephalogram [EEG] data and determine the nature of chaos. Results of similar calculations from some earlier works will be produced for comparison with present results. Also, a brief report on difference of opinion among coworkers regarding tools to characterize chaos will be reported; particularly applicability of LE will be reviewed. The issue of nonlinearity present in experimental time series will be addressed by using surrogate data technique. We have extracted another data set which represented chaotic state of the system considered in our earlier work of mathematical modeling of artificial neural network. By comparing the values of measures employed to the two datasets, it can be concluded that EEG represents high dimensional chaos, whereas the experimental data due to its deterministic nature, is of low dimension. Also results give the evidence that LE exponent is applicable for low dimensional chaotic system while for experimental data, due to their stochasticity and presence of noise- LE is not a reliable tool to characterize chaos.
Photo-induced chaos in the Briggs-Rauscher reaction
NASA Astrophysics Data System (ADS)
Okazaki, Noriaki; Hanazaki, Ichiro
1998-07-01
Discovery of the photo-induced chaos in the Briggs-Rauscher system is reported. The chaotic oscillations were observed between the large- and the small-amplitude simple oscillatory states existent in low and high light intensity regions, respectively. Period-doubling sequence from the large-amplitude oscillations to the chaos was observed. Deterministic nature of the chaos was confirmed by the next-amplitude return map. The stretching and folding mechanism of the trajectories was revealed through the three-dimensional attractor reconstructed via the singular value decomposition method. The chemical origin of the photoinduced chaos is discussed based on the photoautocatalysis of HIO2.
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.
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
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.
NASA Astrophysics Data System (ADS)
2008-12-01
Laser noise and chaos are unwanted elements in most circumstances. However, scientists have now learnt how to put them to good use to generate high-quality random bit sequences. Atsushi Uchida from Saitama University in Japan tells Nature Photonics how.
Milonni, P.W.
1989-01-01
The theoretical and experimental status of chaos in nonlinear optics and laser physics will be reviewed. Attention will then be focused on the possibility of chaotic behavior in individual atoms and molecules driven by intense radiation fields. 46 refs., 7 figs.
Improvement and empirical research on chaos control by theory of "chaos + chaos = order".
Fulai, Wang
2012-12-01
This paper focuses on advancing the understanding of Parrondian effects and their paradoxical behavior in nonlinear dynamical systems. Some examples are given to show that a dynamics combined by more than two discrete chaotic dynamics in deterministic manners can give rise to order when combined. The chaotic maps in our study are more general than those in the current literatures as far as "chaos + chaos = order" is concerned. Some problems left over in the current literatures are solved. It is proved both theoretically and numerically that, given any m chaotic dynamics generated by the one-dimensional real Mandelbrot maps, it is no possible to get a periodic system when all the m chaotic dynamics are alternated in random manner, but for any integer m(m ≥ 2) a dynamics combined in deterministic manner by m Mandelbrot chaotic dynamics can be found to give rise to a periodic dynamics of m periods. Numerical and mathematical analysis prove that the paradoxical phenomenon of "chaos + chaos = order" also exist in the dynamics generated by non-Mandelbrot maps.
Chaos in an imperfectly premixed model combustor
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.
Deterministic Walks with Choice
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.
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
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
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
Spirals, chaos, and new mechanisms of wave propagation.
Chen, P S; Garfinkel, A; Weiss, J N; Karagueuzian, H S
1997-02-01
The chaos theory is based on the idea that phenomena that appear disordered and random may actually be produced by relatively simple deterministic mechanisms. The disordered (aperiodic) activation that characterizes a chaotic motion is reached through one of a few well-defined paths that are characteristic of nonlinear dynamical systems. Our group has been studying VF using computerized mapping techniques. We found that in electrically induced VF, reentrant wavefronts (spiral waves) are present both in the initial tachysystolic stage (resembling VT) and the later tremulous incoordination stage (true VF). The electrophysiological characteristics associated with the transition from VT to VF is compatible with the quasiperiodic route to chaos as described in the Ruelle-Takens theorem. We propose that specific restitution of action potential duration (APD) and conduction velocity properties can cause a spiral wave (the primary oscillator) to develop additional oscillatory modes that lead to spiral meander and breakup. When spiral waves begin to meander and are modulated by other oscillatory processes, the periodic activity is replaced by unstable quasiperiodic oscillation, which then undergoes transition to chaos, signaling the onset of VF. We conclude that VF is a form of deterministic chaos. The development of VF is compatible with quasiperiodic transition to chaos. These results indicate that both the prediction and the control of fibrillation are possible based on the chaos theory and with the advent of chaos control algorithms.
Detecting nonlinearity and chaos in epidemic data
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.
Decoherence, determinism and chaos
NASA Astrophysics Data System (ADS)
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 nonlinearities 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.
Decoherence, determinism and chaos
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.
Quantum signatures of chaos or quantum chaos?
NASA Astrophysics Data System (ADS)
Bunakov, V. E.
2016-11-01
A critical analysis of the present-day concept of chaos in quantum systems as nothing but a "quantum signature" of chaos in classical mechanics is given. In contrast to the existing semi-intuitive guesses, a definition of classical and quantum chaos is proposed on the basis of the Liouville-Arnold theorem: a quantum chaotic system featuring N degrees of freedom should have M < N independent first integrals of motion (good quantum numbers) specified by the symmetry of the Hamiltonian of the system. Quantitative measures of quantum chaos that, in the classical limit, go over to the Lyapunov exponent and the classical stability parameter are proposed. The proposed criteria of quantum chaos are applied to solving standard problems of modern dynamical chaos theory.
Signatures of deterministic chaos in dyslipidemic erythrocytes under shear stress.
Korol, A M; Rasia, R
2003-03-01
The erythrocytes deformation under shear stress, the viscoelastic properties and the effects observed on healthy donors and on dyslipidemic patients are investigated from the point of view of nonlinear dynamics. Finally it is suggested that the different results obtained could be useful with regard to pathophysiological disturbances and their treatment.
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.
CHAOS AND STOCHASTICITY IN DETERMINISTICALLY GENERATED MULTIFRACTAL MEASURES. (R824780)
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...
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)
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…
Menstruation, perimenopause, and chaos theory.
Derry, Paula S; Derry, Gregory N
2012-01-01
This article argues that menstruation, including the transition to menopause, results from a specific kind of complex system, namely, one that is nonlinear, dynamical, and chaotic. A complexity-based perspective changes how we think about and research menstruation-related health problems and positive health. Chaotic systems are deterministic but not predictable, characterized by sensitivity to initial conditions and strange attractors. Chaos theory provides a coherent framework that qualitatively accounts for puzzling results from perimenopause research. It directs attention to variability within and between women, adaptation, lifespan development, and the need for complex explanations of disease. Whether the menstrual cycle is chaotic can be empirically tested, and a summary of our research on 20- to 40-year-old women is provided.
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.
Detecting chaos from time series
NASA Astrophysics Data System (ADS)
Xiaofeng, Gong; Lai, C. H.
2000-02-01
In this paper, an entirely data-based method to detect chaos from the time series is developed by introducing icons/Journals/Common/epsilon" ALT="epsilon" ALIGN="TOP"/> p -neighbour points (the p -steps icons/Journals/Common/epsilon" ALT="epsilon" ALIGN="TOP"/> -neighbour points). We demonstrate that for deterministic chaotic systems, there exists a linear relationship between the logarithm of the average number of icons/Journals/Common/epsilon" ALT="epsilon" ALIGN="TOP"/> p -neighbour points, lnn p ,icons/Journals/Common/epsilon" ALT="epsilon" ALIGN="TOP"/> , and the time step, p . The coefficient can be related to the KS entropy of the system. The effects of the embedding dimension and noise are also discussed.
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)
Deterministic Entangled Nanosource
2008-08-01
currently valid OMB control number . PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 1. REPORT DATE (DD-MM-YYYY) 01-09-2008 2. REPORT TYPE...Final Report 3. DATES COVERED (From - To) Sep 2005 – Sep 2008 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER FA9550-05-1-0455...Deterministic Entangled Nanosource 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER Khitrova, Galina 5e. TASK
Creutz, M.
1986-03-01
A deterministic cellular automation rule is presented which simulates the Ising model. On each cell in addition to an Ising spin is a space-time parity bit and a variable playing the role of a momentum conjugate to the spin. The procedure permits study of nonequilibrium phenomena, heat flow, mixing, and time correlations. The algorithm can make full use of multispin coding, thus permitting fast programs involving parallel processing on serial machines.
Chaos and microbial systems. Progress report, July 1989--July 1990
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.
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.
Noise can prevent onset of chaos in spatiotemporal population dynamics
NASA Astrophysics Data System (ADS)
Petrovskii, S.; Morozov, A.; Malchow, H.; Sieber, M.
2010-11-01
Many theoretical approaches predict the dynamics of interacting populations to be chaotic but that has very rarely been observed in ecological data. It has therefore risen a question about factors that can prevent the onset of chaos by, for instance, making the population fluctuations synchronized over the whole habitat. One such factor is stochasticity. The so-called Moran effect predicts that a spatially correlated noise can synchronize the local population dynamics in a spatially discrete system, thus preventing the onset of spatiotemporal chaos. On the whole, however, the issue of noise has remained controversial and insufficiently understood. In particular, a well-built nonspatial theory infers that noise enhances chaos by making the system more sensitive to the initial conditions. In this paper, we address the problem of the interplay between deterministic dynamics and noise by considering a spatially explicit predator-prey system where some parameters are affected by noise. Our findings are rather counter-intuitive. We show that a small noise (i.e. preserving the deterministic skeleton) can indeed synchronize the population oscillations throughout space and hence keep the dynamics regular, but the dependence of the chaos prevention probability on the noise intensity is of resonance type. Once chaos has developed, it appears to be stable with respect to a small noise but it can be suppressed by a large noise. Finally, we show that our results are in a good qualitative agreement with some available field data.
ERIC Educational Resources Information Center
Costellano, Janet; Scaffa, Matthew
The product of a Special Studies Institute, this teacher developed resource guide for the emotionally handicapped (K-6) presents 37 activities designed to develop mathematics concepts and skills utilizing the urban out-of-doors. Focus is on experiencing math models, patterns, problems, and relationships found in an urban environment. Activities…
NASA Astrophysics Data System (ADS)
Schmid, Gary Bruno
Underlying idea: A new hypothesis about how the mental state of psychosis may arise in the brain as a "linear" information processing pathology is briefly introduced. This hypothesis is proposed in the context of a complementary approach to psychiatry founded in the logical paradigm of chaos theory. To best understand the relation between chaos theory and psychiatry, the semantic structure of chaos theory is analyzed with the help of six general, and six specific, fundamental characteristics which can be directly inferred from empirical observations on chaotic systems. This enables a mathematically and physically stringent perspective on psychological phenomena which until now could only be grasped intuitively: Chaotic systems are in a general sense dynamic, intrinsically coherent, deterministic, recursive, reactive and structured: in a specific sense, self-organizing, unpredictable, nonreproducible, triadic, unstable and self-similar. To a great extent, certain concepts of chaos theory can be associated with corresponding concepts in psychiatry, psychology and psychotherapy, thus enabling an understanding of the human psyche in general as a (fractal) chaotic system and an explanation of certain mental developments, such as the course of schizophrenia, the course of psychosis and psychotherapy as chaotic processes. General overview: A short comparison and contrast of classical and chaotic physical theory leads to four postulates and one hypothesis motivating a new, dynamic, nonlinear approach to classical, causal psychiatry:
Generalized Deterministic Traffic Rules
NASA Astrophysics Data System (ADS)
Fuks, Henryk; Boccara, Nino
We study a family of deterministic models for highway traffic flow which generalize cellular automaton rule 184. This family is parameterized by the speed limit m and another parameter k that represents a "degree of aggressiveness" in driving, strictly related to the distance between two consecutive cars. We compare two driving strategies with identical maximum throughput: "conservative" driving with high speed limit and "aggressive" driving with low speed limit. Those two strategies are evaluated in terms of accident probability. We also discuss fundamental diagrams of generalized traffic rules and examine limitations of maximum achievable throughput. Possible modifications of the model are considered.
Deterministic Entangled Nanosource
2008-08-01
control number PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 1. REPORT DATE (DD-MM-YYYY) 01-09-2008 2. REPORT TYPE Final Report 3...DATES COVERED (From - To) Sep 2005 - Sep 200? 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER FA9550-05-1-0455 5b. GRANT NUMBER Deterministic...Entangled Nanosource 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER Khitrova, Galina 5f. WORK UNIT NUMBER 7. PERFORMING
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.
Gravitational collapse, chaos in CFT correlators and the information paradox
NASA Astrophysics Data System (ADS)
Farahi, Arya; Pando Zayas, Leopoldo A.
2014-06-01
We consider gravitational collapse of a massless scalar field in asymptotically anti-de Sitter spacetime. Following the AdS/CFT dictionary we further study correlations in the field theory side by way of the Klein-Gordon equation of a probe scalar field in the collapsing background. We present evidence that in a certain regime the probe scalar field behaves chaotically, thus supporting Hawking's argument in the black hole information paradox proposing that although the information can be retrieved in principle, deterministic chaos impairs, in practice, the process of unitary extraction of information from a black hole. We emphasize that quantum chaos will change this picture. .
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.
Unpredictable points and chaos
NASA Astrophysics Data System (ADS)
Akhmet, Marat; Fen, Mehmet Onur
2016-11-01
It is revealed that a special kind of Poisson stable point, which we call an unpredictable point, gives rise to the existence of chaos in the quasi-minimal set. The existing definitions of chaos are formulated in sets of motions. This is the first time in the literature that description of chaos is initiated from a single motion. The theoretical results are exemplified by means of the symbolic dynamics.
Spatiotemporal Chaos Induces Extreme Events in an Extended Microcavity Laser.
Selmi, F; Coulibaly, S; Loghmari, Z; Sagnes, I; Beaudoin, G; Clerc, M G; Barbay, S
2016-01-08
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.
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…
NASA Astrophysics Data System (ADS)
Garity, Dennis J.; Repovš, Dušan
2008-11-01
We discuss some basic topological techniques used in the study of chaotic dynamical systems. This paper is partially motivated by a talk given by the second author at the 7th international summer school and conference Chaos 2008: Let's Face Chaos Through Nonlinear Dynamics (CAMTP, University of Maribor, Slovenia, 29 June-13 July 2008).
Understanding chaos via nuclei
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.
NASA Astrophysics Data System (ADS)
Gekelman, W. N.; DeHaas, T.; Van Compernolle, B.
2013-12-01
Magnetic Flux Ropes Immersed in a uniform magnetoplasma are observed to twist about themselves, writhe about each other and rotate about a central axis. They are kink unstable and smash into one another as they move. Full three dimensional magnetic field and flows are measured at thousands of time steps. Each collision results in magnetic field line generation and the generation of a quasi-seperatrix layer and induced electric fields. Three dimensional magnetic field lines are computed by conditionally averaging the data using correlation techniques. The permutation entropy1 ,which is related to the Lyapunov exponent, can be calculated from the the time series of the magnetic field data (this is also done with flows) and used to calculate the positions of the data on a Jensen Shannon complexity map2. The location of data on this map indicates if the magnetic fields are stochastic, or fall into regions of minimal or maximal complexity. The complexity is a function of space and time. The complexity map, and analysis will be explained in the course of the talk. Other types of chaotic dynamical models such as the Lorentz, Gissinger and Henon process also fall on the map and can give a clue to the nature of the flux rope turbulence. The ropes fall in the region of the C-H plane where chaotic systems lie. The entropy and complexity change in space and time which reflects the change and possibly type of chaos associated with the ropes. The maps give insight as to the type of chaos (deterministic chaos, fractional diffusion , Levi flights..) and underlying dynamical process. The power spectra of much of the magnetic and flow data is exponential and Lorentzian structures in the time domain are embedded in them. Other quantities such as the Hurst exponent are evaluated for both magnetic fields and plasma flow. Work Supported by a UC-LANL Lab fund and the Basic Plasma Science Facility which is funded by DOE and NSF. 1) C. Bandt, B. Pompe, Phys. Rev. Lett., 88,174102 (2007) 2
NASA Astrophysics Data System (ADS)
Kandrup, H. E.
2002-09-01
This talk summarises a combined theoretical and numerical investigation of the role of chaos and transient chaos in time-dependent Hamiltonian systems which aim to model elliptical galaxies. The existence of large amounts of chaos in near-equilibrium configurations is of potential importance because configurations incorporating large numbers of chaotic orbits appear to be substantially more susceptible than nearly integrable systems to various irregularities associated with, e.g., internal substructures, satellite galaxies, and/or the effects of a high density environment. Alternatively, transient chaos, reflecting exponential sensitivity over comparatively short time intervals, can prove important by significantly increasing the overall efficiency of violent relaxation so as to facilitate a more rapid evolution towards a `well-mixed' equilibrium. Completely conclusive `smoking gun' evidence for chaos and chaotic mixing has not yet been obtained, although evidence for the presence of chaos can in principle be extracted from such data sets as provided by the Sloan Digital Sky Survey. Interestingly, however, arguments completely analogous to those applied to self-gravitating systems also suggest the presence of chaos in charged particle beams, a setting which is amenable to controlled experiments.
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.
Competitive coexistence in stoichiometric chaos.
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.
Self-stabilizing Deterministic Gathering
NASA Astrophysics Data System (ADS)
Dieudonné, Yoann; Petit, Franck
In this paper, we investigate the possibility to deterministically solve the gathering problem (GP) with weak robots (anonymous, autonomous, disoriented, oblivious, deaf, and dumb). We introduce strong multiplicity detection as the ability for the robots to detect the exact number of robots located at a given position. We show that with strong multiplicity detection, there exists a deterministic self-stabilizing algorithm solving GP for n robots if, and only if, n is odd.
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)
Exploiting chaos for applications
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.
[Chaos theory: a fascinating concept for oncologists].
Denis, F; Letellier, C
2012-05-01
The oncologist is confronted daily by questions related to the fact that any patient presents a specific evolution for his cancer: he is challenged by very different, unexpected and often unpredictable outcomes, in some of his patients. The mathematical approach used today to describe this evolution has recourse to statistics and probability laws: such an approach does not ultimately apply to one particular patient, but to a given more or less heterogeneous population. This approach therefore poorly characterizes the dynamics of this disease and does not allow to state whether a patient is cured, to predict if he will relapse and when this could occur, and in what form, nor to predict the response to treatment and, in particular, to radiation therapy. Chaos theory, not well known by oncologists, could allow a better understanding of these issues. Developed to investigate complex systems producing behaviours that cannot be predicted due to a great sensitivity to initial conditions, chaos theory is rich of suitable concepts for a new approach of cancer dynamics. This article is three-fold: to provide a brief introduction to chaos theory, to clarify the main connecting points between chaos and carcinogenesis and to point out few promising research perspectives, especially in radiotherapy.
Chaos theory applied to the caloric response of the vestibular system.
Aasen, T
1993-12-01
Developments in the field of nonlinear dynamics has given us a new conceptual framework for understanding the mechanisms involved in the regulation of complex nonlinear systems. This concept, called "chaos" or "deterministic chaos," has been applied to EKG, EEG, and other physiological signals, but not yet to the ENG signal. The underlying geometrical structure in chaotic dynamics is fractal (noninteger dimension), and calculating the fractal dimension of the electronystagmographic recording from caloric testing gave a dimension ranging from 3.3 to 7.7. This result demonstrates that the multidimensional vestibular system, with its numerous neurological pathways, can somehow reduce the degrees of freedom and give rise to an irregular dynamic low-dimensional behavior, which is associated with deterministic chaos.
Chaos, Fractals and Their Applications
NASA Astrophysics Data System (ADS)
Thompson, J. Michael T.
2016-12-01
This paper gives an up-to-date account of chaos and fractals, in a popular pictorial style for the general scientific reader. A brief historical account covers the development of the subject from Newton’s laws of motion to the astronomy of Poincaré and the weather forecasting of Lorenz. Emphasis is given to the important underlying concepts, embracing the fractal properties of coastlines and the logistics of population dynamics. A wide variety of applications include: NASA’s discovery and use of zero-fuel chaotic “superhighways” between the planets; erratic chaotic solutions generated by Euler’s method in mathematics; atomic force microscopy; spontaneous pattern formation in chemical and biological systems; impact mechanics in offshore engineering and the chatter of cutting tools; controlling chaotic heartbeats. Reference is made to a number of interactive simulations and movies accessible on the web.
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.
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.
Mixed deterministic and probabilistic networks.
Mateescu, Robert; Dechter, Rina
2008-11-01
The paper introduces mixed networks, a new graphical model framework for expressing and reasoning with probabilistic and deterministic information. The motivation to develop mixed networks stems from the desire to fully exploit the deterministic information (constraints) that is often present in graphical models. Several concepts and algorithms specific to belief networks and constraint networks are combined, achieving computational efficiency, semantic coherence and user-interface convenience. We define the semantics and graphical representation of mixed networks, and discuss the two main types of algorithms for processing them: inference-based and search-based. A preliminary experimental evaluation shows the benefits of the new model.
Mixed deterministic and probabilistic networks
Dechter, Rina
2010-01-01
The paper introduces mixed networks, a new graphical model framework for expressing and reasoning with probabilistic and deterministic information. The motivation to develop mixed networks stems from the desire to fully exploit the deterministic information (constraints) that is often present in graphical models. Several concepts and algorithms specific to belief networks and constraint networks are combined, achieving computational efficiency, semantic coherence and user-interface convenience. We define the semantics and graphical representation of mixed networks, and discuss the two main types of algorithms for processing them: inference-based and search-based. A preliminary experimental evaluation shows the benefits of the new model. PMID:20981243
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.
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…
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.
NASA Astrophysics Data System (ADS)
Jacquelin, E.; Adhikari, S.; Sinou, J.-J.; Friswell, M. I.
2015-11-01
Polynomial chaos solution for the frequency response of linear non-proportionally damped dynamic systems has been considered. It has been observed that for lightly damped systems the convergence of the solution can be very poor in the vicinity of the deterministic resonance frequencies. To address this, Aitken's transformation and its generalizations are suggested. The proposed approach is successfully applied to the sequences defined by the first two moments of the responses, and this process significantly accelerates the polynomial chaos convergence. In particular, a 2-dof system with respectively 1 and 2 parameter uncertainties has been studied. The first two moments of the frequency response were calculated by Monte Carlo simulation, polynomial chaos expansion and Aitken's transformation of the polynomial chaos expansion. Whereas 200 polynomials are required to have a good agreement with Monte Carlo results around the deterministic eigenfrequencies, less than 50 polynomials transformed by the Aitken's method are enough. This latter result is improved if a generalization of Aitken's method (recursive Aitken's transformation, Shank's transformation) is applied. With the proposed convergence acceleration, polynomial chaos may be reconsidered as an efficient method to estimate the first two moments of a random dynamic response.
Preface to the Focus Issue: Chaos Detection Methods and Predictability
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.
Preface to the Focus Issue: chaos detection methods and predictability.
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.
Failure in distinguishing colored noise from chaos using the ``noise titration'' technique
NASA Astrophysics Data System (ADS)
Freitas, Ubiratan S.; Letellier, Christophe; Aguirre, Luis A.
2009-03-01
Identifying chaos in experimental data—noisy data—remains a challenging problem for which conclusive arguments are still very difficult to provide. In order to avoid problems usually encountered with techniques based on geometrical invariants (dimensions, Lyapunov exponent, etc.), Poon and Barahona introduced a numerical titration procedure which compares one-step-ahead predictions of linear and nonlinear models [Proc. Natl. Acad. Sci. U.S.A. 98, 7107 (2001)]. We investigate the aformentioned technique in the context of colored noise or other types of nonchaotic behaviors. The main conclusion is that in several examples noise titration fails to distinguish such nonchaotic signals from low-dimensional deterministic chaos.
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.
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.
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.
Quantum chaos meets coherent control.
Gong, Jiangbin; Brumer, Paul
2005-01-01
Coherent control of atomic and molecular processes has been a rapidly developing field. Applications of coherent control to large and complex molecular systems are expected to encounter the effects of chaos in the underlying classical dynamics, i.e., quantum chaos. Hence, recent work has focused on examining control in model chaotic systems. This work is reviewed, with an emphasis on a variety of new quantum phenomena that are of interest to both areas of quantum chaos and coherent control.
Hosur, Pavan; Qi, Xiao-Liang; Roberts, Daniel A.; ...
2016-02-01
For this research, we study chaos and scrambling in unitary channels by considering their entanglement properties as states. Using out-of-time-order correlation functions to diagnose chaos, we characterize the ability of a channel to process quantum information. We show that the generic decay of such correlators implies that any input subsystem must have near vanishing mutual information with almost all partitions of the output. Additionally, we propose the negativity of the tripartite information of the channel as a general diagnostic of scrambling. This measures the delocalization of information and is closely related to the decay of out-of-time-order correlators. We back upmore » our results with numerics in two non-integrable models and analytic results in a perfect tensor network model of chaotic time evolution. In conclusion, these results show that the butterfly effect in quantum systems implies the information-theoretic definition of scrambling.« less
Hosur, Pavan; Qi, Xiao-Liang; Roberts, Daniel A.; Yoshida, Beni
2016-02-01
For this research, we study chaos and scrambling in unitary channels by considering their entanglement properties as states. Using out-of-time-order correlation functions to diagnose chaos, we characterize the ability of a channel to process quantum information. We show that the generic decay of such correlators implies that any input subsystem must have near vanishing mutual information with almost all partitions of the output. Additionally, we propose the negativity of the tripartite information of the channel as a general diagnostic of scrambling. This measures the delocalization of information and is closely related to the decay of out-of-time-order correlators. We back up our results with numerics in two non-integrable models and analytic results in a perfect tensor network model of chaotic time evolution. In conclusion, these results show that the butterfly effect in quantum systems implies the information-theoretic definition of scrambling.
Wireless communication with chaos.
Ren, Hai-Peng; Baptista, Murilo S; Grebogi, Celso
2013-05-03
The modern world fully relies on wireless communication. Because of intrinsic physical constraints of the wireless physical media (multipath, damping, and filtering), signals carrying information are strongly modified, preventing information from being transmitted with a high bit rate. We show that, though a chaotic signal is strongly modified by the wireless physical media, its Lyapunov exponents remain unaltered, suggesting that the information transmitted is not modified by the channel. For some particular chaotic signals, we have indeed proved that the dynamic description of both the transmitted and the received signals is identical and shown that the capacity of the chaos-based wireless channel is unaffected by the multipath propagation of the physical media. These physical properties of chaotic signals warrant an effective chaos-based wireless communication system.
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.
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
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.
Noise tolerant spatiotemporal chaos computing
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.
Tailoring wavelets for chaos control.
Wei, G W; Zhan, Meng; Lai, C-H
2002-12-31
Chaos is a class of ubiquitous phenomena and controlling chaos is of great interest and importance. In this Letter, we introduce wavelet controlled dynamics as a new paradigm of dynamical control. We find that by modifying a tiny fraction of the wavelet subspaces of a coupling matrix, we could dramatically enhance the transverse stability of the synchronous manifold of a chaotic system. Wavelet controlled Hopf bifurcation from chaos is observed. Our approach provides a robust strategy for controlling chaos and other dynamical systems in nature.
Noise tolerant spatiotemporal chaos computing.
Kia, Behnam; Kia, Sarvenaz; Lindner, John F; Sinha, Sudeshna; Ditto, William L
2014-12-01
We introduce and design a noise tolerant chaos computing system based on a coupled map lattice (CML) and the noise reduction capabilities inherent in coupled dynamical systems. The resulting spatiotemporal chaos computing system is more robust to noise than a single map chaos computing system. In this CML based approach to computing, under the coupled dynamics, the local noise from different nodes of the lattice diffuses across the lattice, and it attenuates each other's effects, resulting in a system with less noise content and a more robust chaos computing architecture.
van De Water W; de Weger J
2000-11-01
We study the control of chaos in an experiment on a parametrically excited pendulum whose excitation mechanism is not perfect. This imperfection leads to a weakly excited degree of freedom with an associated small eigenvalue. Although the state of the pendulum could be characterized well and although the perturbation is weak, we fail to control chaos. From a numerical model we learn that the small eigenvalue cannot be ignored when attempting control. However, the estimate of this eigenvalue from an (experimental) time series is elusive. The reason is that points in an experimental time series are distributed according to the natural measure. It is this extremely uneven distribution of points that thwarts attempts to measure eigenvalues that are very different. Another consequence of the phase-space distribution of points for control is the occurrence of logarithmic-oscillations in the waiting time before control can be attempted. We come to the conclusion that chaos needs to be destroyed before the information needed for its control can be obtained.
Generalized Polynomial Chaos Based Uncertainty Quantification for Planning MRgLITT Procedures
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
Chaos, brain and divided consciousness.
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.
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…
NASA Astrophysics Data System (ADS)
Kaszás, Bálint; Feudel, Ulrike; Tél, Tamás
2016-12-01
We investigate the death and revival of chaos under the impact of a monotonous time-dependent forcing that changes its strength with a non-negligible rate. Starting on a chaotic attractor it is found that the complexity of the dynamics remains very pronounced even when the driving amplitude has decayed to rather small values. When after the death of chaos the strength of the forcing is increased again with the same rate of change, chaos is found to revive but with a different history. This leads to the appearance of a hysteresis in the complexity of the dynamics. To characterize these dynamics, the concept of snapshot attractors is used, and the corresponding ensemble approach proves to be superior to a single trajectory description, that turns out to be nonrepresentative. The death (revival) of chaos is manifested in a drop (jump) of the standard deviation of one of the phase-space coordinates of the ensemble; the details of this chaos-nonchaos transition depend on the ratio of the characteristic times of the amplitude change and of the internal dynamics. It is demonstrated that chaos cannot die out as long as underlying transient chaos is present in the parameter space. As a condition for a "quasistatically slow" switch-off, we derive an inequality which cannot be fulfilled in practice over extended parameter ranges where transient chaos is present. These observations need to be taken into account when discussing the implications of "climate change scenarios" in any nonlinear dynamical system.
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.
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.
[Shedding light on chaos theory].
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.
Chaos suppression in gas-solid fluidization.
Pence, Deborah V.; Beasley, Donald E.
1998-06-01
Fluidization in granular materials occurs primarily as a result of a dynamic balance between gravitational forces and forces resulting from the flow of a fluid through a bed of discrete particles. For systems where the fluidizing medium and the particles have significantly different densities, density wave instabilities create local pockets of very high void fraction termed bubbles. The fluidization regime is termed the bubbling regime. Such a system is appropriately termed a self-excited nonlinear system. The present study examines chaos suppression resulting from an opposing oscillatory flow in gas-solid fluidization. Time series data representing local, instantaneous pressure were acquired at the surface of a horizontal cylinder submerged in a bubbling fluidized bed. The particles had a weight mean diameter of 345 &mgr;m and a narrow size distribution. The state of fluidization corresponded to the bubbling regime and total air flow rates employed in the present study ranged from 10% to 40% greater than that required for minimum fluidization. The behavior of time-varying local pressure in fluidized beds in the absence of a secondary flow is consistent with deterministic chaos. Kolmogorov entropy estimates from local, instantaneous pressure suggest that the degree of chaotic behavior can be substantially suppressed by the presence of an opposing, oscillatory secondary flow. Pressure signals clearly show a "phase-locking" phenomenon coincident with the imposed frequency. In the present study, the greatest degree of suppression occurred for operating conditions with low primary and secondary flow rates, and a secondary flow oscillation frequency of 15 Hz. (c) 1998 American Institute of Physics.
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.
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.
Survivability of Deterministic Dynamical Systems
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
NASA Technical Reports Server (NTRS)
2002-01-01
(Released 18 June 2002) Among the many varied landscapes on Mars the term chaos is applied to those places that have a jumbled, blocky appearance. Most of the better known chaotic terrain occurs in the northern hemisphere but there are other occurrences in the southern hemisphere, three of which are centered on 180 degrees west longitude. Ariadnes Colles, Atlantis, and Gorgonum Chaos all share similar features: relatively bright, irregularly shaped knobs and mesas that rise above a dark, sand-covered, hummocky floor. Close inspection of this THEMIS image shows that the darker material tends to lap up to the base of the knobs and stops where the slopes are steep. On some of the lowest knobs, the dark material appears to overtop them. The knobs themselves are highly eroded, many having a pitted appearance. Images from the camera on Mars Global Surveyor clearly show that the dark material is sand, based on its mantling appearance and the presence of dunes. It looks as though the material that composes the knobs was probably a continuous layer that was subsequently heavily eroded. While it is likely that the dark sand is responsible for some of the erosion it is also possible that the this landscape was eroded by some other process and the sand was emplaced at a later time.
Demographic noise can reverse the direction of deterministic selection
Constable, George W. A.; Rogers, Tim; McKane, Alan J.; Tarnita, Corina E.
2016-01-01
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 r−K theory, by which small populations can evolve to higher densities in the absence of disturbance. PMID:27450085
Deterministic weak localization in periodic structures.
Tian, C; Larkin, A
2005-12-09
In some perfect periodic structures classical motion exhibits deterministic diffusion. For such systems we present the weak localization theory. As a manifestation for the velocity autocorrelation function a universal power law decay is predicted to appear at four Ehrenfest times. This deterministic weak localization is robust against weak quenched disorders, which may be confirmed by coherent backscattering measurements of periodic photonic crystals.
Stalling chaos control accelerates convergence
NASA Astrophysics Data System (ADS)
Bick, Christian; Kolodziejski, Christoph; Timme, Marc
2013-06-01
Since chaos control has found its way into many applications, the development of fast, easy-to-implement and universally applicable chaos control methods is of crucial importance. Predictive feedback control has been widely applied but suffers from a speed limit imposed by highly unstable periodic orbits. We show that this limit can be overcome by stalling the control, thereby taking advantage of the stable directions of the uncontrolled chaotic map. This analytical finding is confirmed by numerical simulations, giving a chaos-control method that is capable of successfully stabilizing periodic orbits of high period.
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.
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...
Grondona, M.
2007-08-22
The CHAOS dchroot utilities is a set of software used to prepare and manage "alternate root" filesystems on Linux systems. These alternate roots can be used to provide an alternate set of system software for testing and compatibility purposes.
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
Deterministic quantum teleportation with atoms.
Riebe, M; Häffner, H; Roos, C F; Hänsel, W; Benhelm, J; Lancaster, G P T; Körber, T W; Becher, C; Schmidt-Kaler, F; James, D F V; Blatt, R
2004-06-17
Teleportation of a quantum state encompasses the complete transfer of information from one particle to another. The complete specification of the quantum state of a system generally requires an infinite amount of information, even for simple two-level systems (qubits). Moreover, the principles of quantum mechanics dictate that any measurement on a system immediately alters its state, while yielding at most one bit of information. The transfer of a state from one system to another (by performing measurements on the first and operations on the second) might therefore appear impossible. However, it has been shown that the entangling properties of quantum mechanics, in combination with classical communication, allow quantum-state teleportation to be performed. Teleportation using pairs of entangled photons has been demonstrated, but such techniques are probabilistic, requiring post-selection of measured photons. Here, we report deterministic quantum-state teleportation between a pair of trapped calcium ions. Following closely the original proposal, we create a highly entangled pair of ions and perform a complete Bell-state measurement involving one ion from this pair and a third source ion. State reconstruction conditioned on this measurement is then performed on the other half of the entangled pair. The measured fidelity is 75%, demonstrating unequivocally the quantum nature of the process.
Deterministic patterns in cell motility
NASA Astrophysics Data System (ADS)
Lavi, Ido; Piel, Matthieu; Lennon-Duménil, Ana-Maria; Voituriez, Raphaël; Gov, Nir S.
2016-12-01
Cell migration paths are generally described as random walks, associated with both intrinsic and extrinsic noise. However, complex cell locomotion is not merely related to such fluctuations, but is often determined by the underlying machinery. Cell motility is driven mechanically by actin and myosin, two molecular components that generate contractile forces. Other cell functions make use of the same components and, therefore, will compete with the migratory apparatus. Here, we propose a physical model of such a competitive system, namely dendritic cells whose antigen capture function and migratory ability are coupled by myosin II. The model predicts that this coupling gives rise to a dynamic instability, whereby cells switch from persistent migration to unidirectional self-oscillation, through a Hopf bifurcation. Cells can then switch to periodic polarity reversals through a homoclinic bifurcation. These predicted dynamic regimes are characterized by robust features that we identify through in vitro trajectories of dendritic cells over long timescales and distances. We expect that competition for limited resources in other migrating cell types can lead to similar deterministic migration modes.
Stochastic Estimation via Polynomial Chaos
2015-10-01
Program Manager Lethality, Vulnerability and Survivability Branch This report is published in the interest of scientific and technical...initial conditions for partial differential equations. Here, the elementary theory of the polynomial chaos is presented followed by the details of a...the elementary theory of the polynomial chaos is presented followed by the details of a number of example calculations where the statistical mean and
Regularization of chaos by noise in electrically driven nanowire systems
NASA Astrophysics Data System (ADS)
Hessari, Peyman; Do, Younghae; Lai, Ying-Cheng; Chae, Junseok; Park, Cheol Woo; Lee, GyuWon
2014-04-01
The electrically driven nanowire systems are of great importance to nanoscience and engineering. Due to strong nonlinearity, chaos can arise, but in many applications it is desirable to suppress chaos. The intrinsically high-dimensional nature of the system prevents application of the conventional method of controlling chaos. Remarkably, we find that the phenomenon of coherence resonance, which has been well documented but for low-dimensional chaotic systems, can occur in the nanowire system that mathematically is described by two coupled nonlinear partial differential equations, subject to periodic driving and noise. Especially, we find that, when the nanowire is in either the weakly chaotic or the extensively chaotic regime, an optimal level of noise can significantly enhance the regularity of the oscillations. This result is robust because it holds regardless of whether noise is white or colored, and of whether the stochastic drivings in the two independent directions transverse to the nanowire are correlated or independent of each other. Noise can thus regularize chaotic oscillations through the mechanism of coherence resonance in the nanowire system. More generally, we posit that noise can provide a practical way to harness chaos in nanoscale systems.
Robustness analysis of an air heating plant and control law by using polynomial chaos
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.
A simple guide to chaos and complexity
Rickles, Dean; Hawe, Penelope; Shiell, Alan
2007-01-01
The concepts of complexity and chaos are being invoked with increasing frequency in the health sciences literature. However, the concepts underpinning these concepts are foreign to many health scientists and there is some looseness in how they have been translated from their origins in mathematics and physics, which is leading to confusion and error in their application. Nonetheless, used carefully, “complexity science” has the potential to invigorate many areas of health science and may lead to important practical outcomes; but if it is to do so, we need the discipline that comes from a proper and responsible usage of its concepts. Hopefully, this glossary will go some way towards achieving that objective. PMID:17933949
Universality classes for deterministic surface growth
NASA Technical Reports Server (NTRS)
Krug, J.; Spohn, H.
1988-01-01
A scaling theory for the generalized deterministic Kardar-Parisi-Zhang (1986) equation with beta greater than 1, is developed to study the growth of a surface through deterministic local rules. A one-dimensional surface model corresponding to beta = 1 is presented and solved exactly. The model can be studied as a limiting case of ballistic deposition, or as the deterministic limit of the Eden (1961) model. The scaling exponents, the correlation functions, and the skewness of the surface are determined. The results are compared with those of Burgers' (1974) equation for the case of beta = 2.
Connecting deterministic and stochastic metapopulation models.
Barbour, A D; McVinish, R; Pollett, P K
2015-12-01
In this paper, we study the relationship between certain stochastic and deterministic versions of Hanski's incidence function model and the spatially realistic Levins model. We show that the stochastic version can be well approximated in a certain sense by the deterministic version when the number of habitat patches is large, provided that the presence or absence of individuals in a given patch is influenced by a large number of other patches. Explicit bounds on the deviation between the stochastic and deterministic models are given.
Efficient topological chaos embedded in the blinking vortex system.
Kin, Eiko; Sakajo, Takashi
2005-06-01
We consider the particle mixing in the plane by two vortex points appearing one after the other, called the blinking vortex system. Mathematical and numerical studies of the system reveal that the chaotic particle mixing, i.e., the chaotic advection, is observed due to the homoclinic chaos, but the mixing region is restricted locally in the neighborhood of the vortex points. The present article shows that it is possible to realize a global and efficient chaotic advection in the blinking vortex system with the help of the Thurston-Nielsen theory, which classifies periodic orbits for homeomorphisms in the plane into three types: periodic, reducible, and pseudo-Anosov (pA). It is mathematically shown that periodic orbits of pA type generate a complicated dynamics, which is called topological chaos. We show that the combination of the local chaotic mixing due to the topological chaos and the dipole-like return orbits realize an efficient and global particle mixing in the blinking vortex system.
Deterministic noiseless amplification of coherent states
NASA Astrophysics Data System (ADS)
Hu, Meng-Jun; Zhang, Yong-Sheng
2015-08-01
A universal deterministic noiseless quantum amplifier has been shown to be impossible. However, probabilistic noiseless amplification of a certain set of states is physically permissible. Regarding quantum state amplification as quantum state transformation, we show that deterministic noiseless amplification of coherent states chosen from a proper set is attainable. The relation between input coherent states and gain of amplification for deterministic noiseless amplification is thus derived. Furthermore, we extend our result to more general situation and show that deterministic noiseless amplification of Gaussian states is also possible. As an example of application, we find that our amplification model can obtain better performance in homodyne detection to measure the phase of state selected from a certain set. Besides, other possible applications are also discussed.
Relations between distributional and Devaney chaos.
Oprocha, Piotr
2006-09-01
Recently, it was proven that chaos in the sense of Devaney and weak mixing both imply chaos in the sense of Li and Yorke. In this article we give explicit examples that any of these two implications do not hold for distributional chaos.
NASA Astrophysics Data System (ADS)
Pagnacco, E.; de Cursi, E. Souza; Sampaio, R.
2016-07-01
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.
Chaos forgets and remembers: Measuring information creation, destruction, and storage
NASA Astrophysics Data System (ADS)
James, Ryan G.; Burke, Korana; Crutchfield, James P.
2014-06-01
The hallmark of deterministic chaos is that it creates information-the rate being given by the Kolmogorov-Sinai metric entropy. Since its introduction half a century ago, the metric entropy has been used as a unitary quantity to measure a system's intrinsic unpredictability. Here, we show that it naturally decomposes into two structurally meaningful components: A portion of the created information-the ephemeral information-is forgotten and a portion-the bound information-is remembered. The bound information is a new kind of intrinsic computation that differs fundamentally from information creation: it measures the rate of active information storage. We show that it can be directly and accurately calculated via symbolic dynamics, revealing a hitherto unknown richness in how dynamical systems compute.
2012-03-01
rem for a minimum. Bolza and Bliss built upon Weierstrass’ work at the University of Chicago giving CV its current rigorous mathematical structure...M. S. “Recent Advances in Non- Intrusive Polynomial Chaos and Stochas- tic Collocation Methods for Uncertainty Analysis and Design”. 50th AIAA/AS- ME
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.
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.
NASA Astrophysics Data System (ADS)
Angius, S.; Bisegni, C.; Ciuffetti, P.; Di Pirro, G.; Foggetta, L. G.; Galletti, F.; Gargana, R.; Gioscio, E.; Maselli, D.; Mazzitelli, G.; Michelotti, A.; Orrù, R.; Pistoni, M.; Spagnoli, F.; Spigone, D.; Stecchi, A.; Tonto, T.; Tota, M. A.; Catani, L.; Di Giulio, C.; Salina, G.; Buzzi, P.; Checcucci, B.; Lubrano, P.; Piccini, M.; Fattibene, E.; Michelotto, M.; Cavallaro, S. R.; Diana, B. F.; Enrico, F.; Pulvirenti, S.
2016-01-01
The paper is aimed to present the !CHAOS open source project aimed to develop a prototype of a national private Cloud Computing infrastructure, devoted to accelerator control systems and large experiments of High Energy Physics (HEP). The !CHAOS project has been financed by MIUR (Italian Ministry of Research and Education) and aims to develop a new concept of control system and data acquisition framework by providing, with a high level of aaabstraction, all the services needed for controlling and managing a large scientific, or non-scientific, infrastructure. A beta version of the !CHAOS infrastructure will be released at the end of December 2015 and will run on private Cloud infrastructures based on OpenStack.
NASA Astrophysics Data System (ADS)
Turiaci, Gustavo J.; Verlinde, Herman
2016-12-01
We make three observations that help clarify the relation between CFT and quantum chaos. We show that any 1+1-D system in which conformal symmetry is non-linearly realized exhibits two main characteristics of chaos: maximal Lyapunov behavior and a spectrum of Ruelle resonances. We use this insight to identify a lattice model for quantum chaos, built from parafermionic spin variables with an equation of motion given by a Y-system. Finally we point to a relation between the spectrum of Ruelle resonances of a CFT and the analytic properties of OPE coefficients between light and heavy operators. In our model, this spectrum agrees with the quasi-normal modes of the BTZ black hole.
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.
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.
Dynamic chaos in the solution of the Gross-Pitaevskii equation for a periodic potential
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.
Controlling chaos with simple limiters
Corron; Pethel; Hopper
2000-04-24
New experimental results demonstrate that chaos control can be accomplished using controllers that are very simple relative to the system being controlled. Chaotic dynamics in a driven pendulum and a double scroll circuit are controlled using an adjustable, passive limiter-a weight for the pendulum and a diode for the circuit. For both experiments, multiple unstable periodic orbits are selectively controlled using minimal perturbations. These physical examples suggest that chaos control can be practically applied to a much wider array of important problems than initially thought possible.
Enhancing chaoticity of spatiotemporal chaos.
Li, Xiaowen; Zhang, Heqiao; Xue, Yu; Hu, Gang
2005-01-01
In some practical situations strong chaos is needed. This introduces the task of chaos control with enhancing chaoticity rather than suppressing chaoticity. In this paper a simple method of linear amplifications incorporating modulo operations is suggested to make spatiotemporal systems, which may be originally chaotic or nonchaotic, strongly chaotic. Specifically, this control can eliminate periodic windows, increase the values and the number of positive Lyapunov exponents, make the probability distributions of the output chaotic sequences more homogeneous, and reduce the correlations of chaotic outputs for different times and different space units. The applicability of the method to practical tasks, in particular to random number generators and secure communications, is briefly discussed.
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.
Synchronicity from synchronized chaos
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”.
Synchronicity from synchronized chaos
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
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.
Accessing Creativity: Jungian Night Sea Journeys, Wandering Minds, and Chaos.
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.
Improving ground-penetrating radar data in sedimentary rocks using deterministic deconvolution
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
Deterministic versus evidence-based attitude towards clinical diagnosis.
Soltani, Akbar; Moayyeri, Alireza
2007-08-01
Generally, two basic classes have been proposed for scientific explanation of events. Deductive reasoning emphasizes on reaching conclusions about a hypothesis based on verification of universal laws pertinent to that hypothesis, while inductive or probabilistic reasoning explains an event by calculation of some probabilities for that event to be related to a given hypothesis. Although both types of reasoning are used in clinical practice, evidence-based medicine stresses on the advantages of the second approach for most instances in medical decision making. While 'probabilistic or evidence-based' reasoning seems to involve more mathematical formulas at the first look, this attitude is more dynamic and less imprisoned by the rigidity of mathematics comparing with 'deterministic or mathematical attitude'. In the field of medical diagnosis, appreciation of uncertainty in clinical encounters and utilization of likelihood ratio as measure of accuracy seem to be the most important characteristics of evidence-based doctors. Other characteristics include use of series of tests for refining probability, changing diagnostic thresholds considering external evidences and nature of the disease, and attention to confidence intervals to estimate uncertainty of research-derived parameters.
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.
Optimal partial deterministic quantum teleportation of qubits
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.
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.
NASA Astrophysics Data System (ADS)
Itoh, Kosuke; Nakada, Tsutomu
2013-04-01
Deterministic nonlinear dynamical processes are ubiquitous in nature. Chaotic sounds generated by such processes may appear irregular and random in waveform, but these sounds are mathematically distinguished from random stochastic sounds in that they contain deterministic short-time predictability in their temporal fine structures. We show that the human brain distinguishes deterministic chaotic sounds from spectrally matched stochastic sounds in neural processing and perception. Deterministic chaotic sounds, even without being attended to, elicited greater cerebral cortical responses than the surrogate control sounds after about 150 ms in latency after sound onset. Listeners also clearly discriminated these sounds in perception. The results support the hypothesis that the human auditory system is sensitive to the subtle short-time predictability embedded in the temporal fine structure of sounds.
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.
Chaos in the pulse spacing of passive Q-switched all-solid-state lasers.
Kovalsky, Marcelo; Hnilo, Alejandro
2010-10-15
We report the experimental and theoretical verification that, in a diode-pumped Nd:YAG+Cr:YAGQ-switched laser, the instabilities in the pulse spacing ("jitter") are ruled by low-dimensional deterministic chaos. From our experimental time series, we determine the embedding and fractal dimensions of the attractor, as well as the values of the Lyapunov exponents. We also present a simplified theoretical description in terms of a map of the same universality class as the logistic map, which explains the bifurcations' cascade and the period-three window of stability observed. The achieved characterization of the dynamics and its main parameters opens a door to effective ways to reduce the jitter, which is of practical interest, through mechanisms of control of chaos. Conversely, the difficulty in the prediction of the interpulse spacing makes this system attractive for high power, robust FM chaotic laser cryptography in free-space propagation.
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)
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
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.
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.
A deterministic discrete ordinates transport proxy application
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.
Deterministic Quantization by Dynamical Boundary Conditions
Dolce, Donatello
2010-06-15
We propose an unexplored quantization method. It is based on the assumption of dynamical space-time intrinsic periodicities for relativistic fields, which in turn can be regarded as dual to extra-dimensional fields. As a consequence we obtain a unified and consistent interpretation of Special Relativity and Quantum Mechanics in terms of Deterministic Geometrodynamics.
Deterministic geologic processes and stochastic modeling
Rautman, C.A.; Flint, A.L.
1991-12-31
Recent outcrop sampling at Yucca Mountain, Nevada, has produced significant new information regarding the distribution of physical properties at the site of a potential high-level nuclear waste repository. Consideration of the spatial distribution of measured values and geostatistical measures of spatial variability indicates that there are a number of widespread deterministic geologic features at the site that have important implications for numerical modeling of such performance aspects as ground water flow and radionuclide transport. These deterministic features have their origin in the complex, yet logical, interplay of a number of deterministic geologic processes, including magmatic evolution; volcanic eruption, transport, and emplacement; post-emplacement cooling and alteration; and late-stage (diagenetic) alteration. Because of geologic processes responsible for formation of Yucca Mountain are relatively well understood and operate on a more-or-less regional scale, understanding of these processes can be used in modeling the physical properties and performance of the site. Information reflecting these deterministic geologic processes may be incorporated into the modeling program explicitly, using geostatistical concepts such as soft information, or implicitly, through the adoption of a particular approach to modeling. It is unlikely that any single representation of physical properties at the site will be suitable for all modeling purposes. Instead, the same underlying physical reality will need to be described many times, each in a manner conducive to assessing specific performance issues.
Topological chaos of the spatial prisoner's dilemma game on regular networks.
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.
SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos
Ahlfeld, R. Belkouchi, B.; Montomoli, F.
2016-09-01
A new arbitrary Polynomial Chaos (aPC) method is presented for moderately high-dimensional problems characterised by limited input data availability. The proposed methodology improves the algorithm of aPC and extends the method, that was previously only introduced as tensor product expansion, to moderately high-dimensional stochastic problems. The fundamental idea of aPC is to use the statistical moments of the input random variables to develop the polynomial chaos expansion. This approach provides the possibility to propagate continuous or discrete probability density functions and also histograms (data sets) as long as their moments exist, are finite and the determinant of the moment matrix is strictly positive. For cases with limited data availability, this approach avoids bias and fitting errors caused by wrong assumptions. In this work, an alternative way to calculate the aPC is suggested, which provides the optimal polynomials, Gaussian quadrature collocation points and weights from the moments using only a handful of matrix operations on the Hankel matrix of moments. It can therefore be implemented without requiring prior knowledge about statistical data analysis or a detailed understanding of the mathematics of polynomial chaos expansions. The extension to more input variables suggested in this work, is an anisotropic and adaptive version of Smolyak's algorithm that is solely based on the moments of the input probability distributions. It is referred to as SAMBA (PC), which is short for Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos. It is illustrated that for moderately high-dimensional problems (up to 20 different input variables or histograms) SAMBA can significantly simplify the calculation of sparse Gaussian quadrature rules. SAMBA's efficiency for multivariate functions with regard to data availability is further demonstrated by analysing higher order convergence and accuracy for a set of nonlinear test functions with 2, 5 and 10
Does chaos assist localization or delocalization?
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.
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.
Multiple Scenarios of Transition to Chaos in the Alternative Splicing Model
NASA Astrophysics Data System (ADS)
Kogai, Vladislav V.; Likhoshvai, Vitaly A.; Fadeev, Stanislav I.; Khlebodarova, Tamara M.
We have investigated the scenarios of transition to chaos in the mathematical model of a genetic system constituted by a single transcription factor-encoding gene, the expression of which is self-regulated by a feedback loop that involves protein isoforms. Alternative splicing results in the synthesis of protein isoforms providing opposite regulatory outcomes — activation or repression. The model is represented by a differential equation with two delayed arguments. The possibility of transition to chaos dynamics via all classical scenarios: a cascade of period-doubling bifurcations, quasiperiodicity and type-I, type-II and type-III intermittencies, has been numerically demonstrated. The parametric features of each type of transition to chaos have been described.
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
Spatiotemporal chaos from bursting dynamics
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.
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.
Controlling fast chaos in delay dynamical systems.
Blakely, Jonathan N; Illing, Lucas; Gauthier, Daniel J
2004-05-14
We introduce a novel approach for controlling fast chaos in time-delay dynamical systems and use it to control a chaotic photonic device with a characteristic time scale of approximately 12 ns. Our approach is a prescription for how to implement existing chaos-control algorithms in a way that exploits the system's inherent time delay and allows control even in the presence of substantial control-loop latency (the finite time it takes signals to propagate through the components in the controller). This research paves the way for applications exploiting fast control of chaos, such as chaos-based communication schemes and stabilizing the behavior of ultrafast lasers.
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.
Sheridan, T.E.
2005-08-15
Chaotic dynamics is observed experimentally in a complex (dusty) plasma of three particles. A low-frequency sinusoidal modulation of the plasma density excites both the center-of-mass and breathing modes. Low-dimensional chaos is seen for a 1:2 resonance between these modes. A strange attractor with a dimension of 2.48{+-}0.05 is observed. The largest Lyapunov exponent is positive.
Temperature chaos and quenched heterogeneities
NASA Astrophysics Data System (ADS)
Barucca, Paolo; Parisi, Giorgio; Rizzo, Tommaso
2014-03-01
We present a treatable generalization of the Sherrington-Kirkpatrick (SK) model which introduces correlations in the elements of the coupling matrix through multiplicative disorder on the single variables and investigate the consequences on the phase diagram. We define a generalized qEA parameter and test the structural stability of the SK results in this correlated case evaluating the de Almeida-Thouless line of the model. As a main result we demonstrate the increase of temperature chaos effects due to heterogeneities.
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)
Interactive Workshop Discusses Nonlinear Waves and Chaos
NASA Astrophysics Data System (ADS)
Tsurutani, Bruce; Morales, George; Passot, Thierry
2010-07-01
Eighth International Nonlinear Wave Workshop; La Jolla, California, 1-5 March 2010; Nonlinear waves and chaos were the focus of a weeklong series of informal and interactive discussions at the Eighth International Nonlinear Wave Workshop (NWW8), held in California. The workshop gathered nonlinear plasma and water wave experts from the United States, France, Czech Republic, Germany, Greece, Holland, India, and Japan. Attendees were from the fields of space, laboratory, and fusion plasma physics, astrophysics, and applied mathematics. Special focus was placed on nonlinear waves and turbulence in the terrestrial environment as well as in the interstellar medium from observational, laboratory, and theoretical perspectives. Discussions covered temperature anisotropies and related instabilities, the properties and origin of the so-called dissipation range, and various coherent structures of electromagnetic as well as electrostatic nature. Reconnection and shocks were also topics of discussion, as were properties of magnetospheric whistler and chorus waves. Examples and analysis techniques for superdiffusion and subdiffusion were identified. On this last topic, a good exchange of ideas and results occurred between a water wave expert and a plasma expert, with the rest of the audience listening intently.
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.
Deterministic nanoassembly: Neutral or plasma route?
NASA Astrophysics Data System (ADS)
Levchenko, I.; Ostrikov, K.; Keidar, M.; Xu, S.
2006-07-01
It is shown that, owing to selective delivery of ionic and neutral building blocks directly from the ionized gas phase and via surface migration, plasma environments offer a better deal of deterministic synthesis of ordered nanoassemblies compared to thermal chemical vapor deposition. The results of hybrid Monte Carlo (gas phase) and adatom self-organization (surface) simulation suggest that higher aspect ratios and better size and pattern uniformity of carbon nanotip microemitters can be achieved via the plasma route.
Deterministic Mean-Field Ensemble Kalman Filtering
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 < 2κ. The fidelity of approximation of the true distribution is also established using an extension of the total variation metric to random measures. Lastly, this is limited by a Gaussian bias term arising from nonlinearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.
Deterministic Mean-Field Ensemble Kalman Filtering
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
Multi-scale dynamical behavior of spatially distributed systems: a deterministic point of view
NASA Astrophysics Data System (ADS)
Mangiarotti, S.; Le Jean, F.; Drapeau, L.; Huc, M.
2015-12-01
Physical and biophysical systems are spatially distributed systems. Their behavior can be observed or modelled spatially at various resolutions. In this work, a deterministic point of view is adopted to analyze multi-scale behavior taking a set of ordinary differential equation (ODE) as elementary part of the system.To perform analyses, scenes of study are thus generated based on ensembles of identical elementary ODE systems. Without any loss of generality, their dynamics is chosen chaotic in order to ensure sensitivity to initial conditions, that is, one fundamental property of atmosphere under instable conditions [1]. The Rössler system [2] is used for this purpose for both its topological and algebraic simplicity [3,4].Two cases are thus considered: the chaotic oscillators composing the scene of study are taken either independent, or in phase synchronization. Scale behaviors are analyzed considering the scene of study as aggregations (basically obtained by spatially averaging the signal) or as associations (obtained by concatenating the time series). The global modeling technique is used to perform the numerical analyses [5].One important result of this work is that, under phase synchronization, a scene of aggregated dynamics can be approximated by the elementary system composing the scene, but modifying its parameterization [6]. This is shown based on numerical analyses. It is then demonstrated analytically and generalized to a larger class of ODE systems. Preliminary applications to cereal crops observed from satellite are also presented.[1] Lorenz, Deterministic nonperiodic flow. J. Atmos. Sci., 20, 130-141 (1963).[2] Rössler, An equation for continuous chaos, Phys. Lett. A, 57, 397-398 (1976).[3] Gouesbet & Letellier, Global vector-field reconstruction by using a multivariate polynomial L2 approximation on nets, Phys. Rev. E 49, 4955-4972 (1994).[4] Letellier, Roulin & Rössler, Inequivalent topologies of chaos in simple equations, Chaos, Solitons
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.
How Complex, Probable, and Predictable is Genetically Driven Red Queen Chaos?
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.
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.
On the Weakest Version of Distributional Chaos
NASA Astrophysics Data System (ADS)
Doleželová-Hantáková, Jana; Roth, Zuzana; Roth, Samuel
2016-12-01
The aim of the paper is to correct and improve some results concerning distributional chaos of type 3. We show that in a general compact metric space, distributional chaos of type 3, denoted DC3, even when assuming the existence of an uncountable scrambled set, is a very weak form of chaos. In particular, (i) the chaos can be unstable (it can be destroyed by conjugacy), and (ii) such an unstable system may contain no Li-Yorke pair. However, the definition can be strengthened to get DC21 2 which is a topological invariant and implies Li-Yorke chaos, similarly as types DC1 and DC2; but unlike them, strict DC21 2 systems must have zero topological entropy.
Scaling of chaos in strongly nonlinear lattices
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.
Chaos-order transition in foraging behavior of ants.
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.
Monohydrated Sulfates in Aurorae Chaos
NASA Technical Reports Server (NTRS)
2008-01-01
This image of sulfate-containing deposits in Aurorae Chaos was taken by the Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) at 0653 UTC (2:53 a.m. EDT) on June 10, 2007, near 7.5 degrees south latitude, 327.25 degrees east longitude. CRISM's image was taken in 544 colors covering 0.36-3.92 micrometers, and shows features as small as 40 meters (132 feet) across. The region covered is roughly 12 kilometers (7.5 miles) wide at its narrowest point.
Aurorae Chaos lies east of the Valles Marineris canyon system. Its western edge extends toward Capri and Eos Chasmata, while its eastern edge connects with Aureum Chaos. Some 750 kilometers (466 miles) wide, Aurorae Chaos is most likely the result of collapsed surface material that settled when subsurface ice or water was released.
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 covers an area featuring several knobs of erosion-resistant material at one end of what appears to be a large teardrop shaped plateau. Similar plateaus occur throughout the interior of Valles Marineris, and they are formed of younger, typically layered rocks that post-date formation of the canyon system. Many of the deposits contain sulfate-rich layers, hinting at ancient saltwater.
The center left image, an infrared false color image, reveals a swath of light-colored material draped over the knobs. The center right image unveils the mineralogical composition of the area, with yellow representing monohydrated sulfates (sulfates with one water molecule incorporated into each molecule of the mineral).
The lower two images are renderings of data draped over topography with 5 times vertical exaggeration. These images provide a view of the topography and reveal how the monohydrated sulfate-containing deposits drape over the knobs and also an outcrop in lower-elevation parts of the
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.
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.
Input reconstruction of chaos sensors.
Yu, Dongchuan; Liu, Fang; Lai, Pik-Yin
2008-06-01
Although the sensitivity of sensors can be significantly enhanced using chaotic dynamics due to its extremely sensitive dependence on initial conditions and parameters, how to reconstruct the measured signal from the distorted sensor response becomes challenging. In this paper we suggest an effective method to reconstruct the measured signal from the distorted (chaotic) response of chaos sensors. This measurement signal reconstruction method applies the neural network techniques for system structure identification and therefore does not require the precise information of the sensor's dynamics. We discuss also how to improve the robustness of reconstruction. Some examples are presented to illustrate the measurement signal reconstruction method suggested.
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
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.
Deterministic Folding in Stiff Elastic Membranes
NASA Astrophysics Data System (ADS)
Tallinen, T.; Åström, J. A.; Timonen, J.
2008-09-01
Crumpled membranes have been found to be characterized by complex patterns of spatially seemingly random facets separated by narrow ridges of high elastic energy. We demonstrate by numerical simulations that compression of stiff elastic membranes with small randomness in their initial configurations leads to either random ridge configurations (high entropy) or nearly deterministic folds (low elastic energy). For folding with symmetric ridge configurations to appear in part of the crumpling processes, the crumpling rate must be slow enough. Folding stops when the thickness of the folded structure becomes important, and crumpling continues thereafter as a random process.
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.
Invoking the muse: Dada's chaos.
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.
Quantifying chaos for ecological stoichiometry.
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.
The topography of chaos terrain on Europa
NASA Astrophysics Data System (ADS)
Patterson, G.; Prockter, L. M.; Schenk, P.
2010-12-01
Chaos terrain and lenticulae are commonly observed surface features unique to the Galilean satellite Europa. Chaos terrain occurs as discrete regions of the satellite’s surface 10s to 100s of km in size that are disrupted into isolated plates surrounded by hummocky matrix material. Lenticulae occur as positive- or negative-relief domes km to 10s of km in diameter that can disrupt the original surface in a manner similar to chaos terrain. Evidence suggests that they each form via an endogenic process involving the interaction of a mobile substrate with the brittle surface and it has been proposed that ice shell thinning or surface yielding coupled with brine production represents the most plausible mechanism for the formation of these features. These similarities in morphology and formation mechanism indicate they may represent a continuum process. We explore whether larger chaos terrain represent the coalescence of smaller lenticulae by examining topography within chaos to determine whether it contains domes on length scales similar to lenticulae. Schenk and Pappalardo (2004) alluded to the presence of several prominent domes within Conamara Chaos and we have previously shown that at least 4 and as many as 9 domes with length scales similar to lenticulae are present within and along the margins of the feature. This was accomplished by using Fourier analysis to decompose the topographic signature of Conamara Chaos and the surrounding terrain into discrete wavelength components. A low-pass filter was then used to strip away shorter wavelength components of the topography associated with the region and determine if longer wavelength features were present within the terrain. Here we present new work identifying the presence, size, and distribution of domes within the boundaries of other chaos terrains across the surface of Europa and discuss implications for chaos formation.
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.
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.
Deterministic Creation of Macroscopic Cat States
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
Deterministic forward scatter from surface gravity waves.
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.
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.
Insights into the deterministic skill of air quality ensembles ...
Simulations from chemical weather models are subject to uncertainties in the input data (e.g. emission inventory, initial and boundary conditions) as well as those intrinsic to the model (e.g. physical parameterization, chemical mechanism). Multi-model ensembles can improve the forecast skill, provided that certain mathematical conditions are fulfilled. In this work, four ensemble methods were applied to two different datasets, and their performance was compared for ozone (O3), nitrogen dioxide (NO2) and particulate matter (PM10). Apart from the unconditional ensemble average, the approach behind the other three methods relies on adding optimum weights to members or constraining the ensemble to those members that meet certain conditions in time or frequency domain. The two different datasets were created for the first and second phase of the Air Quality Model Evaluation International Initiative (AQMEII). The methods are evaluated against ground level observations collected from the EMEP (European Monitoring and Evaluation Programme) and AirBase databases. The goal of the study is to quantify to what extent we can extract predictable signals from an ensemble with superior skill over the single models and the ensemble mean. Verification statistics show that the deterministic models simulate better O3 than NO2 and PM10, linked to different levels of complexity in the represented processes. The unconditional ensemble mean achieves higher skill compared to each stati
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.
Order-to-chaos transition in the hardness of random Boolean satisfiability problems.
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.
Delay driven spatiotemporal chaos in single species population dynamics models.
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.
From Order to Chaos in Earth Satellite Orbits
NASA Astrophysics Data System (ADS)
Gkolias, Ioannis; Daquin, Jérôme; Gachet, Fabien; Rosengren, Aaron J.
2016-11-01
We consider Earth satellite orbits in the range of semimajor axes where the perturbing effects of Earth’s oblateness and lunisolar gravity are of comparable order. This range covers the medium-Earth orbits (MEO) of the Global Navigation Satellite Systems and the geosynchronous orbits (GEO) of the communication satellites. We recall a secular and quadrupolar model, based on the Milankovitch vector formulation of perturbation theory, which governs the long-term orbital evolution subject to the predominant gravitational interactions. We study the global dynamics of this two-and-a-half degrees-of-freedom Hamiltonian system by means of the fast Lyapunov indicator (FLI), used in a statistical sense. Specifically, we characterize the degree of chaoticity of the action space using angle-averaged normalized FLI maps, thereby overcoming the angle dependencies of the conventional stability maps. Emphasis is placed upon the phase-space structures near secular resonances, which are of primary importance to the space debris community. We confirm and quantify the transition from order to chaos in MEO, stemming from the critical inclinations and find that highly inclined GEO orbits are particularly unstable. Despite their reputed normality, Earth satellite orbits can possess an extraordinarily rich spectrum of dynamical behaviors and, from a mathematical perspective, have all the complications that make them very interesting candidates for testing the modern tools of chaos theory.
Cai, Y.; Wambsganss, M.W.; Jendrzejczyk, J.A.
1996-02-01
Various measurement tools of chaos theory were applied to analyze two-phase pressure signals with the objective to identify and interpret flow pattern transitions for two-phase flows in a small, horizontal rectangular channel. These measurement tools included power spectral density function, autocorrelation function, pseudo-phase-plane trajectory, Lyapunov exponents, and fractal dimensions. It was demonstrated that the randomlike pressure fluctuations characteristic of two-phase flow in small rectangular channels are chaotic in nature. As such, they are governed by a high-order deterministic system. The correlation dimension is potentially a new approach for identification of certain two-phase flow patterns and transitions.
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.
Optimized chaos control with simple limiters.
Wagner, C; Stoop, R
2001-01-01
We present an elementary derivation of chaos control with simple limiters using the logistic map and the Henon map as examples. This derivation provides conditions for optimal stabilization of unstable periodic orbits of a chaotic attractor.
Adapted polynomial chaos expansion for failure detection
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.
Adapted polynomial chaos expansion for failure detection
NASA Astrophysics Data System (ADS)
Paffrath, M.; Wever, U.
2007-09-01
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.
Homoclinic chaos and energy condition violation
NASA Astrophysics Data System (ADS)
Heinzle, J. Mark; Röhr, Niklas; Uggla, Claes
2006-09-01
In this letter we discuss the connection between so-called homoclinic chaos and the violation of energy conditions in locally rotationally symmetric Bianchi type IX models, where the matter is assumed to be nontilted dust and a positive cosmological constant. We show that homoclinic chaos in these models is an artifact of unphysical assumptions: it requires that there exist solutions with positive matter energy density ρ>0 that evolve through the singularity and beyond as solutions with negative matter energy density ρ<0. Homoclinic chaos is absent when it is assumed that the dust particles always retain their positive mass. In addition, we discuss more general models: for solutions that are not locally rotationally symmetric we demonstrate that the construction of extensions through the singularity, which is required for homoclinic chaos, is not possible in general.
Chaos automata: iterated function systems with memory
NASA Astrophysics Data System (ADS)
Ashlock, Dan; Golden, Jim
2003-07-01
Transforming biological sequences into fractals in order to visualize them is a long standing technique, in the form of the traditional four-cornered chaos game. In this paper we give a generalization of the standard chaos game visualization for DNA sequences. It incorporates iterated function systems that are called under the control of a finite state automaton, yielding a DNA to fractal transformation system with memory. We term these fractal visualizers chaos automata. The use of memory enables association of widely separated sequence events in the drawing of the fractal, finessing the “forgetfulness” of other fractal visualization methods. We use a genetic algorithm to train chaos automata to distinguish introns and exons in Zea mays (corn). A substantial issue treated here is the creation of a fitness function that leads to good visual separation of distinct data types.
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
Control of collective network chaos.
Wagemakers, Alexandre; Barreto, Ernest; Sanjuán, Miguel A F; So, Paul
2014-06-01
Under certain conditions, the collective behavior of a large globally-coupled heterogeneous network of coupled oscillators, as quantified by the macroscopic mean field or order parameter, can exhibit low-dimensional chaotic behavior. Recent advances describe how a small set of "reduced" ordinary differential equations can be derived that captures this mean field behavior. Here, we show that chaos control algorithms designed using the reduced equations can be successfully applied to imperfect realizations of the full network. To systematically study the effectiveness of this technique, we measure the quality of control as we relax conditions that are required for the strict accuracy of the reduced equations, and hence, the controller. Although the effects are network-dependent, we show that the method is effective for surprisingly small networks, for modest departures from global coupling, and even with mild inaccuracy in the estimate of network heterogeneity.
Control of collective network chaos
NASA Astrophysics Data System (ADS)
Wagemakers, Alexandre; Barreto, Ernest; Sanjuán, Miguel A. F.; So, Paul
2014-06-01
Under certain conditions, the collective behavior of a large globally-coupled heterogeneous network of coupled oscillators, as quantified by the macroscopic mean field or order parameter, can exhibit low-dimensional chaotic behavior. Recent advances describe how a small set of "reduced" ordinary differential equations can be derived that captures this mean field behavior. Here, we show that chaos control algorithms designed using the reduced equations can be successfully applied to imperfect realizations of the full network. To systematically study the effectiveness of this technique, we measure the quality of control as we relax conditions that are required for the strict accuracy of the reduced equations, and hence, the controller. Although the effects are network-dependent, we show that the method is effective for surprisingly small networks, for modest departures from global coupling, and even with mild inaccuracy in the estimate of network heterogeneity.
Compressive Sensing with Optical Chaos
NASA Astrophysics Data System (ADS)
Rontani, D.; Choi, D.; Chang, C.-Y.; Locquet, A.; Citrin, D. S.
2016-12-01
Compressive sensing (CS) is a technique to sample a sparse signal below the Nyquist-Shannon limit, yet still enabling its reconstruction. As such, CS permits an extremely parsimonious way to store and transmit large and important classes of signals and images that would be far more data intensive should they be sampled following the prescription of the Nyquist-Shannon theorem. CS has found applications as diverse as seismology and biomedical imaging. In this work, we use actual optical signals generated from temporal intensity chaos from external-cavity semiconductor lasers (ECSL) to construct the sensing matrix that is employed to compress a sparse signal. The chaotic time series produced having their relevant dynamics on the 100 ps timescale, our results open the way to ultrahigh-speed compression of sparse signals.
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
Fundamental concepts of quantum chaos
NASA Astrophysics Data System (ADS)
Robnik, M.
2016-09-01
We review the fundamental concepts of quantum chaos in Hamiltonian systems. The quantum evolution of bound systems does not possess the sensitive dependence on initial conditions, and thus no chaotic behaviour occurs, whereas the study of the stationary solutions of the Schrödinger equation in the quantum phase space (Wigner functions) reveals precise analogy of the structure of the classical phase portrait. We analyze the regular eigenstates associated with invariant tori in the classical phase space, and the chaotic eigenstates associated with the classically chaotic regions, and the corresponding energy spectra. The effects of quantum localization of the chaotic eigenstates are treated phenomenologically, resulting in Brody-like level statistics, which can be found also at very high-lying levels, while the coupling between the regular and the irregular eigenstates due to tunneling, and of the corresponding levels, manifests itself only in low-lying levels.
Compressive Sensing with Optical Chaos
Rontani, D.; Choi, D.; Chang, C.-Y.; Locquet, A.; Citrin, D. S.
2016-01-01
Compressive sensing (CS) is a technique to sample a sparse signal below the Nyquist-Shannon limit, yet still enabling its reconstruction. As such, CS permits an extremely parsimonious way to store and transmit large and important classes of signals and images that would be far more data intensive should they be sampled following the prescription of the Nyquist-Shannon theorem. CS has found applications as diverse as seismology and biomedical imaging. In this work, we use actual optical signals generated from temporal intensity chaos from external-cavity semiconductor lasers (ECSL) to construct the sensing matrix that is employed to compress a sparse signal. The chaotic time series produced having their relevant dynamics on the 100 ps timescale, our results open the way to ultrahigh-speed compression of sparse signals. PMID:27910863
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).
Chaos in blood pressure control.
Wagner, C D; Nafz, B; Persson, P B
1996-03-01
A number of control mechanisms are comprised within blood pressure regulation, ranging from events on the cellular level up to circulating hormones. Despite their vast number, blood pressure fluctuations occur preferably within a certain range (under physiological conditions). A specific class of dynamic systems has been extensively studied over the past several years: nonlinear coupled systems, which often reveal a characteristic form of motion termed "chaos". The system is restricted to a certain range in phase space, but the motion is never periodic. The attractor the system moves on has a non-integer dimension. What all chaotic systems have in common is their sensitive dependence on initial conditions. The question arises as to whether blood pressure regulation can be explained by such models. Many efforts have been made to characterise heart rate variability and EEG dynamics by parameters of chaos theory (e.g., fractal dimensions and Lyapunov exponents). These method were successfully applied to dynamics observed in single organs, but very few studies have dealt with blood pressure dynamics. This mini-review first gives an overview on the history of blood pressure dynamics and the methods suitable to characterise the dynamics by means of tools derived from the field of nonlinear dynamics. Then applications to systemic blood pressure are discussed. After a short survey on heart rate variability, which is indirectly reflected in blood pressure variability, some dynamic aspects of resistance vessels are given. Intriguingly, systemic blood pressure reveals a change in fractal dimensions and Lyapunov exponents, when the major short-term control mechanism--the arterial baroreflex--is disrupted. Indeed it seems that cardiovascular time series can be described by tools from nonlinear dynamics [66]. These methods allow a novel description of some important aspects of biological systems. Both the linear and the nonlinear tools complement each other and can be useful in
Electromagnetic field enhancement and light localization in deterministic aperiodic nanostructures
NASA Astrophysics Data System (ADS)
Gopinath, Ashwin
The control of light matter interaction in periodic and random media has been investigated in depth during the last few decades, yet structures with controlled degree of disorder such as Deterministic Aperiodic Nano Structures (DANS) have been relatively unexplored. DANS are characterized by non-periodic yet long-range correlated (deterministic) morphologies and can be generated by the mathematical rules of symbolic dynamics and number theory. In this thesis, I have experimentally investigated the unique light transport and localization properties in planar dielectric and metal (plasmonics) DANS. In particular, I have focused on the design, nanofabrication and optical characterization of DANS, formed by arranging metal/dielectric nanoparticles in an aperiodic lattice. This effort is directed towards development of on-chip nanophotonic applications with emphasis on label-free bio-sensing and enhanced light emission. The DANS designed as Surface Enhanced Raman Scattering (SERS) substrate is composed of multi-scale aperiodic nanoparticle arrays fabricated by e-beam lithography and are capable of reproducibly demonstrating enhancement factors as high as ˜107. Further improvement of SERS efficiency is achieved by combining DANS formed by top-down approach with bottom-up reduction of gold nanoparticles, to fabricate novel nanostructures called plasmonic "nano-galaxies" which increases the SERS enhancement factors by 2--3 orders of magnitude while preserving the reproducibility. In this thesis, along with presenting details of fabrication and SERS characterization of these "rationally designed" SERS substrates, I will also present results on using these substrates for detection of DNA nucleobases, as well as reproducible label-free detection of pathogenic bacteria with species specificity. In addition to biochemical detection, the combination of broadband light scattering behavior and the ability for the generation of reproducible high fields in DANS make these
Terminal chaos for information processing in neurodynamics.
Zak, M
1991-01-01
New nonlinear phenomenon-terminal chaos caused by failure of the Lipschitz condition at equilibrium points of dynamical systems is introduced. It is shown that terminal chaos has a well organized probabilistic structure which can be predicted and controlled. This gives an opportunity to exploit this phenomenon for information processing. It appears that chaotic states of neurons activity are associated with higher level of cognitive processes such as generalization and abstraction.
Effect of Chaos on Relativistic Quantum Tunneling
2012-06-01
Effect of chaos on relativistic quantum tunneling This article has been downloaded from IOPscience. Please scroll down to see the full text article...of chaos on relativistic quantum tunneling 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e...tunneling dynamics even in the relativistic quantum regime. Similar phenomena have been observed in graphene. A physical theory is developed to
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.
Inertia and scaling in deterministic lateral displacement.
Bowman, Timothy J; Drazer, German; Frechette, Joelle
2013-01-01
The ability to separate and analyze chemical species with high resolution, sensitivity, and throughput is central to the development of microfluidics systems. Deterministic lateral displacement (DLD) is a continuous separation method based on the transport of species through an array of obstacles. In the case of force-driven DLD (f-DLD), size-based separation can be modelled effectively using a simple particle-obstacle collision model. We use a macroscopic model to study f-DLD and demonstrate, via a simple scaling, that the method is indeed predominantly a size-based phenomenon at low Reynolds numbers. More importantly, we demonstrate that inertia effects provide the additional capability to separate same size particles but of different densities and could enhance separation at high throughput conditions. We also show that a direct conversion of macroscopic results to microfluidic settings is possible with a simple scaling based on the size of the obstacles that results in a universal curve.
Deterministic phase slips in mesoscopic superconducting rings
NASA Astrophysics Data System (ADS)
Petković, I.; Lollo, A.; Glazman, L. I.; Harris, J. G. E.
2016-11-01
The properties of one-dimensional superconductors are strongly influenced by topological fluctuations of the order parameter, known as phase slips, which cause the decay of persistent current in superconducting rings and the appearance of resistance in superconducting wires. Despite extensive work, quantitative studies of phase slips have been limited by uncertainty regarding the order parameter's free-energy landscape. Here we show detailed agreement between measurements of the persistent current in isolated flux-biased rings and Ginzburg-Landau theory over a wide range of temperature, magnetic field and ring size; this agreement provides a quantitative picture of the free-energy landscape. We also demonstrate that phase slips occur deterministically as the barrier separating two competing order parameter configurations vanishes. These results will enable studies of quantum and thermal phase slips in a well-characterized system and will provide access to outstanding questions regarding the nature of one-dimensional superconductivity.
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.
Deterministic remote preparation via the Brown state
NASA Astrophysics Data System (ADS)
Ma, Song-Ya; Gao, Cong; Zhang, Pei; Qu, Zhi-Guo
2017-04-01
We propose two deterministic remote state preparation (DRSP) schemes by using the Brown state as the entangled channel. Firstly, the remote preparation of an arbitrary two-qubit state is considered. It is worth mentioning that the construction of measurement bases plays a key role in our scheme. Then, the remote preparation of an arbitrary three-qubit state is investigated. The proposed schemes can be extended to controlled remote state preparation (CRSP) with unit success probabilities. At variance with the existing CRSP schemes via the Brown state, the derived schemes have no restriction on the coefficients, while the success probabilities can reach 100%. It means the success probabilities are greatly improved. Moreover, we pay attention to the DRSP in noisy environments under two important decoherence models, the amplitude-damping noise and phase-damping noise.
Block variables for deterministic aperiodic sequences
NASA Astrophysics Data System (ADS)
Hörnquist, Michael
1997-10-01
We use the concept of block variables to obtain a measure of order/disorder for some one-dimensional deterministic aperiodic sequences. For the Thue - Morse sequence, the Rudin - Shapiro sequence and the period-doubling sequence it is possible to obtain analytical expressions in the limit of infinite sequences. For the Fibonacci sequence, we present some analytical results which can be supported by numerical arguments. It turns out that the block variables show a wide range of different behaviour, some of them indicating that some of the considered sequences are more `random' than other. However, the method does not give any definite answer to the question of which sequence is more disordered than the other and, in this sense, the results obtained are negative. We compare this with some other ways of measuring the amount of order/disorder in such systems, and there seems to be no direct correspondence between the measures.
Deterministic approaches to coherent diffractive imaging
NASA Astrophysics Data System (ADS)
Allen, L. J.; D'Alfonso, A. J.; Martin, A. V.; Morgan, A. J.; Quiney, H. M.
2016-01-01
In this review we will consider the retrieval of the wave at the exit surface of an object illuminated by a coherent probe from one or more measured diffraction patterns. These patterns may be taken in the near-field (often referred to as images) or in the far field (the Fraunhofer diffraction pattern, where the wave is the Fourier transform of that at the exit surface). The retrieval of the exit surface wave from such data is an inverse scattering problem. This inverse problem has historically been solved using nonlinear iterative methods, which suffer from convergence and uniqueness issues. Here we review deterministic approaches to obtaining the exit surface wave which ameliorate those problems.
Deterministic phase slips in mesoscopic superconducting rings
Petković, I.; Lollo, A.; Glazman, L. I.; Harris, J. G. E.
2016-01-01
The properties of one-dimensional superconductors are strongly influenced by topological fluctuations of the order parameter, known as phase slips, which cause the decay of persistent current in superconducting rings and the appearance of resistance in superconducting wires. Despite extensive work, quantitative studies of phase slips have been limited by uncertainty regarding the order parameter's free-energy landscape. Here we show detailed agreement between measurements of the persistent current in isolated flux-biased rings and Ginzburg–Landau theory over a wide range of temperature, magnetic field and ring size; this agreement provides a quantitative picture of the free-energy landscape. We also demonstrate that phase slips occur deterministically as the barrier separating two competing order parameter configurations vanishes. These results will enable studies of quantum and thermal phase slips in a well-characterized system and will provide access to outstanding questions regarding the nature of one-dimensional superconductivity. PMID:27882924
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
Chaos in World Politics: A Reflection
NASA Astrophysics Data System (ADS)
Ferreira, Manuel Alberto Martins; Filipe, José António Candeias Bonito; Coelho, Manuel F. P.; Pedro, Isabel C.
Chaos theory results from natural scientists' findings in the area of non-linear dynamics. The importance of related models has increased in the last decades, by studying the temporal evolution of non-linear systems. In consequence, chaos is one of the concepts that most rapidly have been expanded in what research topics respects. Considering that relationships in non-linear systems are unstable, chaos theory aims to understand and to explain this kind of unpredictable aspects of nature, social life, the uncertainties, the nonlinearities, the disorders and confusion, scientifically it represents a disarray connection, but basically it involves much more than that. The existing close relationship between change and time seems essential to understand what happens in the basics of chaos theory. In fact, this theory got a crucial role in the explanation of many phenomena. The relevance of this kind of theories has been well recognized to explain social phenomena and has permitted new advances in the study of social systems. Chaos theory has also been applied, particularly in the context of politics, in this area. The goal of this chapter is to make a reflection on chaos theory - and dynamical systems such as the theories of complexity - in terms of the interpretation of political issues, considering some kind of events in the political context and also considering the macro-strategic ideas of states positioning in the international stage.
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.
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
Chang, T; Schiff, S J; Sauer, T; Gossard, J P; Burke, R E
1994-08-01
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.
NASA Astrophysics Data System (ADS)
He, Chong; Chiam, Keng-Hwee; Chew, Lock Yue
2016-10-01
Ultradian cycles are frequently observed in biological systems. They serve important roles in regulating, for example, cell fate and the development of the organism. Many mathematical models have been developed to analyze their behavior. Generally, these models can be classified into two classes: Deterministic models that generate oscillatory behavior by incorporating time delays or Hopf bifurcations, and stochastic models that generate oscillatory behavior by noise driven resonance. However, it is still unclear which of these two mechanisms applies to cellular oscillations. In this paper, we show through theoretical analysis and numerical simulation that we can distinguish which of these two mechanisms govern cellular oscillations, by measuring statistics of oscillation amplitudes for cells of different sizes. We found that, for oscillations driven deterministically, the normalized average amplitude is constant with respect to cell size, while the coefficient of variation of the amplitude scales with cell size with an exponent of -0.5 . On the other hand, for oscillations driven stochastically, the coefficient of variation of the amplitude is constant with respect to cell size, while the normalized average amplitude scales with cell size with an exponent of -0.5 . Our results provide a theoretical basis to discern whether a particular oscillatory behavior is governed by a deterministic or stochastic mechanism.
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.
Non-Deterministic Context and Aspect Choice in Russian.
ERIC Educational Resources Information Center
Koubourlis, Demetrius J.
In any given context, a Russian verb form may be either perfective or imperfective. Perfective aspect signals the completion or result of an action, whereas imperfective does not. Aspect choice is a function of context, and two types of context are distinguished: deterministic and non-deterministic. This paper is part of a larger study whose aim…
Use of deterministic models in sports and exercise biomechanics research.
Chow, John W; Knudson, Duane V
2011-09-01
A deterministic model is a modeling paradigm that determines the relationships between a movement outcome measure and the biomechanical factors that produce such a measure. This review provides an overview of the use of deterministic models in biomechanics research, a historical summary of this research, and an analysis of the advantages and disadvantages of using deterministic models. The deterministic model approach has been utilized in technique analysis over the last three decades, especially in swimming, athletics field events, and gymnastics. In addition to their applications in sports and exercise biomechanics, deterministic models have been applied successfully in research on selected motor skills. The advantage of the deterministic model approach is that it helps to avoid selecting performance or injury variables arbitrarily and to provide the necessary theoretical basis for examining the relative importance of various factors that influence the outcome of a movement task. Several disadvantages of deterministic models, such as the use of subjective measures for the performance outcome, were discussed. It is recommended that exercise and sports biomechanics scholars should consider using deterministic models to help identify meaningful dependent variables in their studies.
An improved surrogate method for detecting the presence of chaos in gait.
Miller, David J; Stergiou, Nicholas; Kurz, Max J
2006-01-01
It has been suggested that the intercycle variability present in the time series of biomechanical gait data is of chaotic nature. However, the proper methodology for the correct determination of whether intercycle fluctuations in the data are deterministic chaos or random noise has not been identified. Our goal was to evaluate the pseudoperiodic surrogation (PPS) [Small et al., 2001. Surrogate test for pseudoperiodic time series data. Physical Review Letters 87(18), 188,101-188,104], and the surrogation algorithms of Theiler et al. [1992. Testing for nonlinearity in time series: the method of surrogate data. Physica D 58(1-4), 77-94] and of Theiler and Rapp [1996. Re-examination of the evidence for low-dimensional, nonlinear structure in the human electroencephalogram. Electroencephalography and Clinical Neurophysiology 98, 213-222], to determine which is the more robust procedure for the verification of the presence of chaos in gait time series. The knee angle kinematic time series from six healthy subjects, generated from a 2-min walk, were processed with both algorithms. The Lyapunov exponent (LyE) and the approximate entropy (ApEn) were calculated from the original data and both surrogates. Paired t-tests that compared the LyE and the ApEn values revealed significant differences between both surrogated time series and the original data, indicating the presence of deterministic chaos in the original data. However, the Theiler algorithm affected the intracycle dynamics of the gait time series by changing their overall shape. This resulted in significantly higher LyE and ApEn values for the Theiler-surrogated data when compared with both the original and the PPS-generated data. Thus, the discovery of significant differences was a false positive because it was not based on differences in the intercycle dynamics but rather on the fact that the time series was of a completely different shape. The PPS algorithm, on the other hand, preserved the intracycle dynamics of
Optimal Deterministic Ring Exploration with Oblivious Asynchronous Robots
NASA Astrophysics Data System (ADS)
Lamani, Anissa; Potop-Butucaru, Maria Gradinariu; Tixeuil, Sébastien
We consider the problem of exploring an anonymous unoriented ring of size n by k identical, oblivious, asynchronous mobile robots, that are unable to communicate, yet have the ability to sense their environment and take decisions based on their local view. Previous works in this weak scenario prove that k must not divide n for a deterministic solution to exist. Also, it is known that the minimum number of robots (either deterministic or probabilistic) to explore a ring of size n is 4. An upper bound of 17 robots holds in the deterministic case while 4 probabilistic robots are sufficient. In this paper, we close the complexity gap in the deterministic setting, by proving that no deterministic exploration is feasible with less than five robots, and that five robots are sufficient for any n that is coprime with five. Our protocol completes exploration in O(n) robot moves, which is also optimal.
Mathematical modeling in metal metabolism: overview and perspectives.
Curis, Emmanuel; Nicolis, Ioannis; Bensaci, Jalil; Deschamps, Patrick; Bénazeth, Simone
2009-10-01
A review of mathematical modeling in metal metabolism is presented. Both endogenous and exogenous metals are considered. Four classes of methods are considered: Petri nets, multi-agent systems, determinist models based on differential equations and stochastic models. For each, a basic theoretical background is given, then examples of applications are given, detailed and commented. Advantages and disadvantages of each class of model are presented. A special attention is given to determinist differential equation models, since almost all models belong to this class.
Fractal geometry and chaos theory: Their application in the Earth sciences
Barton, C.C. )
1990-11-01
Fractal geometry and chaos theory are major advances over previous methods for quantifying complex pattern encountered in nature. They provide methods for quantifying complex patterns encountered in nature. They provide methods for creating highly complex, detailed, and accurate synthetic analogs of natural systems. They redefine the way we think mathematically about the behavior of natural systems, much as the theory of relatively brought a deeper level of understanding to physics. Like other branches of mathematics, they do not necessarily provide a physical or mechanistic understanding. However, in natural systems, fractal behavior often breaks down or changes to a different fractal dimension at scales where the physical changes. Systems and processes that exhibit fractal scaling, such as earthquakes, have been shown to be self-organized critical phenomena, which means that they internally establish their own dynamically stable critical points and transfer energy on cascading fractal structures. A challenge for the future will be to develop methods to go from a fractal pattern in nature to its governing nonlinear iterated equation. The use of fractal geometry and chaos theory in the earth sciences has increased greatly in the past five years. Fractal geometry and chaos theory are redefining the way that they conceptualize, measure, and model natural systems in the earth sciences.
Genome chaos: survival strategy during crisis.
Liu, Guo; Stevens, Joshua B; Horne, Steven D; Abdallah, Batoul Y; Ye, Karen J; Bremer, Steven W; Ye, Christine J; Chen, David J; Heng, Henry H
2014-01-01
Genome chaos, a process of complex, rapid genome re-organization, results in the formation of chaotic genomes, which is followed by the potential to establish stable genomes. It was initially detected through cytogenetic analyses, and recently confirmed by whole-genome sequencing efforts which identified multiple subtypes including "chromothripsis", "chromoplexy", "chromoanasynthesis", and "chromoanagenesis". Although genome chaos occurs commonly in tumors, both the mechanism and detailed aspects of the process are unknown due to the inability of observing its evolution over time in clinical samples. Here, an experimental system to monitor the evolutionary process of genome chaos was developed to elucidate its mechanisms. Genome chaos occurs following exposure to chemotherapeutics with different mechanisms, which act collectively as stressors. Characterization of the karyotype and its dynamic changes prior to, during, and after induction of genome chaos demonstrates that chromosome fragmentation (C-Frag) occurs just prior to chaotic genome formation. Chaotic genomes seem to form by random rejoining of chromosomal fragments, in part through non-homologous end joining (NHEJ). Stress induced genome chaos results in increased karyotypic heterogeneity. Such increased evolutionary potential is demonstrated by the identification of increased transcriptome dynamics associated with high levels of karyotypic variance. In contrast to impacting on a limited number of cancer genes, re-organized genomes lead to new system dynamics essential for cancer evolution. Genome chaos acts as a mechanism of rapid, adaptive, genome-based evolution that plays an essential role in promoting rapid macroevolution of new genome-defined systems during crisis, which may explain some unwanted consequences of cancer treatment.
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…
Analysis of pinching in deterministic particle separation
NASA Astrophysics Data System (ADS)
Risbud, Sumedh; Luo, Mingxiang; Frechette, Joelle; Drazer, German
2011-11-01
We investigate the problem of spherical particles vertically settling parallel to Y-axis (under gravity), through a pinching gap created by an obstacle (spherical or cylindrical, center at the origin) and a wall (normal to X axis), to uncover the physics governing microfluidic separation techniques such as deterministic lateral displacement and pinched flow fractionation: (1) theoretically, by linearly superimposing the resistances offered by the wall and the obstacle separately, (2) computationally, using the lattice Boltzmann method for particulate systems and (3) experimentally, by conducting macroscopic experiments. Both, theory and simulations, show that for a given initial separation between the particle centre and the Y-axis, presence of a wall pushes the particles closer to the obstacle, than its absence. Experimentally, this is expected to result in an early onset of the short-range repulsive forces caused by solid-solid contact. We indeed observe such an early onset, which we quantify by measuring the asymmetry in the trajectories of the spherical particles around the obstacle. This work is partially supported by the National Science Foundation Grant Nos. CBET- 0731032, CMMI-0748094, and CBET-0954840.
3D deterministic lateral displacement separation systems
NASA Astrophysics Data System (ADS)
Du, Siqi; Drazer, German
2016-11-01
We present a simple modification to enhance the separation ability of deterministic lateral displacement (DLD) systems by expanding the two-dimensional nature of these devices and driving the particles into size-dependent, fully three-dimensional trajectories. Specifically, we drive the particles through an array of long cylindrical posts, such that they not only move parallel to the basal plane of the posts as in traditional two-dimensional DLD systems (in-plane motion), but also along the axial direction of the solid posts (out-of-plane motion). We show that the (projected) in-plane motion of the particles is completely analogous to that observed in 2D-DLD systems and the observed trajectories can be predicted based on a model developed in the 2D case. More importantly, we analyze the particles out-of-plane motion and observe significant differences in the net displacement depending on particle size. Therefore, taking advantage of both the in-plane and out-of-plane motion of the particles, it is possible to achieve the simultaneous fractionation of a polydisperse suspension into multiple streams. We also discuss other modifications to the obstacle array and driving forces that could enhance separation in microfluidic devices.
Deterministically Driven Avalanche Models of Solar Flares
NASA Astrophysics Data System (ADS)
Strugarek, Antoine; Charbonneau, Paul; Joseph, Richard; Pirot, Dorian
2014-08-01
We develop and discuss the properties of a new class of lattice-based avalanche models of solar flares. These models are readily amenable to a relatively unambiguous physical interpretation in terms of slow twisting of a coronal loop. They share similarities with other avalanche models, such as the classical stick-slip self-organized critical model of earthquakes, in that they are driven globally by a fully deterministic energy-loading process. The model design leads to a systematic deficit of small-scale avalanches. In some portions of model space, mid-size and large avalanching behavior is scale-free, being characterized by event size distributions that have the form of power-laws with index values, which, in some parameter regimes, compare favorably to those inferred from solar EUV and X-ray flare data. For models using conservative or near-conservative redistribution rules, a population of large, quasiperiodic avalanches can also appear. Although without direct counterparts in the observational global statistics of flare energy release, this latter behavior may be relevant to recurrent flaring in individual coronal loops. This class of models could provide a basis for the prediction of large solar flares.
Deterministic transfer function for transionospheric propagation
NASA Astrophysics Data System (ADS)
Roussel-Dupre, R.; Argo, P.
Recent interest in ground-to-satellite propagation of broadband signals has prompted investigation into the development of a transfer function for the ionosphere that includes effects such as dispersion, refraction, changes in polarization, reflection, absorption, and scattering. Depending on the application (e.g. geolocation), it may be necessary to incorporate all of these processes in order to extract the information of interest from the measured transionospheric signal. A transfer function for midlatitudes at VBF from 25 - 175 MHz is one of the goals of the BLACKBEARD program in characterizing propagation distortion. In support of this program we discuss in this paper an analytic model for the deterministic transfer function of the ionosphere that includes the effects of dispersion, refraction, and changes in polarization to second order in the parameter X = omega(sub pe)(exp 2)/(omega)(exp 2) where X is assumed to be small compared to one, (omega)(sub pe) is the peak plasma frequency of the ionosphere, and omega is the wave frequency. Analytic expressions for the total phase change, group delay, and polarization change in a spherical geometry assuming a radial, electron density profile are presented. A computer code ITF (Ionospheric Transfer Function) that makes use of the ICED (Ionospheric Conductivity and Electron Density) model to, venerate electron density profiles was developed to calculate the ionospheric transfer function along a specified transmitter-to-receiver path. Details of this code will be presented as well as comparisons made between ITF analytic results and ray-tracing calculations.
Regularly timed events amid chaos
NASA Astrophysics Data System (ADS)
Blakely, Jonathan N.; Cooper, Roy M.; Corron, Ned J.
2015-11-01
We show rigorously that the solutions of a class of chaotic oscillators are characterized by regularly timed events in which the derivative of the solution is instantaneously zero. The perfect regularity of these events is in stark contrast with the well-known unpredictability of chaos. We explore some consequences of these regularly timed events through experiments using chaotic electronic circuits. First, we show that a feedback loop can be implemented to phase lock the regularly timed events to a periodic external signal. In this arrangement the external signal regulates the timing of the chaotic signal but does not strictly lock its phase. That is, phase slips of the chaotic oscillation persist without disturbing timing of the regular events. Second, we couple the regularly timed events of one chaotic oscillator to those of another. A state of synchronization is observed where the oscillators exhibit synchronized regular events while their chaotic amplitudes and phases evolve independently. Finally, we add additional coupling to synchronize the amplitudes, as well, however in the opposite direction illustrating the independence of the amplitudes from the regularly timed events.
Irreversible evolution of quantum chaos
NASA Astrophysics Data System (ADS)
Ugulava, A.; Chotorlishvili, L.; Nickoladze, K.
2005-05-01
The pendulum is the simplest system having all the basic properties inherent in dynamic stochastic systems. In the present paper we investigate the pendulum with the aim to reveal the properties of a quantum analogue of dynamic stochasticity or, in other words, to obtain the basic properties of quantum chaos. It is shown that a periodic perturbation of the quantum pendulum (similarly to the classical one) in the neighborhood of the separatrix can bring about irreversible phenomena. As a result of recurrent passages between degenerate states, the system gets self-chaotized and passes from the pure state to the mixed one. Chaotization involves the states, the branch points of whose levels participate in a slow “drift” of the system along the Mathieu characteristics this “drift” being caused by a slowly changing variable field. Recurrent relations are obtained for populations of levels participating in the irreversible evolution process. It is shown that the entropy of the system first grows and, after reaching the equilibrium state, acquires a constant value.
Elucidating Mechanisms of Extensive Chaos
NASA Astrophysics Data System (ADS)
Egolf, David A.; Melnikov, Ilarion V.; Pesch, Werner; Ecke, Robert E.
2001-06-01
We report studies of the mechanism for the generation of chaotic disorder in a phenomenon found in nature, Rayleigh-Bénard convection (RBC), in a regime exhaustively studied experimentally. Through large-scale, parallel-computational studies of the detailed space-time evolution of the dynamical degrees of freedom, we find that the Spiral Defect Chaos (SDC) state of RBC is spatially- and temporally- localized to defect creation/annihilation events (D.A. Egolf, I.V. Melnikov, W. Pesch, and R.E. Ecke, Nature, 404:733--736, 2000), and we elucidate how these divergent, but very brief, events lead to eventual macroscopic differences between initially similar flow patterns. We also demonstrate that SDC is extensively chaotic, in that the number of dynamical degrees of freedom (the fractal dimension) is proportional to the system size, suggesting the possibility for a hydrodynamic-like description of the long-wavelength properties of SDC. The computational technique employed shows promise for analyzing a wide variety of extended dynamical systems.
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.
Control design and robustness analysis of a ball and plate system by using polynomial chaos
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.
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.
Generic superweak chaos induced by Hall effect.
Ben-Harush, Moti; Dana, Itzhack
2016-05-01
We introduce and study the "kicked Hall system" (KHS), i.e., charged particles periodically kicked in the presence of uniform magnetic (B) and electric (E) fields that are perpendicular to each other and to the kicking direction. We show that for resonant values of B and E and in the weak-chaos regime of sufficiently small nonintegrability parameter κ (the kicking strength), there exists a generic family of periodic kicking potentials for which the Hall effect from B and E significantly suppresses the weak chaos, replacing it by "superweak" chaos (SWC). This means that the system behaves as if the kicking strength were κ^{2} rather than κ. For E=0, SWC is known to be a classical fingerprint of quantum antiresonance, but it occurs under much less generic conditions, in particular only for very special kicking potentials. Manifestations of SWC are a decrease in the instability of periodic orbits and a narrowing of the chaotic layers, relative to the ordinary weak-chaos case. Also, for global SWC, taking place on an infinite "stochastic web" in phase space, the chaotic diffusion on the web is much slower than the weak-chaos one. Thus, the Hall effect can be relatively stabilizing for small κ. In some special cases, the effect is shown to cause ballistic motion for almost all parameter values. The generic global SWC on stochastic webs in the KHS appears to be the two-dimensional closest analog to the Arnol'd web in higher dimensional systems.
The Capabilities of Chaos and Complexity
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
Stochastic and Deterministic Assembly Processes in Subsurface Microbial Communities
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.
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…
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:…
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…
Ikeda-like chaos on a dynamically filtered supercontinuum light source
NASA Astrophysics Data System (ADS)
Chembo, Yanne K.; Jacquot, Maxime; Dudley, John M.; Larger, Laurent
2016-08-01
We demonstrate temporal chaos in a color-selection mechanism from the visible spectrum of a supercontinuum light source. The color-selection mechanism is governed by an acousto-optoelectronic nonlinear delayed-feedback scheme modeled by an Ikeda-like equation. Initially motivated by the design of a broad audience live demonstrator in the framework of the International Year of Light 2015, the setup also provides a different experimental tool to investigate the dynamical complexity of delayed-feedback dynamics. Deterministic hyperchaos is analyzed here from the experimental time series. A projection method identifies the delay parameter, for which the chaotic strange attractor originally evolving in an infinite-dimensional phase space can be revealed in a two-dimensional subspace.
Chaos and Correlated Avalanches in Excitatory Neural Networks with Synaptic Plasticity
NASA Astrophysics Data System (ADS)
Pittorino, Fabrizio; Ibáñez-Berganza, Miguel; di Volo, Matteo; Vezzani, Alessandro; Burioni, Raffaella
2017-03-01
A collective chaotic phase with power law scaling of activity events is observed in a disordered mean field network of purely excitatory leaky integrate-and-fire neurons with short-term synaptic plasticity. The dynamical phase diagram exhibits two transitions from quasisynchronous and asynchronous regimes to the nontrivial, collective, bursty regime with avalanches. In the homogeneous case without disorder, the system synchronizes and the bursty behavior is reflected into a period doubling transition to chaos for a two dimensional discrete map. Numerical simulations show that the bursty chaotic phase with avalanches exhibits a spontaneous emergence of persistent time correlations and enhanced Kolmogorov complexity. Our analysis reveals a mechanism for the generation of irregular avalanches that emerges from the combination of disorder and deterministic underlying chaotic dynamics.
Chaos and Correlated Avalanches in Excitatory Neural Networks with Synaptic Plasticity.
Pittorino, Fabrizio; Ibáñez-Berganza, Miguel; di Volo, Matteo; Vezzani, Alessandro; Burioni, Raffaella
2017-03-03
A collective chaotic phase with power law scaling of activity events is observed in a disordered mean field network of purely excitatory leaky integrate-and-fire neurons with short-term synaptic plasticity. The dynamical phase diagram exhibits two transitions from quasisynchronous and asynchronous regimes to the nontrivial, collective, bursty regime with avalanches. In the homogeneous case without disorder, the system synchronizes and the bursty behavior is reflected into a period doubling transition to chaos for a two dimensional discrete map. Numerical simulations show that the bursty chaotic phase with avalanches exhibits a spontaneous emergence of persistent time correlations and enhanced Kolmogorov complexity. Our analysis reveals a mechanism for the generation of irregular avalanches that emerges from the combination of disorder and deterministic underlying chaotic dynamics.
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.
Classical Chaos in Mesoscale Ocean Dynamics: Lateral Stirring and Geometric Acoustics.
NASA Astrophysics Data System (ADS)
Smith, Kevin Barkley
Chaos is unpredictable behavior in a deterministic low-order dynamical system. Two dynamical systems which arise naturally in ocean physics are examined here, midocean fluid motion and underwater acoustic ray propagation. Both have Hamiltonian form with one degree of freedom. Chaotic solutions appear, in general, when the Hamiltonian is explicitly time-dependent and the canonical equations of motion are nonintegrable. When the Hamiltonian is not explicitly time-dependent, the equations of motion are integrable, and trajectories are regular and predictable for all times. Neighboring trajectories are found to diverge rapidly (exponentially, on average) or slowly (according to a power law, on average) when the motion is chaotic or regular, respectively. Midocean fluid particle trajectories are assumed to obey Lagrangian equations of motion with Hamiltonian form. The presence of chaos is observed to stir passive tracers efficiently, enhancing diffusive processes. To determine if observed behavior in the midocean is chaotic, power spectra of SOFAR float trajectory data are computed and found to contain structure on all resolvable scales. Attempts to directly estimate Lyapunov exponents, a measure of the exponential divergence, from a reconstructed streamfunction are unsuccessful. The Kolmogorov entropy (here equivalent to the Lyapunov exponent) is estimated to be ~ (140 day)^{-1}. These results suggest the presence of chaos. Furthermore, analysis of SOFAR float trajectories suggests, albeit ambiguously, that the underlying dynamics are those of a low-order system. The fractal dimension of the trajectories is estimated to be ~1.2. A possible rationale for this value, and the associated implications for anomalous diffusion, are addressed. Underwater acoustic rays obey equations of Hamiltonian form where range plays the role of the time-like variable. The appearance of chaos implies a limited ability to predict eigenrays at long range. Power spectra calculations and
Nanotransfer and nanoreplication using deterministically grown sacrificial nanotemplates
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.
Surface plasmon field enhancements in deterministic aperiodic structures.
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.
Harnessing quantum transport by transient chaos.
Yang, Rui; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso; Pecora, Louis M
2013-03-01
Chaos has long been recognized to be generally advantageous from the perspective of control. In particular, the infinite number of unstable periodic orbits embedded in a chaotic set and the intrinsically sensitive dependence on initial conditions imply that a chaotic system can be controlled to a desirable state by using small perturbations. Investigation of chaos control, however, was largely limited to nonlinear dynamical systems in the classical realm. In this paper, we show that chaos may be used to modulate or harness quantum mechanical systems. To be concrete, we focus on quantum transport through nanostructures, a problem of considerable interest in nanoscience, where a key feature is conductance fluctuations. We articulate and demonstrate that chaos, more specifically transient chaos, can be effective in modulating the conductance-fluctuation patterns. Experimentally, this can be achieved by applying an external gate voltage in a device of suitable geometry to generate classically inaccessible potential barriers. Adjusting the gate voltage allows the characteristics of the dynamical invariant set responsible for transient chaos to be varied in a desirable manner which, in turn, can induce continuous changes in the statistical characteristics of the quantum conductance-fluctuation pattern. To understand the physical mechanism of our scheme, we develop a theory based on analyzing the spectrum of the generalized non-Hermitian Hamiltonian that includes the effect of leads, or electronic waveguides, as self-energy terms. As the escape rate of the underlying non-attracting chaotic set is increased, the imaginary part of the complex eigenenergy becomes increasingly large so that pointer states are more difficult to form, making smoother the conductance-fluctuation pattern.
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.
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.
Understanding Vertical Jump Potentiation: A Deterministic Model.
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.
ZERODUR: deterministic approach for strength design
NASA Astrophysics Data System (ADS)
Hartmann, Peter
2012-12-01
There is an increasing request for zero expansion glass ceramic ZERODUR substrates being capable of enduring higher operational static loads or accelerations. The integrity of structures such as optical or mechanical elements for satellites surviving rocket launches, filigree lightweight mirrors, wobbling mirrors, and reticle and wafer stages in microlithography must be guaranteed with low failure probability. Their design requires statistically relevant strength data. The traditional approach using the statistical two-parameter Weibull distribution suffered from two problems. The data sets were too small to obtain distribution parameters with sufficient accuracy and also too small to decide on the validity of the model. This holds especially for the low failure probability levels that are required for reliable applications. Extrapolation to 0.1% failure probability and below led to design strengths so low that higher load applications seemed to be not feasible. New data have been collected with numbers per set large enough to enable tests on the applicability of the three-parameter Weibull distribution. This distribution revealed to provide much better fitting of the data. Moreover it delivers a lower threshold value, which means a minimum value for breakage stress, allowing of removing statistical uncertainty by introducing a deterministic method to calculate design strength. Considerations taken from the theory of fracture mechanics as have been proven to be reliable with proof test qualifications of delicate structures made from brittle materials enable including fatigue due to stress corrosion in a straight forward way. With the formulae derived, either lifetime can be calculated from given stress or allowable stress from minimum required lifetime. The data, distributions, and design strength calculations for several practically relevant surface conditions of ZERODUR are given. The values obtained are significantly higher than those resulting from the two
Deterministic transfer function for transionospheric propagation
Roussel-Dupre, R.; Argo, P.
1992-01-01
Recent interest in ground-to-satellite propagation of broadband signals has prompted investigation into the development of a transfer function for the ionosphere that includes effects such as dispersion, refraction, changes in polarization, reflection, absorption, and scattering. Depending on the application (e.g. geolocation), it may be necessary to incorporate all of these processes in order to extract the information of interest from the measured transionospheric signal. A transfer function for midlatitudes at VBF from 25--175 MHz is one of the goals of the BLACKBEARD program in characterizing propagation distortion. In support of this program we discuss in this paper an analytic model for the deterministic transfer function of the ionosphere that includes the effects of dispersion, refraction, and changes in polarization to second order in the parameter X = {omega}{sub pe}{sup 2}/{omega}{sup 2} where X is assumed to be small compared to one, {omega}{sub pe} is the peak plasma frequency of the ionosphere, and {omega} is the wave frequency. Analytic expressions for the total phase change, group delay, and polarization change in a spherical geometry assuming a radial, electron density profile are presented. A computer code ITF (Ionospheric Transfer Function) that makes use of the ICED (Ionospheric Conductivity and Electron Density) model to ,venerate electron density profiles was developed to calculate the ionospheric transfer function along a specified transmitter-to-receiver path. Details of this code will be presented as well as comparisons made between ITF analytic results and ray-tracing calculations.
Deterministic transfer function for transionospheric propagation
Roussel-Dupre, R.; Argo, P.
1992-09-01
Recent interest in ground-to-satellite propagation of broadband signals has prompted investigation into the development of a transfer function for the ionosphere that includes effects such as dispersion, refraction, changes in polarization, reflection, absorption, and scattering. Depending on the application (e.g. geolocation), it may be necessary to incorporate all of these processes in order to extract the information of interest from the measured transionospheric signal. A transfer function for midlatitudes at VBF from 25--175 MHz is one of the goals of the BLACKBEARD program in characterizing propagation distortion. In support of this program we discuss in this paper an analytic model for the deterministic transfer function of the ionosphere that includes the effects of dispersion, refraction, and changes in polarization to second order in the parameter X = {omega}{sub pe}{sup 2}/{omega}{sup 2} where X is assumed to be small compared to one, {omega}{sub pe} is the peak plasma frequency of the ionosphere, and {omega} is the wave frequency. Analytic expressions for the total phase change, group delay, and polarization change in a spherical geometry assuming a radial, electron density profile are presented. A computer code ITF (Ionospheric Transfer Function) that makes use of the ICED (Ionospheric Conductivity and Electron Density) model to ,venerate electron density profiles was developed to calculate the ionospheric transfer function along a specified transmitter-to-receiver path. Details of this code will be presented as well as comparisons made between ITF analytic results and ray-tracing calculations.
Problems with Chaos in String Cosmology
NASA Astrophysics Data System (ADS)
Dąbrowski, Mariusz P.
I review the main ideas of the pre-big-bang cosmology scenario emphasizing the role of different boundary conditions in comparison to the standard ones which appear in quantum cosmology. My main issue is duality symmetry - a very general feature of string theory - and its role in suppressing chaos in Bianchi type IX "Mixmaster" universes within the framework of the tree-level low-energy-effectiveactions for strings. Finally, I discuss the ways to possibly `generate' chaos in string cosmology by admitting dilaton potential/massive string modes, more spacetime dimensions or nonlinear Yang-Mills-Lorentz-Chern-Simons terms into the action.
Quantum chaos and thermalization in gapped systems
Rigol, Marcos; Santos, Lea F.
2010-07-15
We investigate the onset of thermalization and quantum chaos in finite one-dimensional gapped systems of hard-core bosons. Integrability in these systems is broken by next-nearest-neighbor repulsive interactions, which also generate a superfluid to insulator transition. By employing full exact diagonalization, we study chaos indicators and few-body observables. We show that with increasing system size, chaotic behavior is seen over a broader range of parameters and, in particular, deeper into the insulating phase. Concomitantly, we observe that, as the system size increases, the eigenstate thermalization hypothesis extends its range of validity inside the insulating phase and is accompanied by the thermalization of the system.
Experimental realization of chaos control by thresholding.
Murali, K; Sinha, Sudeshna
2003-07-01
We report the experimental verification of thresholding as a versatile tool for efficient and flexible chaos control. The strategy here simply involves monitoring a single state variable and resetting it when it exceeds a threshold. We demonstrate the success of the technique in rapidly controlling different chaotic electrical circuits, including a hyperchaotic circuit, onto stable fixed points and limit cycles of different periods, by thresholding just one variable. The simplicity of this controller entailing no run-time computation, and the ease and rapidity of switching between different targets it offers, suggests a potent tool for chaos based applications.
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.
Quantum chaos on a critical Fermi surface.
Patel, Aavishkar A; Sachdev, Subir
2017-02-21
We compute parameters characterizing many-body quantum chaos for a critical Fermi surface without quasiparticle excitations. We examine a theory of [Formula: see text] species of fermions at nonzero density coupled to a [Formula: see text] gauge field in two spatial dimensions and determine the Lyapunov rate and the butterfly velocity in an extended random-phase approximation. The thermal diffusivity is found to be universally related to these chaos parameters; i.e., the relationship is independent of [Formula: see text], the gauge-coupling constant, the Fermi velocity, the Fermi surface curvature, and high-energy details.
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.
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.
Conservative spatial chaos of buckled elastic linkages.
Kocsis, Attila; Károlyi, György
2006-09-01
Buckling of an elastic linkage under general loading is investigated. We show that buckling is related to an initial value problem, which is always a conservative, area-preserving mapping, even if the original static problem is nonconservative. In some special cases, we construct the global bifurcation diagrams, and argue that their complicated structure is a consequence of spatial chaos. We characterize spatial chaos by the associated initial value problem's topological entropy, which turns out to be related to the number of buckled configurations.
AIDS in India: constructive chaos?
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.
Singh, Brajendra K.; Parham, Paul E.; Hu, Chin-Kun
2011-01-01
Background Simple models of insect populations with non-overlapping generations have been instrumental in understanding the mechanisms behind population cycles, including wild (chaotic) fluctuations. The presence of deterministic chaos in natural populations, however, has never been unequivocally accepted. Recently, it has been proposed that the application of chaos control theory can be useful in unravelling the complexity observed in real population data. This approach is based on structural perturbations to simple population models (population skeletons). The mechanism behind such perturbations to control chaotic dynamics thus far is model dependent and constant (in size and direction) through time. In addition, the outcome of such structurally perturbed models is [almost] always equilibrium type, which fails to commensurate with the patterns observed in population data. Methodology/Principal Findings We present a proportional feedback mechanism that is independent of model formulation and capable of perturbing population skeletons in an evolutionary way, as opposed to requiring constant feedbacks. We observe the same repertoire of patterns, from equilibrium states to non-chaotic aperiodic oscillations to chaotic behaviour, across different population models, in agreement with observations in real population data. Model outputs also indicate the existence of multiple attractors in some parameter regimes and this coexistence is found to depend on initial population densities or the duration of transient dynamics. Our results suggest that such a feedback mechanism may enable a better understanding of the regulatory processes in natural populations. PMID:21980342
NASA Astrophysics Data System (ADS)
Takatsuka, Kazuo
Nonlinear dynamics and chaos are studied in a system for which a complete set of equations of motion such as equations of Newton, Navier-Stokes and Van der Pol, is not available. As a very general system as such, we consider coupled classical spins (pendulums), each of which is under control by a fuzzy system that is designed to align the spin to an unstable fixed point. The fuzzy system provides a deterministic procedure to control an object without use of a differential equation. The positions and velocities of the spins are monitored periodically and each fuzzy control gives a momentum to its associated spin in the reverse directions. If the monitoring is made with an interval short enough, the spin-spin interactions are overwhelmed by the fuzzy control and the system converges to a state as designed. However, a long-interval monitoring induces dynamics of “too-late response”, and thereby results in chaos. A great variety of dynamics are generated under very delicate balance between the fuzzy control and the spin-spin interaction, in which two independent mechanisms of creating negative and positive “Liapunov exponents” interact with each other.
Chaos Control for Chua's Circuits
NASA Astrophysics Data System (ADS)
Tôrres, L. A. B.; Aguirre, L. A.; Palhares, R. M.; Mendes, E. M. A. M.
The practical implementation of Chua's circuit control methods is discussed in this chapter. In order to better address this subject, an inductorless Chua's circuit realization is first presented, followed by practical issues related to data analysis, mathematical modelling, and dynamical characterization associated to this electronic chaotic oscillator. As a consequence of the investigation of different control strategies applied to Chua's circuit, a tradeoff among control objective, control energy, and model complexity is devised, which quite naturally leads to a principle that seems to be of general nature: the Information Transmission Via Control (ITVC) for nonlinear oscillators. The main purpose of the present chapter is to serve as an introductory guide to the universe of Chua's circuit control, synchronization, and mathematical modelling.
Chaos and Complexity in Astrophysics
NASA Astrophysics Data System (ADS)
Regev, Oded
2006-03-01
Part I. Dynamical Systems - General: 1. Introduction to Part I; 2. Astrophysical examples; 3. Mathematical properties of dynamical systems; 4. Properties of chaotic dynamics; 5. Analysis of time series; 6. Regular and irregular motion in Hamiltonian systems; 7. Extended systems - instabilities and patterns; Part II. Astrophysical Applications: 8. Introduction to Part II; 9. Planetary, stellar and galactic dynamics; 10. Irregularly variable astronomical point sources; 11. Complex spatial patterns in astrophysics; 12. Topics in astrophysical fluid dynamics; References; Index.
Deterministic and Advanced Statistical Modeling of Wind-Driven Sea
2015-07-06
COVERED (From - To) 01/09/2010-06/07/2015 4. TITLE AND SUBTITLE Deterministic and advanced statistical modeling of wind-driven sea 5a. CONTRACT...Technical Report Deterministic and advanced statistical modeling of wind-driven sea Vladimir Zakharov, Andrei Pushkarev Waves and Solitons LLC, 1719 W...Development of accurate and fast advanced statistical and dynamical nonlinear models of ocean surface waves, based on first physical principles, which will
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.
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…
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.
The recursive deterministic perceptron neural network.
Tajine, Mohamed; Elizondo, David
1998-12-01
We introduce a feedforward multilayer neural network which is a generalization of the single layer perceptron topology (SLPT), called recursive deterministic perceptron (RDP). This new model is capable of solving any two-class classification problem, as opposed to the single layer perceptron which can only solve classification problems dealing with linearly separable sets (two subsets X and Y of R(d) are said to be linearly separable if there exists a hyperplane such that the elements of X and Y lie on the two opposite sides of R(d) delimited by this hyperplane). We propose several growing methods for constructing a RDP. These growing methods build a RDP by successively adding intermediate neurons (IN) to the topology (an IN corresponds to a SLPT). Thus, as a result, we obtain a multilayer perceptron topology, which together with the weights, are determined automatically by the constructing algorithms. Each IN augments the affine dimension of the set of input vectors. This augmentation is done by adding the output of each of these INs, as a new component, to every input vector. The construction of a new IN is made by selecting a subset from the set of augmented input vectors which is LS from the rest of this set. This process ends with LS classes in almost n-1 steps where n is the number of input vectors. For this construction, if we assume that the selected LS subsets are of maximum cardinality, the problem is proven to be NP-complete. We also introduce a generalization of the RDP model for classification of m classes (m>2) allowing to always separate m classes. This generalization is based on a new notion of linear separability for m classes, and it follows naturally from the RDP. This new model can be used to compute functions with a finite domain, and thus, to approximate continuous functions. We have also compared - over several classification problems - the percentage of test data correctly classified, or the topology of the 2 and m classes RDPs with that of
Single Ion Implantation and Deterministic Doping
Schenkel, Thomas
2010-06-11
The presence of single atoms, e.g. dopant atoms, in sub-100 nm scale electronic devices can affect the device characteristics, such as the threshold voltage of transistors, or the sub-threshold currents. Fluctuations of the number of dopant atoms thus poses a complication for transistor scaling. In a complementary view, new opportunities emerge when novel functionality can be implemented in devices deterministically doped with single atoms. The grand price of the latter might be a large scale quantum computer, where quantum bits (qubits) are encoded e.g. in the spin states of electrons and nuclei of single dopant atoms in silicon, or in color centers in diamond. Both the possible detrimental effects of dopant fluctuations and single atom device ideas motivate the development of reliable single atom doping techniques which are the subject of this chapter. Single atom doping can be approached with top down and bottom up techniques. Top down refers to the placement of dopant atoms into a more or less structured matrix environment, like a transistor in silicon. Bottom up refers to approaches to introduce single dopant atoms during the growth of the host matrix e.g. by directed self-assembly and scanning probe assisted lithography. Bottom up approaches are discussed in Chapter XYZ. Since the late 1960's, ion implantation has been a widely used technique to introduce dopant atoms into silicon and other materials in order to modify their electronic properties. It works particularly well in silicon since the damage to the crystal lattice that is induced by ion implantation can be repaired by thermal annealing. In addition, the introduced dopant atoms can be incorporated with high efficiency into lattice position in the silicon host crystal which makes them electrically active. This is not the case for e.g. diamond, which makes ion implantation doping to engineer the electrical properties of diamond, especially for n-type doping much harder then for silicon. Ion
Chaos Theory and the Effort in Afghanistan
2008-02-29
since the fall of the Soviet Union. A society’s strategic culture is a result of its history, geography , and political culture. A strategic culture...Xnext = RX(1-X). 8 Gleick, 133-135. 9 James, 29. 10 Chaos & Fractals Home Page, Strange Attractors, available from http://www.pha.jhu.edu/ ~ldb
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,…
Chaos Theory in the Arts and Design.
ERIC Educational Resources Information Center
McWhinnie, Harold J.
This paper explores questions associated with chaos theory as it relates to problems in the arts. It reviews the work of several scholars including Minai, Eckersley, Pickover, the Kirsches, and the Molnars. The document directs special attention toward three basic areas in art and design education, which are: (1) the integration of the computer…
Control and synchronization of spatiotemporal chaos.
Ahlborn, Alexander; Parlitz, Ulrich
2008-01-01
Chaos control methods for the Ginzburg-Landau equation are presented using homogeneously, inhomogeneously, and locally applied multiple delayed feedback signals. In particular, it is shown that a small number of control cells is sufficient for stabilizing plane waves or for trapping spiral waves, and that successful control is closely connected to synchronization of the dynamics in regions close to the control cells.
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.
Chaos, Collaboration, and Curriculum: A Deliberative Process.
ERIC Educational Resources Information Center
Goff, Katherine E.
1998-01-01
Presents curriculum as a complex social process. Explores chaos theory as a metaphor for understanding curriculum and a framework for viewing the curriculum-development process. Provides examples of collaborative leadership (described by David Chrislip and Carl Larson) and shows how they might answer Joseph Schwab's call for a deliberative…
Chaos: Connecting Science and the Humanities
ERIC Educational Resources Information Center
Lagan, Seamus; Paddy, David
2005-01-01
We describe a team-taught course entitled Chaos in Science and Literature. Our course goals were to place science in a nontechnological context, emphasizing its intellectual and cultural aspects, and to provide a forum for the exchange of ideas between "scientists" and "humanists," with the authors serving as role models. (Contains 4 figures.)
Order, chaos and nuclear dynamics: An introduction
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.
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.
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.
Classical chaos in atom-field systems.
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.
A robust and efficient stepwise regression method for building sparse polynomial chaos expansions
NASA Astrophysics Data System (ADS)
Abraham, Simon; Raisee, Mehrdad; Ghorbaniasl, Ghader; Contino, Francesco; Lacor, Chris
2017-03-01
Polynomial Chaos (PC) expansions are widely used in various engineering fields for quantifying uncertainties arising from uncertain parameters. The computational cost of classical PC solution schemes is unaffordable as the number of deterministic simulations to be calculated grows dramatically with the number of stochastic dimension. This considerably restricts the practical use of PC at the industrial level. A common approach to address such problems is to make use of sparse PC expansions. This paper presents a non-intrusive regression-based method for building sparse PC expansions. The most important PC contributions are detected sequentially through an automatic search procedure. The variable selection criterion is based on efficient tools relevant to probabilistic method. Two benchmark analytical functions are used to validate the proposed algorithm. The computational efficiency of the method is then illustrated by a more realistic CFD application, consisting of the non-deterministic flow around a transonic airfoil subject to geometrical uncertainties. To assess the performance of the developed methodology, a detailed comparison is made with the well established LAR-based selection technique. The results show that the developed sparse regression technique is able to identify the most significant PC contributions describing the problem. Moreover, the most important stochastic features are captured at a reduced computational cost compared to the LAR method. The results also demonstrate the superior robustness of the method by repeating the analyses using random experimental designs.
Excitability, mixed-mode oscillations and transition to chaos in a stochastic ice ages model
NASA Astrophysics Data System (ADS)
Alexandrov, D. V.; Bashkirtseva, I. A.; Ryashko, L. B.
2017-03-01
Motivated by an important geophysical significance, we consider the influence of stochastic forcing on a simple three-dimensional climate model previously derived by Saltzman and Sutera. A nonlinear dynamical system governing three physical variables, the bulk ocean temperature, continental and marine ice masses, is analyzed in deterministic and stochastic cases. It is shown that the attractor of deterministic model is either a stable equilibrium or a limit cycle. We demonstrate that the process of continental ice melting occurs with a noise-dependent time delay as compared with marine ice melting. The paleoclimate cyclicity which is near 100 ky in a wide range of model parameters abruptly increases in the vicinity of a bifurcation point and depends on the noise intensity. In a zone of stable equilibria, the 3D climate model under consideration is extremely excitable. Even for a weak random noise, the stochastic trajectories demonstrate a transition from small- to large-amplitude stochastic oscillations (SLASO). In a zone of stable cycles, SLASO transitions are analyzed too. We show that such stochastic transitions play an important role in the formation of a mixed-mode paleoclimate scenario. This mixed-mode dynamics with the intermittency of large- and small-amplitude stochastic oscillations and coherence resonance are investigated via analysis of interspike intervals. A tendency of dynamic paleoclimate to abrupt and rapid glaciations and deglaciations as well as its transition from order to chaos with increasing noise are shown.
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
THEORY OF SECULAR CHAOS AND MERCURY'S ORBIT
Lithwick, Yoram; Wu Yanqin
2011-09-20
We study the chaotic orbital evolution of planetary systems, focusing on secular (i.e., orbit-averaged) interactions, which dominate on long timescales. We first focus on the evolution of a test particle that is forced by multiple planets. To linear order in eccentricity and inclination, its orbit precesses with constant frequencies. But nonlinearities modify the frequencies, and can shift them into and out of resonance with either the planets' eigenfrequencies (forming eccentricity or inclination secular resonances), or with linear combinations of those frequencies (forming mixed high-order secular resonances). The overlap of these nonlinear secular resonances drives secular chaos. We calculate the locations and widths of nonlinear secular resonances, display them together on a newly developed map (the 'map of the mean momenta'), and find good agreement between analytical and numerical results. This map also graphically demonstrates how chaos emerges from overlapping secular resonances. We then apply this newfound understanding to Mercury to elucidate the origin of its orbital chaos. We find that since Mercury's two free precession frequencies (in eccentricity and inclination) lie within {approx}25% of two other eigenfrequencies in the solar system (those of the Jupiter-dominated eccentricity mode and the Venus-dominated inclination mode), secular resonances involving these four modes overlap and cause Mercury's chaos. We confirm this with N-body integrations by showing that a slew of these resonant angles alternately librate and circulate. Our new analytical understanding allows us to calculate the criterion for Mercury to become chaotic: Jupiter and Venus must have eccentricity and inclination of a few percent. The timescale for Mercury's chaotic diffusion depends sensitively on the forcing. As it is, Mercury appears to be perched on the threshold for chaos, with an instability timescale comparable to the lifetime of the solar system.
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
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
Chaos control in passive walking dynamics of a compass-gait model
NASA Astrophysics Data System (ADS)
Gritli, Hassène; Khraief, Nahla; Belghith, Safya
2013-08-01
The compass-gait walker is a two-degree-of-freedom biped that can walk passively and steadily down an incline without any actuation. The mathematical model of the walking dynamics is represented by an impulsive hybrid nonlinear model. It is capable of displaying cyclic motions and chaos. In this paper, we propose a new approach to controlling chaos cropped up from the passive dynamic walking of the compass-gait model. The proposed technique is to linearize the nonlinear model around a desired passive hybrid limit cycle. Then, we show that the nonlinear model is transformed to an impulsive hybrid linear model with a controlled jump. Basing on the linearized model, we derive an analytical expression of a constrained controlled Poincaré map. We present a method for the numerical simulation of this constrained map where bifurcation diagrams are plotted. Relying on these diagrams, we show that the linear model is fairly close to the nonlinear one. Using the linearized controlled Poincaré map, we design a state feedback controller in order to stabilize the fixed point of the Poincaré map. We show that this controller is very efficient for the control of chaos for the original nonlinear model.
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.
Species fluctuations sustained by a cyclic succession at the edge of chaos
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
Species fluctuations sustained by a cyclic succession at the edge of chaos.
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.
Ergodicity of Truncated Stochastic Navier Stokes with Deterministic Forcing and Dispersion
NASA Astrophysics Data System (ADS)
Majda, Andrew J.; Tong, Xin T.
2016-10-01
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.
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
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.
Kolmogorov Pathways from Integrability to Chaos and Beyond
NASA Astrophysics Data System (ADS)
Livi, Roberto; Ruffo, Stefano; Shepelyansky, Dima
Two limits of Newtonian mechanics were worked out by Kolmogorov. On one side it was shown that in a generic integrable Hamiltonian system, regular quasi-periodic motion persists when a small perturbation is applied. This result, known as Kolmogorov-Arnold-Moser (KAM) theorem, gives mathematical bounds for integrability and perturbations. On the other side it was proven that almost all numbers on the interval between zero and one are uncomputable, have positive Kolmogorov complexity and, therefore, can be considered as random. In the case of nonlinear dynamics with exponential (i.e. Lyapunov) instability this randomnesss, hidden in the initial conditions, rapidly explodes with time, leading to unpredictable chaotic dynamics in a perfectly deterministic system. Fundamental mathematical theorems were obtained in these two limits, but the generic situation corresponds to the intermediate regime between them. This intermediate regime, which still lacks a rigorous description, has been mainly investigated by physicists with the help of theoretical estimates and numerical simulations. In this contribution we outline the main achievements in this area with reference to speci.c examples of both lowdimensional and high-dimensional dynamical systems. We shall also discuss the successes and limitations of numerical methods and the modern trends in physical applications, including quantum computations.
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
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)
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)
... 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 ...
[Chaos and fractals and their applications in electrocardial signal research].
Jiao, Qing; Guo, Yongxin; Zhang, Zhengguo
2009-06-01
Chaos and fractals are ubiquitous phenomena of nature. A system with fractal structure usually behaves chaos. As a complicated nonlinear dynamics system, heart has fractals structure and behaves as chaos. The deeper inherent mechanism of heart can be opened out when the chaos and fractals theory is utilized in the research of the electrical activity of heart. Generally a time series of a system was used for describing the status of the strange attractor of the system. The indices include Poincare plot, fractals dimension, Lyapunov exponent, entropy, scaling exponent, Hurst index and so on. In this article, the basic concepts and the methods of chaos and fractals were introduced firstly. Then the applications of chaos and fractals theories in the study of electrocardial signal were expounded with example of how they are used for ventricular fibrillation.
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.
Deterministic teleportation of electrons in a quantum dot nanostructure.
de Visser, R L; Blaauboer, M
2006-06-23
We present a proposal for deterministic quantum teleportation of electrons in a semiconductor nanostructure consisting of a single and a double quantum dot. The central issue addressed in this Letter is how to design and implement the most efficient--in terms of the required number of single and two-qubit operations--deterministic teleportation protocol for this system. Using a group-theoretical analysis, we show that deterministic teleportation requires a minimum of three single-qubit rotations and two entangling (square root SWAP) operations. These can be implemented for spin qubits in quantum dots using electron-spin resonance (for single-spin rotations) and exchange interaction (for square root SWAP operations).
Deterministic sensing matrices in compressive sensing: a survey.
Nguyen, Thu L N; Shin, Yoan
2013-01-01
Compressive sensing is a sampling method which provides a new approach to efficient signal compression and recovery by exploiting the fact that a sparse signal can be suitably reconstructed from very few measurements. One of the most concerns in compressive sensing is the construction of the sensing matrices. While random sensing matrices have been widely studied, only a few deterministic sensing matrices have been considered. These matrices are highly desirable on structure which allows fast implementation with reduced storage requirements. In this paper, a survey of deterministic sensing matrices for compressive sensing is presented. We introduce a basic problem in compressive sensing and some disadvantage of the random sensing matrices. Some recent results on construction of the deterministic sensing matrices are discussed.
Estimating the epidemic threshold on networks by deterministic connections
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.
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…
Temperature Chaos in Some Spherical Mixed p-Spin Models
NASA Astrophysics Data System (ADS)
Chen, Wei-Kuo; Panchenko, Dmitry
2017-03-01
We give two types of examples of the spherical mixed even- p-spin models for which chaos in temperature holds. These complement some known results for the spherical pure p-spin models and for models with Ising spins. For example, in contrast to a recent result of Subag who showed absence of chaos in temperature in the spherical pure p-spin models for p≥3, we show that even a smaller order perturbation induces temperature chaos.
Quasiperiodicity and chaos in cardiac fibrillation.
Garfinkel, A; Chen, P S; Walter, D O; Karagueuzian, H S; Kogan, B; Evans, S J; Karpoukhin, M; Hwang, C; Uchida, T; Gotoh, M; Nwasokwa, O; Sager, P; Weiss, J N
1997-01-01
In cardiac fibrillation, disorganized waves of electrical activity meander through the heart, and coherent contractile function is lost. We studied fibrillation in three stationary forms: in human chronic atrial fibrillation, in a stabilized form of canine ventricular fibrillation, and in fibrillation-like activity in thin sheets of canine and human ventricular tissue in vitro. We also created a computer model of fibrillation. In all four studies, evidence indicated that fibrillation arose through a quasiperiodic stage of period and amplitude modulation, thus exemplifying the "quasiperiodic transition to chaos" first suggested by Ruelle and Takens. This suggests that fibrillation is a form of spatio-temporal chaos, a finding that implies new therapeutic approaches. PMID:9005999
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.
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
Polynomial chaos representation of databases on manifolds
NASA Astrophysics Data System (ADS)
Soize, C.; Ghanem, R.
2017-04-01
Characterizing the polynomial chaos expansion (PCE) of a vector-valued random variable with probability distribution concentrated on a manifold is a relevant problem in data-driven settings. The probability distribution of such random vectors is multimodal in general, leading to potentially very slow convergence of the PCE. In this paper, we build on a recent development for estimating and sampling from probabilities concentrated on a diffusion manifold. The proposed methodology constructs a PCE of the random vector together with an associated generator that samples from the target probability distribution which is estimated from data concentrated in the neighborhood of the manifold. The method is robust and remains efficient for high dimension and large datasets. The resulting polynomial chaos construction on manifolds permits the adaptation of many uncertainty quantification and statistical tools to emerging questions motivated by data-driven queries.
Tuning quantum measurements to control chaos
NASA Astrophysics Data System (ADS)
Eastman, Jessica K.; Hope, Joseph J.; Carvalho, André R. R.
2017-03-01
Environment-induced decoherence has long been recognised as being of crucial importance in the study of chaos in quantum systems. In particular, the exact form and strength of the system-environment interaction play a major role in the quantum-to-classical transition of chaotic systems. In this work we focus on the effect of varying monitoring strategies, i.e. for a given decoherence model and a fixed environmental coupling, there is still freedom on how to monitor a quantum system. We show here that there is a region between the deep quantum regime and the classical limit where the choice of the monitoring parameter allows one to control the complex behaviour of the system, leading to either the emergence or suppression of chaos. Our work shows that this is a result from the interplay between quantum interference effects induced by the nonlinear dynamics and the effectiveness of the decoherence for different measurement schemes.
Tuning quantum measurements to control chaos
Eastman, Jessica K.; Hope, Joseph J.; Carvalho, André R. R.
2017-01-01
Environment-induced decoherence has long been recognised as being of crucial importance in the study of chaos in quantum systems. In particular, the exact form and strength of the system-environment interaction play a major role in the quantum-to-classical transition of chaotic systems. In this work we focus on the effect of varying monitoring strategies, i.e. for a given decoherence model and a fixed environmental coupling, there is still freedom on how to monitor a quantum system. We show here that there is a region between the deep quantum regime and the classical limit where the choice of the monitoring parameter allows one to control the complex behaviour of the system, leading to either the emergence or suppression of chaos. Our work shows that this is a result from the interplay between quantum interference effects induced by the nonlinear dynamics and the effectiveness of the decoherence for different measurement schemes. PMID:28317933
Chaos synchronization of general complex dynamical networks
NASA Astrophysics Data System (ADS)
Lü, Jinhu; Yu, Xinghuo; Chen, Guanrong
2004-03-01
Recently, it has been demonstrated that many large-scale complex dynamical networks display a collective synchronization motion. Here, we introduce a time-varying complex dynamical network model and further investigate its synchronization phenomenon. Based on this new complex network model, two network chaos synchronization theorems are proved. We show that the chaos synchronization of a time-varying complex network is determined by means of the inner coupled link matrix, the eigenvalues and the corresponding eigenvectors of the coupled configuration matrix, rather than the conventional eigenvalues of the coupled configuration matrix for a uniform network. Especially, we do not assume that the coupled configuration matrix is symmetric and its off-diagonal elements are nonnegative, which in a way generalizes the related results existing in the literature.
Migraine--new perspectives from chaos theory.
Kernick, D
2005-08-01
Converging from a number of disciplines, non-linear systems theory and in particular chaos theory offer new descriptive and prescriptive insights into physiological systems. This paper briefly reviews an approach to physiological systems from these perspectives and outlines how these concepts can be applied to the study of migraine. It suggests a wide range of potential applications including new approaches to classification, treatment and pathophysiological mechanisms. A hypothesis is developed that suggests that dysfunctional consequences can result from a mismatch between the complexity of the environment and the system that is seeking to regulate it and that the migraine phenomenon is caused by an incongruity between the complexity of mid brain sensory integration and cortical control networks. Chaos theory offers a new approach to the study of migraine that complements existing frameworks but may more accurately reflect underlying physiological mechanisms.
Complexity of Monte Carlo and deterministic dose-calculation methods.
Börgers, C
1998-03-01
Grid-based deterministic dose-calculation methods for radiotherapy planning require the use of six-dimensional phase space grids. Because of the large number of phase space dimensions, a growing number of medical physicists appear to believe that grid-based deterministic dose-calculation methods are not competitive with Monte Carlo methods. We argue that this conclusion may be premature. Our results do suggest, however, that finite difference or finite element schemes with orders of accuracy greater than one will probably be needed if such methods are to compete well with Monte Carlo methods for dose calculations.
Deterministic and efficient quantum cryptography based on Bell's theorem
Chen Zengbing; Pan Jianwei; Zhang Qiang; Bao Xiaohui; Schmiedmayer, Joerg
2006-05-15
We propose a double-entanglement-based quantum cryptography protocol that is both efficient and deterministic. The proposal uses photon pairs with entanglement both in polarization and in time degrees of freedom; each measurement in which both of the two communicating parties register a photon can establish one and only one perfect correlation, and thus deterministically create a key bit. Eavesdropping can be detected by violation of local realism. A variation of the protocol shows a higher security, similar to the six-state protocol, under individual attacks. Our scheme allows a robust implementation under the current technology.
Inherent Conservatism in Deterministic Quasi-Static Structural Analysis
NASA Technical Reports Server (NTRS)
Verderaime, V.
1997-01-01
The cause of the long-suspected excessive conservatism in the prevailing structural deterministic safety factor has been identified as an inherent violation of the error propagation laws when reducing statistical data to deterministic values and then combining them algebraically through successive structural computational processes. These errors are restricted to the applied stress computations, and because mean and variations of the tolerance limit format are added, the errors are positive, serially cumulative, and excessively conservative. Reliability methods circumvent these errors and provide more efficient and uniform safe structures. The document is a tutorial on the deficiencies and nature of the current safety factor and of its improvement and transition to absolute reliability.
Deterministic extinction by mixing in cyclically competing species
NASA Astrophysics Data System (ADS)
Feldager, Cilie W.; Mitarai, Namiko; Ohta, Hiroki
2017-03-01
We consider a cyclically competing species model on a ring with global mixing at finite rate, which corresponds to the well-known Lotka-Volterra equation in the limit of infinite mixing rate. Within a perturbation analysis of the model from the infinite mixing rate, we provide analytical evidence that extinction occurs deterministically at sufficiently large but finite values of the mixing rate for any species number N ≥3 . Further, by focusing on the cases of rather small species numbers, we discuss numerical results concerning the trajectories toward such deterministic extinction, including global bifurcations caused by changing the mixing rate.
Temperature chaos is a non-local effect
NASA Astrophysics Data System (ADS)
Fernandez, L. A.; Marinari, E.; Martin-Mayor, V.; Parisi, G.; Yllanes, D.
2016-12-01
Temperature chaos plays a role in important effects, for example memory and rejuvenation, in spin glasses, colloids, polymers. We numerically investigate temperature chaos in spin glasses, exploiting its recent characterization as a rare-event driven phenomenon. The peculiarities of the transformation from periodic to anti-periodic boundary conditions in spin glasses allow us to conclude that temperature chaos is non-local: no bounded region of the system causes it. We precisely show the statistical relationship between temperature chaos and the free-energy changes upon varying boundary conditions.
Chaos control of parametric driven Duffing oscillators
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.
Chaos control of parametric driven Duffing oscillators
NASA Astrophysics Data System (ADS)
Jin, Leisheng; Mei, Jie; Li, Lijie
2014-03-01
Duffing resonators are typical dynamic systems, which can exhibit chaotic oscillations, subject to certain driving conditions. Chaotic oscillations of resonating systems with negative and positive spring constants are identified to investigate in this paper. Parametric driver imposed on these two systems affects nonlinear behaviours, which has been theoretically analyzed with regard to variation of driving parameters (frequency, amplitude). Systematic calculations have been performed for these two systems driven by parametric pumps to unveil the controllability of chaos.
Optimal chaos control through reinforcement learning.
Gadaleta, Sabino; Dangelmayr, Gerhard
1999-09-01
A general purpose chaos control algorithm based on reinforcement learning is introduced and applied to the stabilization of unstable periodic orbits in various chaotic systems and to the targeting problem. The algorithm does not require any information about the dynamical system nor about the location of periodic orbits. Numerical tests demonstrate good and fast performance under noisy and nonstationary conditions. (c) 1999 American Institute of Physics.
Coherence and chaos in extended dynamical systems
Bishop, A.R.
1994-12-31
Coherence, chaos, and pattern formation are characteristic elements of the nonequilibrium statistical mechanics controlling mesoscopic order and disorder in many-degree-of-freedom nonlinear dynamical systems. Competing length scales and/or time scales are the underlying microscopic driving forces for many of these aspects of ``complexity.`` We illustrate the basic concepts with some model examples of classical and quantum, ordered and disordered, nonlinear systems.
Solitons in the midst of chaos
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.
Murakami, A; Ohtsubo, J
2001-06-01
Chaos synchronization using a continuous chaos control method was studied in two identical chaotic laser systems consisting of semiconductor lasers and optical feedback from an external mirror. Numerical calculations for rate equations indicate that the stability of chaos synchronization depends significantly on the external mirror position. We performed a linear stability analysis for the rate equations. Our results show that the stability of the synchronization is much influenced by the mode interaction between the relaxation oscillation frequency of the semiconductor laser and the external cavity frequency. Due to this interaction, an intensive mode competition between the two frequencies destroys the synchronization, but stable synchronization can be achieved when the mode competition is very weak.
Probing temperature chaos through thermal boundary conditions
NASA Astrophysics Data System (ADS)
Wang, Wenlong; Machta, Jonathan; Katzgraber, Helmut
2015-03-01
Using population annealing Monte Carlo, we numerically study temperature chaos in the three-dimensional Edwards-Anderson Ising spin glass using thermal boundary conditions. In thermal boundary conditions all eight combinations of periodic vs antiperiodic boundary conditions in the three spatial directions appear in the ensemble with their respective Boltzmann weights, thus minimizing finite-size corrections due to domain walls. By studying salient features in the specific heat we show evidence of temperature chaos. Our results suggest that these bumps are mainly caused by system-size excitations where the free energy of two boundary conditions cross. Furthermore, we study the scaling of both entropy and energy at boundary condition crossings and find that the scaling of the energy is very different from the scaling obtained by a simple change of boundary conditions. We attribute this difference to the stronger finite-size effects induced via a simple change of boundary conditions. Finally, we show that temperature chaos occurs more frequently at higher temperatures within the spin-glass phase and for larger system sizes, while the normalized distribution function with respect to temperature is about the same for different system sizes. The work is supported from NSF (Grant No. DMR-1208046).
Chaos in Chiral Condensates in Gauge Theories
NASA Astrophysics Data System (ADS)
Hashimoto, Koji; Murata, Keiju; Yoshida, Kentaroh
2016-12-01
Assigning a chaos index for dynamics of generic quantum field theories is a challenging problem because the notion of a Lyapunov exponent, which is useful for singling out chaotic behavior, works only in classical systems. We address the issue by using the AdS /CFT correspondence, as the large Nc limit provides a classicalization (other than the standard ℏ→0 ) while keeping nontrivial quantum condensation. We demonstrate the chaos in the dynamics of quantum gauge theories: The time evolution of homogeneous quark condensates ⟨q ¯q ⟩ and ⟨q ¯γ5q ⟩ in an N =2 supersymmetric QCD with the S U (Nc) gauge group at large Nc and at a large 't Hooft coupling λ ≡NcgYM2 exhibits a positive Lyapunov exponent. The chaos dominates the phase space for energy density E ≳(6 ×1 02)×mq4(Nc/λ2), where mq is the quark mass. We evaluate the largest Lyapunov exponent as a function of (Nc,λ ,E ) and find that the N =2 supersymmetric QCD is more chaotic for smaller Nc.
Detecting chaos in irregularly sampled time series.
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.
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…
Saperstein, A.M.
1988-10-01
The model discussed seems to indicate that if SDI evolves to the points where the defense can overwhelm the offense, the result is a crisis-unstable international system that cannot be mathematically distinguished from a system of war. SDI's acting as envisioned by its supporters does not provide the stable security desired by all. Previous independent qualitative discussions by both US and Soviet analysts have indicated the same instability for SDI. An effective SDI may be very desirable once it is completely in place and functioning, but the process of putting it into place, starting from the present world configuration, seems to be very dangerous. If the proposed defense looks as though it is going to become able to overcome the opponent's offense, then in a crisis, one side is likely to use its offense rather than chance losing it - the very definition of crisis stability. The similarity of the predictions made here and by the US and Soviet analysts concerning the results of SDI deployment lends credence to the forecasts and their underlying assumptions. It appears that SDI cannot be deployed to force major reductions in the offensive strategic nuclear weapons of the superpowers without jeopardizing stability.
Designing a stochastic genetic switch by coupling chaos and bistability
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.
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.
Latanision, R.M.
1990-12-01
Electrochemical corrosion is pervasive in virtually all engineering systems and in virtually all industrial circumstances. Although engineers now understand how to design systems to minimize corrosion in many instances, many fundamental questions remain poorly understood and, therefore, the development of corrosion control strategies is based more on empiricism than on a deep understanding of the processes by which metals corrode in electrolytes. Fluctuations in potential, or current, in electrochemical systems have been observed for many years. To date, all investigations of this phenomenon have utilized non-deterministic analyses. In this work it is proposed to study electrochemical noise from a deterministic viewpoint by comparison of experimental parameters, such as first and second order moments (non-deterministic), with computer simulation of corrosion at metal surfaces. In this way it is proposed to analyze the origins of these fluctuations and to elucidate the relationship between these fluctuations and kinetic parameters associated with metal dissolution and cathodic reduction reactions. This research program addresses in essence two areas of interest: (a) computer modeling of corrosion processes in order to study the electrochemical processes on an atomistic scale, and (b) experimental investigations of fluctuations in electrochemical systems and correlation of experimental results with computer modeling. In effect, the noise generated by mathematical modeling will be analyzed and compared to experimental noise in electrochemical systems. 1 fig.
Comparison of deterministic and Monte Carlo methods in shielding design.
Oliveira, A D; Oliveira, C
2005-01-01
In shielding calculation, deterministic methods have some advantages and also some disadvantages relative to other kind of codes, such as Monte Carlo. The main advantage is the short computer time needed to find solutions while the disadvantages are related to the often-used build-up factor that is extrapolated from high to low energies or with unknown geometrical conditions, which can lead to significant errors in shielding results. The aim of this work is to investigate how good are some deterministic methods to calculating low-energy shielding, using attenuation coefficients and build-up factor corrections. Commercial software MicroShield 5.05 has been used as the deterministic code while MCNP has been used as the Monte Carlo code. Point and cylindrical sources with slab shield have been defined allowing comparison between the capability of both Monte Carlo and deterministic methods in a day-by-day shielding calculation using sensitivity analysis of significant parameters, such as energy and geometrical conditions.
Risk-based versus deterministic explosives safety criteria
Wright, R.E.
1996-12-01
The Department of Defense Explosives Safety Board (DDESB) is actively considering ways to apply risk-based approaches in its decision- making processes. As such, an understanding of the impact of converting to risk-based criteria is required. The objectives of this project are to examine the benefits and drawbacks of risk-based criteria and to define the impact of converting from deterministic to risk-based criteria. Conclusions will be couched in terms that allow meaningful comparisons of deterministic and risk-based approaches. To this end, direct comparisons of the consequences and impacts of both deterministic and risk-based criteria at selected military installations are made. Deterministic criteria used in this report are those in DoD 6055.9-STD, `DoD Ammunition and Explosives Safety Standard.` Risk-based criteria selected for comparison are those used by the government of Switzerland, `Technical Requirements for the Storage of Ammunition (TLM 75).` The risk-based criteria used in Switzerland were selected because they have been successfully applied for over twenty-five years.
A Deterministic Annealing Approach to Clustering AIRS Data
NASA Technical Reports Server (NTRS)
Guillaume, Alexandre; Braverman, Amy; Ruzmaikin, Alexander
2012-01-01
We will examine the validity of means and standard deviations as a basis for climate data products. We will explore the conditions under which these two simple statistics are inadequate summaries of the underlying empirical probability distributions by contrasting them with a nonparametric, method called Deterministic Annealing technique
Deterministic dense coding and faithful teleportation with multipartite graph states
Huang, C.-Y.; Yu, I-C.; Lin, F.-L.; Hsu, L.-Y.
2009-05-15
We propose schemes to perform the deterministic dense coding and faithful teleportation with multipartite graph states. We also find the sufficient and necessary condition of a viable graph state for the proposed schemes. That is, for the associated graph, the reduced adjacency matrix of the Tanner-type subgraph between senders and receivers should be invertible.
Deterministic retrieval of complex Green's functions using hard X rays.
Vine, D J; Paganin, D M; Pavlov, K M; Uesugi, K; Takeuchi, A; Suzuki, Y; Yagi, N; Kämpfe, T; Kley, E-B; Förster, E
2009-01-30
A massively parallel deterministic method is described for reconstructing shift-invariant complex Green's functions. As a first experimental implementation, we use a single phase contrast x-ray image to reconstruct the complex Green's function associated with Bragg reflection from a thick perfect crystal. The reconstruction is in excellent agreement with a classic prediction of dynamical diffraction theory.
NASA Astrophysics Data System (ADS)
Takeda, F.
2009-12-01
Dividing Japan into meshes of about 5 degrees, we collect earthquakes (EQs) for each mesh-area from an on-line JMA focus catalog of Japan with a regionally dependent magnitude window of M ≥ 3-3.5. The time history of each mesh-collection is a string of EQ events, which draw a zigzagged trajectory in a physical space. The space coordinates are the EQ epicenter, focal depth (DEP), inter-EQ time interval (INT), and magnitude (MAG). Thus, each coordinate component of the trajectory is the time series of the corresponding EQ source parameter where time is the chronological event index. The zigzagged motion appears random like Brownian motion; however, it is a deterministic chaos. The evidence is that the largest Lyapunov exponents of each trajectory are all positive, statistically distinct from those surrogated by randomly shuffling only the event index. Thus, the deterministic chaos suggests that any impending large EQ does not rupture randomly and that some deterministic seismogenesis controls the rupture process. Namely, some short-term deterministic forecasting is theoretically possible. Therefore, we first take a moving-average of 15-25 events on each series to reduce the zigzagged motion. We further take its second order difference at the interval of 20-35 events to find its acceleration (seismogenic force) acting on each averaged series. We then find only two unique different triple phase couplings of the acceleration on source parameter DEP, INT, and MAG precursory to every impending large EQs (M > about 6) throughout Japan [Takeda, 2003; Takeda and Takeo, 2004]. Each triple phase coupling begins the MAG with medium MAG of about 4.1 at either small (shallow) DEP and large INT or large (deep) DEP and small INT, then change it to small MAG of about 3.8 at either deep DEP and small INT or shallow DEP and large INT. The transition of the EQ state creates a large linear DEP variation (W) on its series, which is found comparable to the fault width of large EQs
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.
St Aubin, J. Keyvanloo, A.; Fallone, B. G.; Vassiliev, O.
2015-02-15
Purpose: Accurate radiotherapy dose calculation algorithms are essential to any successful radiotherapy program, considering the high level of dose conformity and modulation in many of today’s treatment plans. As technology continues to progress, such as is the case with novel MRI-guided radiotherapy systems, the necessity for dose calculation algorithms to accurately predict delivered dose in increasingly challenging scenarios is vital. To this end, a novel deterministic solution has been developed to the first order linear Boltzmann transport equation which accurately calculates x-ray based radiotherapy doses in the presence of magnetic fields. Methods: The deterministic formalism discussed here with the inclusion of magnetic fields is outlined mathematically using a discrete ordinates angular discretization in an attempt to leverage existing deterministic codes. It is compared against the EGSnrc Monte Carlo code, utilizing the emf-macros addition which calculates the effects of electromagnetic fields. This comparison is performed in an inhomogeneous phantom that was designed to present a challenging calculation for deterministic calculations in 0, 0.6, and 3 T magnetic fields oriented parallel and perpendicular to the radiation beam. The accuracy of the formalism discussed here against Monte Carlo was evaluated with a gamma comparison using a standard 2%/2 mm and a more stringent 1%/1 mm criterion for a standard reference 10 × 10 cm{sup 2} field as well as a smaller 2 × 2 cm{sup 2} field. Results: Greater than 99.8% (94.8%) of all points analyzed passed a 2%/2 mm (1%/1 mm) gamma criterion for all magnetic field strengths and orientations investigated. All dosimetric changes resulting from the inclusion of magnetic fields were accurately calculated using the deterministic formalism. However, despite the algorithm’s high degree of accuracy, it is noticed that this formalism was not unconditionally stable using a discrete ordinate angular discretization
2012-01-01
Background The estimation of parameter values for mathematical models of biological systems is an optimization problem that is particularly challenging due to the nonlinearities involved. One major difficulty is the existence of multiple minima in which standard optimization methods may fall during the search. Deterministic global optimization methods overcome this limitation, ensuring convergence to the global optimum within a desired tolerance. Global optimization techniques are usually classified into stochastic and deterministic. The former typically lead to lower CPU times but offer no guarantee of convergence to the global minimum in a finite number of iterations. In contrast, deterministic methods provide solutions of a given quality (i.e., optimality gap), but tend to lead to large computational burdens. Results This work presents a deterministic outer approximation-based algorithm for the global optimization of dynamic problems arising in the parameter estimation of models of biological systems. Our approach, which offers a theoretical guarantee of convergence to global minimum, is based on reformulating the set of ordinary differential equations into an equivalent set of algebraic equations through the use of orthogonal collocation methods, giving rise to a nonconvex nonlinear programming (NLP) problem. This nonconvex NLP is decomposed into two hierarchical levels: a master mixed-integer linear programming problem (MILP) that provides a rigorous lower bound on the optimal solution, and a reduced-space slave NLP that yields an upper bound. The algorithm iterates between these two levels until a termination criterion is satisfied. Conclusion The capabilities of our approach were tested in two benchmark problems, in which the performance of our algorithm was compared with that of the commercial global optimization package BARON. The proposed strategy produced near optimal solutions (i.e., within a desired tolerance) in a fraction of the CPU time required by
Analysis of Discovery of Chaos: Social and Cognitive Aspects.
ERIC Educational Resources Information Center
Kim, J. B.
The purpose of this study was to examine Edward Lorenz's psychological processes and other environmental aspects in the discovery of chaos at that time. The general concept of chaos is discussed based on relations with previous scientific theories such as Newtonian physics and quantum mechanics. The constraints of discovery in terms of available…
Chaos Theory as a Lens for Advancing Quality Schooling.
ERIC Educational Resources Information Center
Snyder, Karolyn J.; Acker-Hocevar, Michele; Wolf, Kristen M.
Chaos theory provides a useful mental model for guiding change as leaders garner the energy from unpredictable events for realizing transformation goals. The paper considers chaos theory as a framework for managing school change toward Total Quality Management work cultures. Change is possible to manage when plans are made and then followed by a…
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…
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…
Experimental Control of Instabilities and Chaos in Fast Dynamical Systems
1997-06-01
is short (- 10 cm) [153]-[155]; these studies have more recently been considered from the chaos control viewpoint [42]. The apparatus required to...13] Christini, David J., and James A. Collins. Controlling Nonchaotic Neuronal Noise Using Chaos Control Techniques. Phys. Rev. Lett. 75:2782-2785
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)
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…
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
Amplitude death in coupled robust-chaos oscillators
NASA Astrophysics Data System (ADS)
Palazzi, M. J.; Cosenza, M. G.
2014-12-01
We investigate the synchronization behavior of a system of globally coupled, continuous-time oscillators possessing robust chaos. The local dynamics corresponds to the Shimizu-Morioka model where the occurrence of robust chaos in a region of its parameter space has been recently discovered. We show that the global coupling can drive the oscillators to synchronization into a fixed point created by the coupling, resulting in amplitude death in the system. The existence of robust chaos allows to introduce heterogeneity in the local parameters, while guaranteeing the functioning of all the oscillators in a chaotic mode. In this case, the system reaches a state of oscillation death, with coexisting clusters of oscillators in different steady states. The phenomena of amplitude death or oscillation death in coupled robust-chaos flows could be employed as mechanisms for stabilization and control in systems that require reliable operation under chaos.
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.
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.
Deterministically Polarized Fluorescence from Single Dye Molecules Aligned in Liquid Crystal Host
Lukishova, S.G.; Schmid, A.W.; Knox, R.; Freivald, P.; Boyd, R. W.; Stroud, Jr., C. R.; Marshall, K.L.
2005-09-30
We demonstrated for the first time to our konwledge deterministically polarized fluorescence from single dye molecules. Planar aligned nematic liquid crystal hosts provide deterministic alignment of single dye molecules in a preferred direction.
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
'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.
Outer Solar System on the Edge of Chaos
NASA Astrophysics Data System (ADS)
Hayes, Wayne B.
2006-06-01
The existence of chaos among the system of Jovian planets (Jupiter, Saturn, Uranus, and Neptune) is not yet firmly established. Although Laskar originally found no chaos in the outer Solar System, his "averaged" integrations did not account for the possibility of mean-motion resonances. Once full n-body integrations were performed, a dichotomy arose. On one hand, many investigators (Sussman, Wisdom, Murray, Holman, among many others) consistently measured a Lyapunov time of between 5 and 12 million years in the outer Solar System; the chaos can even be explained as the overlap of three-body resonances (Murray + Holman, Science 283, 1999). Furthermore, Murray + Holman's theory has been recently corroborated across a wide range of system parameters (Guzzo 2005), and the chaos does not disappear with decreasing timestep. On the other hand, some other investigators (Newman, Grazier, and Varadi, among several others) have compelling evidence against chaos. Namely, they have convincingly demonstrated that a sympletic integration using the famous Wisdom + Holman (1992) symplectic mapping with a 400-day timestep reproduces the chaos seen by others, but that the chaos disappears and the orbit converges to being regular as the timestep decreases. Their integration remains regular, showing beautiful convergence with decreasing timestep, down to a 2 day timestep. The resolution of this apparent paradox is simple. The orbital positions of the Jovian planets is known only to a few parts in 107, and it turns out that within that observational error ball, there exist both chaotic and regular solutions. I will demonstrate this fact using several initial conditions and several accurate integration algorithms. Thus, whether a particular investigator will see chaos or not depends (essentially randomly) upon the details of how that investigator draws their initial conditions. Thus, some investigators legitimately find chaos, while others legitimately find no chaos.
Exploring Information Chaos in Community Pharmacy Handoffs
Chui, Michelle A; Stone, Jamie A
2013-01-01
Background A handoff is the process of conveying necessary information in order to transfer primary responsibility for providing safe and effective drug therapy to a patient from one community pharmacist to another, typically during a shift change. The handoff information conveyed in pharmacies has been shown to be unstructured and variable, leading to pharmacist stress and frustration, prescription delays, and medication errors. Objective The purpose of this study was to describe and categorize the information hazards present in handoffs in community pharmacies. Methods A qualitative research approach was used to elicit the subjective experiences of community pharmacists. Community pharmacists who float or work in busy community pharmacies were recruited and participated in a face to face semi-structured interview. Using a systematic content data analysis, the study identified five categories of information hazards that can lead to information chaos, a framework grounded in human factors and ergonomics. Results Information hazards including erroneous information and information overload, underload, scatter, and conflict, are experienced routinely by community pharmacists during handoff communication and can result in information chaos. The consequences of information chaos include increased mental workload, which can precipitate problematic prescriptions “falling between the cracks”. This can ultimately impact patient care and pharmacist quality of working life. Conclusions The results suggest that handoffs in community pharmacies result in information hazards. These information hazards can distract pharmacists from their primary work of assessing prescriptions and educating their patients. Further research on how handoffs are conducted can produce information on how hazards in the system can be eliminated. PMID:23665076
Experimental Mathematics and Mathematical Physics
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.
Conduction at the onset of chaos
NASA Astrophysics Data System (ADS)
Baldovin, Fulvio
2017-02-01
After a general discussion of the thermodynamics of conductive processes, we introduce specific observables enabling the connection of the diffusive transport properties with the microscopic dynamics. We solve the case of Brownian particles, both analytically and numerically, and address then whether aspects of the classic Onsager's picture generalize to the non-local non-reversible dynamics described by logistic map iterates. While in the chaotic case numerical evidence of a monotonic relaxation is found, at the onset of chaos complex relaxation patterns emerge.
Semiclassical description of chaos-assisted tunneling.
Podolskiy, Viktor A; Narimanov, Evgenii E
2003-12-31
We study tunneling between regular and chaotic regions in the phase space of Hamiltonian systems. We analytically calculate the transition rate and show that its variation depends only on corresponding phase space area and in this sense is universal. We derive the distribution of level splittings associated with the pairs of quasidegenerate regular eigenstates which in the general case is different from a Cauchy distribution. We show that chaos-assisted tunneling leads to level repulsion between regular eigenstates, solving the longstanding problem of level-spacing distribution in mixed systems.
Quasiperiodic graphs at the onset of chaos.
Luque, B; Cordero-Gracia, M; Gómez, M; Robledo, A
2013-12-01
We examine the connectivity fluctuations across networks obtained when the horizontal visibility (HV) algorithm is used on trajectories generated by nonlinear circle maps at the quasiperiodic transition to chaos. The resultant HV graph is highly anomalous as the degrees fluctuate at all scales with amplitude that increases with the size of the network. We determine families of Pesin-like identities between entropy growth rates and generalized graph-theoretical Lyapunov exponents. An irrational winding number with pure periodic continued fraction characterizes each family. We illustrate our results for the so-called golden, silver, and bronze numbers.
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.
Quantum chaos in Aharonov-Bohm oscillations
Berman, G.P.; Campbell, D.K.; Bulgakov, E.N.; Krive, I.V.
1995-10-01
Aharonov-Bohm oscillations in a mesoscopic ballistic ring are considered under the influence of a resonant magnetic field with one and two frequencies. The authors investigate the oscillations of the time-averaged electron energy at zero temperature in the regime of an isolated quantum nonlinear resonance and at the transition to quantum chaos, when two quantum nonlinear resonances overlap. It is shown that the time-averaged energy exhibits resonant behavior as a function of the magnetic flux, and has a ``staircase`` dependence on the amplitude of the external field. The delocalization of the quasi-energy eigenfunctions is analyzed.
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.
Self-organized chaos through polyhomeostatic optimization.
Markovic, D; Gros, Claudius
2010-08-06
The goal of polyhomeostatic control is to achieve a certain target distribution of behaviors, in contrast to homeostatic regulation, which aims at stabilizing a steady-state dynamical state. We consider polyhomeostasis for individual and networks of firing-rate neurons, adapting to achieve target distributions of firing rates maximizing information entropy. We show that any finite polyhomeostatic adaption rate destroys all attractors in Hopfield-like network setups, leading to intermittently bursting behavior and self-organized chaos. The importance of polyhomeostasis to adapting behavior in general is discussed.
Beyond Benford's Law: Distinguishing Noise from Chaos
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
Kim, Y H; Garfinkel, A; Ikeda, T; Wu, T J; Athill, C A; Weiss, J N; Karagueuzian, H S; Chen, P S
1997-01-01
We have presented evidence that ventricular fibrillation is deterministic chaos arising from quasiperiodicity. The purpose of this study was to determine whether the transition from chaos (ventricular fibrillation, VF) to periodicity (ventricular tachycardia) through quasiperiodicity could be produced by the progressive reduction of tissue mass. In isolated and perfused swine right ventricular free wall, recording of single cell transmembrane potentials and simultaneous mapping (477 bipolar electrodes, 1.6 mm resolution) were performed. The tissue mass was then progressively reduced by sequential cutting. All isolated tissues fibrillated spontaneously. The critical mass to sustain VF was 19.9 +/- 4.2 g. As tissue mass was decreased, the number of wave fronts decreased, the life-span of reentrant wave fronts increased, and the cycle length, the diastolic interval, and the duration of action potential lengthened. There was a parallel decrease in the dynamical complexity of VF as measured by Kolmogorov entropy and Poincaré plots. A period of quasiperiodicity became more evident before the conversion from VF (chaos) to a more regular arrhythmia (periodicity). In conclusion, a decrease in the number of wave fronts in ventricular fibrillation by tissue mass reduction causes a transition from chaotic to periodic dynamics via the quasiperiodic route. PMID:9366563
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…
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…
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…
ERIC Educational Resources Information Center
McClellan, Kathryn T.
Why mathematics should be learned is discussed. Its role as an important active force in the development of our civilization, and as the most useful subject taught in our schools, next to English, is noted. The primary objective of all mathematics work is to help man study nature, and some practical achievements of this connection are noted.…
ERIC Educational Resources Information Center
Martin, Hope
2007-01-01
"Mathematical literacy" implies that a person is able to reason, analyze, formulate, and solve problems in a real-world setting. Mathematically literate individuals are informed citizens and intelligent consumers. They have the ability to interpret and analyze the vast amount of information they are inundated with daily in newspapers, on…
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.
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.
Approaches to implementing deterministic models in a probabilistic framework
Talbott, D.V.
1995-04-01
The increasing use of results from probabilistic risk assessments in the decision-making process makes it ever more important to eliminate simplifications in probabilistic models that might lead to conservative results. One area in which conservative simplifications are often made is modeling the physical interactions that occur during the progression of an accident sequence. This paper demonstrates and compares different approaches for incorporating deterministic models of physical parameters into probabilistic models; parameter range binning, response curves, and integral deterministic models. An example that combines all three approaches in a probabilistic model for the handling of an energetic material (i.e. high explosive, rocket propellant,...) is then presented using a directed graph model.
Deterministic algorithm with agglomerative heuristic for location problems
NASA Astrophysics Data System (ADS)
Kazakovtsev, L.; Stupina, A.
2015-10-01
Authors consider the clustering problem solved with the k-means method and p-median problem with various distance metrics. The p-median problem and the k-means problem as its special case are most popular models of the location theory. They are implemented for solving problems of clustering and many practically important logistic problems such as optimal factory or warehouse location, oil or gas wells, optimal drilling for oil offshore, steam generators in heavy oil fields. Authors propose new deterministic heuristic algorithm based on ideas of the Information Bottleneck Clustering and genetic algorithms with greedy heuristic. In this paper, results of running new algorithm on various data sets are given in comparison with known deterministic and stochastic methods. New algorithm is shown to be significantly faster than the Information Bottleneck Clustering method having analogous preciseness.
Deterministic control of ferroelastic switching in multiferroic materials.
Balke, N; Choudhury, S; Jesse, S; Huijben, M; Chu, Y H; Baddorf, A P; Chen, L Q; Ramesh, R; Kalinin, S V
2009-12-01
Multiferroic materials showing coupled electric, magnetic and elastic orderings provide a platform to explore complexity and new paradigms for memory and logic devices. Until now, the deterministic control of non-ferroelectric order parameters in multiferroics has been elusive. Here, we demonstrate deterministic ferroelastic switching in rhombohedral BiFeO(3) by domain nucleation with a scanning probe. We are able to select among final states that have the same electrostatic energy, but differ dramatically in elastic or magnetic order, by applying voltage to the probe while it is in lateral motion. We also demonstrate the controlled creation of a ferrotoroidal order parameter. The ability to control local elastic, magnetic and torroidal order parameters with an electric field will make it possible to probe local strain and magnetic ordering, and engineer various magnetoelectric, domain-wall-based and strain-coupled devices.
Towards a quasi-deterministic single-photon source
NASA Astrophysics Data System (ADS)
Peters, N. A.; Arnold, K. J.; VanDevender, A. P.; Jeffrey, E. R.; Rangarajan, R.; Hosten, O.; Barreiro, J. T.; Altepeter, J. B.; Kwiat, P. G.
2006-08-01
A source of single photons allows secure quantum key distribution, in addition, to being a critical resource for linear optics quantum computing. We describe our progress on deterministically creating single photons from spontaneous parametric downconversion, an extension of the Pittman, Jacobs and Franson scheme [Phys. Rev A, v66, 042303 (2002)]. Their idea was to conditionally prepare single photons by measuring one member of a spontaneously emitted photon pair and storing the remaining conditionally prepared photon until a predetermined time, when it would be "deterministically" released from storage. Our approach attempts to improve upon this by recycling the pump pulse in order to decrease the possibility of multiple-pair generation, while maintaining a high probability of producing a single pair. Many of the challenges we discuss are central to other quantum information technologies, including the need for low-loss optical storage, switching and detection, and fast feed-forward control.
Deterministic error correction for nonlocal spatial-polarization hyperentanglement.
Li, Tao; Wang, Guan-Yu; Deng, Fu-Guo; Long, Gui-Lu
2016-02-10
Hyperentanglement is an effective quantum source for quantum communication network due to its high capacity, low loss rate, and its unusual character in teleportation of quantum particle fully. Here we present a deterministic error-correction scheme for nonlocal spatial-polarization hyperentangled photon pairs over collective-noise channels. In our scheme, the spatial-polarization hyperentanglement is first encoded into a spatial-defined time-bin entanglement with identical polarization before it is transmitted over collective-noise channels, which leads to the error rejection of the spatial entanglement during the transmission. The polarization noise affecting the polarization entanglement can be corrected with a proper one-step decoding procedure. The two parties in quantum communication can, in principle, obtain a nonlocal maximally entangled spatial-polarization hyperentanglement in a deterministic way, which makes our protocol more convenient than others in long-distance quantum communication.
On the secure obfuscation of deterministic finite automata.
Anderson, William Erik
2008-06-01
In this paper, we show how to construct secure obfuscation for Deterministic Finite Automata, assuming non-uniformly strong one-way functions exist. We revisit the software protection approaches originally proposed by [5, 10, 12, 17] and revise them to the current obfuscation setting of Barak et al. [2]. Under this model, we introduce an efficient oracle that retains some 'small' secret about the original program. Using this secret, we can construct an obfuscator and two-party protocol that securely obfuscates Deterministic Finite Automata against malicious adversaries. The security of this model retains the strong 'virtual black box' property originally proposed in [2] while incorporating the stronger condition of dependent auxiliary inputs in [15]. Additionally, we show that our techniques remain secure under concurrent self-composition with adaptive inputs and that Turing machines are obfuscatable under this model.
Deterministic remote two-qubit state preparation in dissipative environments
NASA Astrophysics Data System (ADS)
Li, Jin-Fang; Liu, Jin-Ming; Feng, Xun-Li; Oh, C. H.
2016-05-01
We propose a new scheme for efficient remote preparation of an arbitrary two-qubit state, introducing two auxiliary qubits and using two Einstein-Podolsky-Rosen (EPR) states as the quantum channel in a non-recursive way. At variance with all existing schemes, our scheme accomplishes deterministic remote state preparation (RSP) with only one sender and the simplest entangled resource (say, EPR pairs). We construct the corresponding quantum logic circuit using a unitary matrix decomposition procedure and analytically obtain the average fidelity of the deterministic RSP process for dissipative environments. Our studies show that, while the average fidelity gradually decreases to a stable value without any revival in the Markovian regime, it decreases to the same stable value with a dampened revival amplitude in the non-Markovian regime. We also find that the average fidelity's approximate maximal value can be preserved for a long time if the non-Markovian and the detuning conditions are satisfied simultaneously.
Nano transfer and nanoreplication using deterministically grown sacrificial nanotemplates
Melechko, Anatoli V [Oak Ridge, TN; McKnight, Timothy E [Greenback, TN; Guillorn, Michael A [Ithaca, NY; Ilic, Bojan [Ithaca, NY; Merkulov, Vladimir I [Knoxville, TX; Doktycz, Mitchel J [Knoxville, TN; Lowndes, Douglas H [Knoxville, TN; Simpson, Michael L [Knoxville, TN
2012-03-27
Methods, manufactures, machines and compositions are described for nanotransfer and nanoreplication using deterministically grown sacrificial nanotemplates. An apparatus, includes a substrate and a nanoconduit material coupled to a surface of the substrate. The substrate defines an aperture and the nanoconduit material defines a nanoconduit that is i) contiguous with the aperture and ii) aligned substantially non-parallel to a plane defined by the surface of the substrate.
A deterministic algorithm for constrained enumeration of transmembrane protein folds.
Brown, William Michael; Young, Malin M.; Sale, Kenneth L.; Faulon, Jean-Loup Michel; Schoeniger, Joseph S.
2004-07-01
A deterministic algorithm for enumeration of transmembrane protein folds is presented. Using a set of sparse pairwise atomic distance constraints (such as those obtained from chemical cross-linking, FRET, or dipolar EPR experiments), the algorithm performs an exhaustive search of secondary structure element packing conformations distributed throughout the entire conformational space. The end result is a set of distinct protein conformations, which can be scored and refined as part of a process designed for computational elucidation of transmembrane protein structures.
Uniform Deterministic Discrete Method for three dimensional systems
NASA Astrophysics Data System (ADS)
Li, Ben-Wen; Tao, Wen-Quan; Nie, Yu-Hong
1997-06-01
For radiative direct exchange areas in three dimensional system, the Uniform Deterministic Discrete Method (UDDM) was adopted. The spherical surface dividing method for sending area element and the regular icosahedron for sending volume element can meet with the direct exchange area computation of any kind of zone pairs. The numerical examples of direct exchange area in three dimensional system with nonhomogeneous attenuation coefficients indicated that the UDDM can give very high numerical accuracy.
Probabilistic versus deterministic hazard assessment in liquefaction susceptible zones
NASA Astrophysics Data System (ADS)
Daminelli, Rosastella; Gerosa, Daniele; Marcellini, Alberto; Tento, Alberto
2015-04-01
Probabilistic seismic hazard assessment (PSHA), usually adopted in the framework of seismic codes redaction, is based on Poissonian description of the temporal occurrence, negative exponential distribution of magnitude and attenuation relationship with log-normal distribution of PGA or response spectrum. The main positive aspect of this approach stems into the fact that is presently a standard for the majority of countries, but there are weak points in particular regarding the physical description of the earthquake phenomenon. Factors like site effects, source characteristics like duration of the strong motion and directivity that could significantly influence the expected motion at the site are not taken into account by PSHA. Deterministic models can better evaluate the ground motion at a site from a physical point of view, but its prediction reliability depends on the degree of knowledge of the source, wave propagation and soil parameters. We compare these two approaches in selected sites affected by the May 2012 Emilia-Romagna and Lombardia earthquake, that caused widespread liquefaction phenomena unusually for magnitude less than 6. We focus on sites liquefiable because of their soil mechanical parameters and water table level. Our analysis shows that the choice between deterministic and probabilistic hazard analysis is strongly dependent on site conditions. The looser the soil and the higher the liquefaction potential, the more suitable is the deterministic approach. Source characteristics, in particular the duration of strong ground motion, have long since recognized as relevant to induce liquefaction; unfortunately a quantitative prediction of these parameters appears very unlikely, dramatically reducing the possibility of their adoption in hazard assessment. Last but not least, the economic factors are relevant in the choice of the approach. The case history of 2012 Emilia-Romagna and Lombardia earthquake, with an officially estimated cost of 6 billions
The deterministic SIS epidemic model in a Markovian random environment.
Economou, Antonis; Lopez-Herrero, Maria Jesus
2016-07-01
We consider the classical deterministic susceptible-infective-susceptible epidemic model, where the infection and recovery rates depend on a background environmental process that is modeled by a continuous time Markov chain. This framework is able to capture several important characteristics that appear in the evolution of real epidemics in large populations, such as seasonality effects and environmental influences. We propose computational approaches for the determination of various distributions that quantify the evolution of the number of infectives in the population.
Deterministic generation of remote entanglement with active quantum feedback
NASA Astrophysics Data System (ADS)
Martin, Leigh; Motzoi, Felix; Li, Hanhan; Sarovar, Mohan; Whaley, K. Birgitta
2015-12-01
We consider the task of deterministically entangling two remote qubits using joint measurement and feedback, but no directly entangling Hamiltonian. In order to formulate the most effective experimentally feasible protocol, we introduce the notion of average-sense locally optimal feedback protocols, which do not require real-time quantum state estimation, a difficult component of real-time quantum feedback control. We use this notion of optimality to construct two protocols that can deterministically create maximal entanglement: a semiclassical feedback protocol for low-efficiency measurements and a quantum feedback protocol for high-efficiency measurements. The latter reduces to direct feedback in the continuous-time limit, whose dynamics can be modeled by a Wiseman-Milburn feedback master equation, which yields an analytic solution in the limit of unit measurement efficiency. Our formalism can smoothly interpolate between continuous-time and discrete-time descriptions of feedback dynamics and we exploit this feature to derive a superior hybrid protocol for arbitrary nonunit measurement efficiency that switches between quantum and semiclassical protocols. Finally, we show using simulations incorporating experimental imperfections that deterministic entanglement of remote superconducting qubits may be achieved with current technology using the continuous-time feedback protocol alone.
Probabilistic vs deterministic views in facing natural hazards
NASA Astrophysics Data System (ADS)
Arattano, Massimo; Coviello, Velio
2015-04-01
Natural hazards can be mitigated through active or passive measures. Among these latter countermeasures, Early Warning Systems (EWSs) are playing an increasing and significant role. In particular, a growing number of studies investigate the reliability of landslide EWSs, their comparability to alternative protection measures and their cost-effectiveness. EWSs, however, inevitably and intrinsically imply the concept of probability of occurrence and/or probability of error. Since a long time science has accepted and integrated the probabilistic nature of reality and its phenomena. The same cannot be told for other fields of knowledge, such as law or politics, with which scientists sometimes have to interact. These disciplines are in fact still linked to more deterministic views of life. The same is true for what is perceived by the public opinion, which often requires or even pretends a deterministic type of answer to its needs. So, as an example, it might be easy for people to feel completely safe because an EWS has been installed. It is also easy for an administrator or a politician to contribute to spread this wrong feeling, together with the idea of having dealt with the problem and done something definitive to face it. May geoethics play a role to create a link between the probabilistic world of nature and science and the tendency of the society to a more deterministic view of things? Answering this question could help scientists to feel more confident in planning and performing their research activities.
Non-equilibrium Thermodynamics of Piecewise Deterministic Markov Processes
NASA Astrophysics Data System (ADS)
Faggionato, A.; Gabrielli, D.; Ribezzi Crivellari, M.
2009-10-01
We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states ( x, σ)∈Ω×Γ, Ω being a region in ℝ d or the d-dimensional torus, Γ being a finite set. The continuous variable x follows a piecewise deterministic dynamics, the discrete variable σ evolves by a stochastic jump dynamics and the two resulting evolutions are fully-coupled. We study stationarity, reversibility and time-reversal symmetries of the process. Increasing the frequency of the σ-jumps, the system behaves asymptotically as deterministic and we investigate the structure of its fluctuations (i.e. deviations from the asymptotic behavior), recovering in a non Markovian frame results obtained by Bertini et al. (Phys. Rev. Lett. 87(4):040601, 2001; J. Stat. Phys. 107(3-4):635-675, 2002; J. Stat. Mech. P07014, 2007; Preprint available online at http://www.arxiv.org/abs/0807.4457, 2008), in the context of Markovian stochastic interacting particle systems. Finally, we discuss a Gallavotti-Cohen-type symmetry relation with involution map different from time-reversal.
How Does Quantum Uncertainty Emerge from Deterministic Bohmian Mechanics?
NASA Astrophysics Data System (ADS)
Solé, A.; Oriols, X.; Marian, D.; Zanghì, N.
2016-10-01
Bohmian mechanics is a theory that provides a consistent explanation of quantum phenomena in terms of point particles whose motion is guided by the wave function. In this theory, the state of a system of particles is defined by the actual positions of the particles and the wave function of the system; and the state of the system evolves deterministically. Thus, the Bohmian state can be compared with the state in classical mechanics, which is given by the positions and momenta of all the particles, and which also evolves deterministically. However, while in classical mechanics it is usually taken for granted and considered unproblematic that the state is, at least in principle, measurable, this is not the case in Bohmian mechanics. Due to the linearity of the quantum dynamical laws, one essential component of the Bohmian state, the wave function, is not directly measurable. Moreover, it turns out that the measurement of the other component of the state — the positions of the particles — must be mediated by the wave function; a fact that in turn implies that the positions of the particles, though measurable, are constrained by absolute uncertainty. This is the key to understanding how Bohmian mechanics, despite being deterministic, can account for all quantum predictions, including quantum randomness and uncertainty.
Iterative acceleration methods for Monte Carlo and deterministic criticality calculations
Urbatsch, T.J.
1995-11-01
If you have ever given up on a nuclear criticality calculation and terminated it because it took so long to converge, you might find this thesis of interest. The author develops three methods for improving the fission source convergence in nuclear criticality calculations for physical systems with high dominance ratios for which convergence is slow. The Fission Matrix Acceleration Method and the Fission Diffusion Synthetic Acceleration (FDSA) Method are acceleration methods that speed fission source convergence for both Monte Carlo and deterministic methods. The third method is a hybrid Monte Carlo method that also converges for difficult problems where the unaccelerated Monte Carlo method fails. The author tested the feasibility of all three methods in a test bed consisting of idealized problems. He has successfully accelerated fission source convergence in both deterministic and Monte Carlo criticality calculations. By filtering statistical noise, he has incorporated deterministic attributes into the Monte Carlo calculations in order to speed their source convergence. He has used both the fission matrix and a diffusion approximation to perform unbiased accelerations. The Fission Matrix Acceleration method has been implemented in the production code MCNP and successfully applied to a real problem. When the unaccelerated calculations are unable to converge to the correct solution, they cannot be accelerated in an unbiased fashion. A Hybrid Monte Carlo method weds Monte Carlo and a modified diffusion calculation to overcome these deficiencies. The Hybrid method additionally possesses reduced statistical errors.
Deterministic form correction of extreme freeform optical surfaces
NASA Astrophysics Data System (ADS)
Lynch, Timothy P.; Myer, Brian W.; Medicus, Kate; DeGroote Nelson, Jessica
2015-10-01
The blistering pace of recent technological advances has led lens designers to rely increasingly on freeform optical components as crucial pieces of their designs. As these freeform components increase in geometrical complexity and continue to deviate further from traditional optical designs, the optical manufacturing community must rethink their fabrication processes in order to keep pace. To meet these new demands, Optimax has developed a variety of new deterministic freeform manufacturing processes. Combining traditional optical fabrication techniques with cutting edge technological innovations has yielded a multifaceted manufacturing approach that can successfully handle even the most extreme freeform optical surfaces. In particular, Optimax has placed emphasis on refining the deterministic form correction process. By developing many of these procedures in house, changes can be implemented quickly and efficiently in order to rapidly converge on an optimal manufacturing method. Advances in metrology techniques allow for rapid identification and quantification of irregularities in freeform surfaces, while deterministic correction algorithms precisely target features on the part and drastically reduce overall correction time. Together, these improvements have yielded significant advances in the realm of freeform manufacturing. With further refinements to these and other aspects of the freeform manufacturing process, the production of increasingly radical freeform optical components is quickly becoming a reality.
Deterministic generation of remote entanglement with active quantum feedback
Martin, Leigh; Motzoi, Felix; Li, Hanhan; Sarovar, Mohan; Whaley, K. Birgitta
2015-12-10
We develop and study protocols for deterministic remote entanglement generation using quantum feedback, without relying on an entangling Hamiltonian. In order to formulate the most effective experimentally feasible protocol, we introduce the notion of average-sense locally optimal feedback protocols, which do not require real-time quantum state estimation, a difficult component of real-time quantum feedback control. We use this notion of optimality to construct two protocols that can deterministically create maximal entanglement: a semiclassical feedback protocol for low-efficiency measurements and a quantum feedback protocol for high-efficiency measurements. The latter reduces to direct feedback in the continuous-time limit, whose dynamics can be modeled by a Wiseman-Milburn feedback master equation, which yields an analytic solution in the limit of unit measurement efficiency. Our formalism can smoothly interpolate between continuous-time and discrete-time descriptions of feedback dynamics and we exploit this feature to derive a superior hybrid protocol for arbitrary nonunit measurement efficiency that switches between quantum and semiclassical protocols. Lastly, we show using simulations incorporating experimental imperfections that deterministic entanglement of remote superconducting qubits may be achieved with current technology using the continuous-time feedback protocol alone.
Deterministic generation of remote entanglement with active quantum feedback
Martin, Leigh; Motzoi, Felix; Li, Hanhan; ...
2015-12-10
We develop and study protocols for deterministic remote entanglement generation using quantum feedback, without relying on an entangling Hamiltonian. In order to formulate the most effective experimentally feasible protocol, we introduce the notion of average-sense locally optimal feedback protocols, which do not require real-time quantum state estimation, a difficult component of real-time quantum feedback control. We use this notion of optimality to construct two protocols that can deterministically create maximal entanglement: a semiclassical feedback protocol for low-efficiency measurements and a quantum feedback protocol for high-efficiency measurements. The latter reduces to direct feedback in the continuous-time limit, whose dynamics can bemore » modeled by a Wiseman-Milburn feedback master equation, which yields an analytic solution in the limit of unit measurement efficiency. Our formalism can smoothly interpolate between continuous-time and discrete-time descriptions of feedback dynamics and we exploit this feature to derive a superior hybrid protocol for arbitrary nonunit measurement efficiency that switches between quantum and semiclassical protocols. Lastly, we show using simulations incorporating experimental imperfections that deterministic entanglement of remote superconducting qubits may be achieved with current technology using the continuous-time feedback protocol alone.« less
Quantum chaos and holographic tensor models
NASA Astrophysics Data System (ADS)
Krishnan, Chethan; Sanyal, Sambuddha; Subramanian, P. N. Bala
2017-03-01
A class of tensor models were recently outlined as potentially calculable examples of holography: their perturbative large- N behavior is similar to the Sachdev-Ye-Kitaev (SYK) model, but they are fully quantum mechanical (in the sense that there is no quenched disorder averaging). These facts make them intriguing tentative models for quantum black holes. In this note, we explicitly diagonalize the simplest non-trivial Gurau-Witten tensor model and study its spectral and late-time properties. We find parallels to (a single sample of) SYK where some of these features were recently attributed to random matrix behavior and quantum chaos. In particular, the spectral form factor exhibits a dip-ramp-plateau structure after a running time average, in qualitative agreement with SYK. But we also observe that even though the spectrum has a unique ground state, it has a huge (quasi-?)degeneracy of intermediate energy states, not seen in SYK. If one ignores the delta function due to the degeneracies however, there is level repulsion in the unfolded spacing distribution hinting chaos. Furthermore, there are gaps in the spectrum. The system also has a spectral mirror symmetry which we trace back to the presence of a unitary operator with which the Hamiltonian anticommutes. We use it to argue that to the extent that the model exhibits random matrix behavior, it is controlled not by the Dyson ensembles, but by the BDI (chiral orthogonal) class in the Altland-Zirnbauer classification.
The dream's navel between chaos and thought.
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.
RAPID DYNAMICAL CHAOS IN AN EXOPLANETARY SYSTEM
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.
Examining topographic variability within chaos terrain on Europa
NASA Astrophysics Data System (ADS)
Patterson, G. W.; Prockter, L. M.; Schenk, P.
2008-12-01
Chaos terrain is a unique and prevalent surface feature on the Galilean satellite Europa that forms as a result of the disruption of subcircular regions of the satellite's surface. Evidence suggests that these features are endogenic and that they form via processes involving the interaction of a mobile substrate with a brittle surface. Based on the morphology and relative topography of prominent and well-imaged examples of chaos terrain, models have been proposed suggesting that the mobile substrate could be either liquid water or ductile ice. Using a digital elevation model (DEM) of Conamara Chaos, Schenk and Pappalardo (2004) alluded to the presence of several prominent domes within the margins of the feature. They concluded that this was best described by a formation mechanism for chaos involving the diapiric upwelling of a ductile ice substrate, with the coalescence of several individual diapirs in the shallow subsurface. To explore this result in more detail, we use Fourier analysis to examine the long-wavelength components of the topography of several regions of chaos utilizing DEMs of Europa's surface produced utilizing stereo-controlled photoclinometry. Through this analysis, we identify the presence, size, and distribution of domes within the boundaries of chaos terrain and, with this information, examine how topographic variability within chaos terrain can be used to constrain proposed formation mechanisms for this unique feature-type.
Quantum chaos in an ultrastrongly coupled bosonic junction.
Naether, Uta; García-Ripoll, Juan José; Mazo, Juan José; Zueco, David
2014-02-21
The semiclassical and quantum dynamics of two ultrastrongly coupled nonlinear resonators cannot be explained using the discrete nonlinear Schrödinger equation or the Bose-Hubbard model, respectively. Instead, a model beyond the rotating wave approximation must be studied. In the semiclassical limit this model is not integrable and becomes chaotic for a finite window of parameters. For the quantum dimer we find corresponding regions of stability and chaos. The more striking consequence for both semiclassical and quantum chaos is that the tunneling time between the sites becomes unpredictable. These results, including the transition to chaos, can be tested in experiments with superconducting microwave resonators.
Controlling spatiotemporal chaos in active dissipative-dispersive nonlinear systems
NASA Astrophysics Data System (ADS)
Gomes, S. N.; Pradas, M.; Kalliadasis, S.; Papageorgiou, D. T.; Pavliotis, G. A.
2015-08-01
We present an alternative methodology for the stabilization and control of infinite-dimensional dynamical systems exhibiting low-dimensional spatiotemporal chaos. We show that with an appropriate choice of time-dependent controls we are able to stabilize and/or control all stable or unstable solutions, including steady solutions, traveling waves (single and multipulse ones or bound states), and spatiotemporal chaos. We exemplify our methodology with the generalized Kuramoto-Sivashinsky equation, a paradigmatic model of spatiotemporal chaos, which is known to exhibit a rich spectrum of wave forms and wave transitions and a rich variety of spatiotemporal structures.
Transient chaos in two coupled, dissipatively perturbed Hamiltonian Duffing oscillators
NASA Astrophysics Data System (ADS)
Sabarathinam, S.; Thamilmaran, K.; Borkowski, L.; Perlikowski, P.; Brzeski, P.; Stefanski, A.; Kapitaniak, T.
2013-11-01
The dynamics of two coupled, dissipatively perturbed, near-integrable Hamiltonian, double-well Duffing oscillators has been studied. We give numerical and experimental (circuit implementation) evidence that in the case of small positive or negative damping there exist two different types of transient chaos. After the decay of the transient chaos in the neighborhood of chaotic saddle we observe the transient chaos in the neighborhood of unstable tori. We argue that our results are robust and they exist in the wide range of system parameters.
Comparison of probabilistic and deterministic fiber tracking of cranial nerves.
Zolal, Amir; Sobottka, Stephan B; Podlesek, Dino; Linn, Jennifer; Rieger, Bernhard; Juratli, Tareq A; Schackert, Gabriele; Kitzler, Hagen H
2016-12-16
OBJECTIVE The depiction of cranial nerves (CNs) using diffusion tensor imaging (DTI) is of great interest in skull base tumor surgery and DTI used with deterministic tracking methods has been reported previously. However, there are still no good methods usable for the elimination of noise from the resulting depictions. The authors have hypothesized that probabilistic tracking could lead to more accurate results, because it more efficiently extracts information from the underlying data. Moreover, the authors have adapted a previously described technique for noise elimination using gradual threshold increases to probabilistic tracking. To evaluate the utility of this new approach, a comparison is provided with this work between the gradual threshold increase method in probabilistic and deterministic tracking of CNs. METHODS Both tracking methods were used to depict CNs II, III, V, and the VII+VIII bundle. Depiction of 240 CNs was attempted with each of the above methods in 30 healthy subjects, which were obtained from 2 public databases: the Kirby repository (KR) and Human Connectome Project (HCP). Elimination of erroneous fibers was attempted by gradually increasing the respective thresholds (fractional anisotropy [FA] and probabilistic index of connectivity [PICo]). The results were compared with predefined ground truth images based on corresponding anatomical scans. Two label overlap measures (false-positive error and Dice similarity coefficient) were used to evaluate the success of both methods in depicting the CN. Moreover, the differences between these parameters obtained from the KR and HCP (with higher angular resolution) databases were evaluated. Additionally, visualization of 10 CNs in 5 clinical cases was attempted with both methods and evaluated by comparing the depictions with intraoperative findings. RESULTS Maximum Dice similarity coefficients were significantly higher with probabilistic tracking (p < 0.001; Wilcoxon signed-rank test). The false
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)
DETERMINISTIC PRODUCTION PLANNING WITH CONCAVE COSTS AND CAPACITY CONSTRAINTS.
INDUSTRIAL PRODUCTION , MANAGEMENT PLANNING AND CONTROL), (*PRODUCTION CONTROL, DYNAMIC PROGRAMMING), INVENTORY ANALYSIS, SCHEDULING, COST EFFECTIVENESS, STORAGE, MANPOWER, OPTIMIZATION, MATHEMATICAL MODELS, ALGORITHMS
Encryption key distribution via chaos synchronization
Keuninckx, Lars; Soriano, Miguel C.; Fischer, Ingo; Mirasso, Claudio R.; Nguimdo, Romain M.; Van der Sande, Guy
2017-01-01
We present a novel encryption scheme, wherein an encryption key is generated by two distant complex nonlinear units, forced into synchronization by a chaotic driver. The concept is sufficiently generic to be implemented on either photonic, optoelectronic or electronic platforms. The method for generating the key bitstream from the chaotic signals is reconfigurable. Although derived from a deterministic process, the obtained bit series fulfill the randomness conditions as defined by the National Institute of Standards test suite. We demonstrate the feasibility of our concept on an electronic delay oscillator circuit and test the robustness against attacks using a state-of-the-art system identification method. PMID:28233876
Encryption key distribution via chaos synchronization.
Keuninckx, Lars; Soriano, Miguel C; Fischer, Ingo; Mirasso, Claudio R; Nguimdo, Romain M; Van der Sande, Guy
2017-02-24
We present a novel encryption scheme, wherein an encryption key is generated by two distant complex nonlinear units, forced into synchronization by a chaotic driver. The concept is sufficiently generic to be implemented on either photonic, optoelectronic or electronic platforms. The method for generating the key bitstream from the chaotic signals is reconfigurable. Although derived from a deterministic process, the obtained bit series fulfill the randomness conditions as defined by the National Institute of Standards test suite. We demonstrate the feasibility of our concept on an electronic delay oscillator circuit and test the robustness against attacks using a state-of-the-art system identification method.
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
Chaos and microbial systems. Final project report, July 1989--July 1992
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.
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.
NASA Astrophysics Data System (ADS)
Cottrill, Gerald C.
A hybrid numerical algorithm combining the Gauss Pseudospectral Method (GPM) with a Generalized Polynomial Chaos (gPC) method to solve nonlinear stochastic optimal control problems with constraint uncertainties is presented. TheGPM and gPC have been shown to be spectrally accurate numerical methods for solving deterministic optimal control problems and stochastic differential equations, respectively. The gPC uses collocation nodes to sample the random space, which are then inserted into the differential equations and solved by applying standard differential equation methods. The resulting set of deterministic solutions is used to characterize the distribution of the solution by constructing a polynomial representation of the output as a function of uncertain parameters. Optimal control problems are especially challenging to solve since they often include path constraints, bounded controls, boundary conditions, and require solutions that minimize a cost functional. Adding random parameters can make these problems even more challenging. The hybrid algorithm presented in this dissertation is the first time the GPM and gPC algorithms have been combined to solve optimal control problems with random parameters. Using the GPM in the gPC construct provides minimum cost deterministic solutions used in stochastic computations that meet path, control, and boundary constraints, thus extending current gPC methods to be applicable to stochastic optimal control problems. The hybrid GPM-gPC algorithm was applied to two concept demonstration problems: a nonlinear optimal control problem with multiplicative uncertain elements and a trajectory optimization problem simulating an aircraft flying through a threat field where exact locations of the threats are unknown. The results show that the expected value, variance, and covariance statistics of the polynomial output function approximations of the state, control, cost, and terminal time variables agree with Monte-Carlo simulation
ERIC Educational Resources Information Center
Bossé, Michael J.; Adu-Gyamfi, Kwaku; Chandler, Kayla; Lynch-Davis, Kathleen
2016-01-01
Dynamic mathematical environments allow users to reify mathematical concepts through multiple representations, transform mathematical relations and organically explore mathematical properties, investigate integrated mathematics, and develop conceptual understanding. Herein, we integrate Boolean algebra, the functionalities of a dynamic…
Steady induction effects in geomagnetism. Part 1A: Steady motional induction of geomagnetic chaos
NASA Technical Reports Server (NTRS)
Voorhies, Coerte V.
1992-01-01
Geomagnetic effects of magnetic induction by hypothetically steady fluid motion and steady magnetic flux diffusion near the top of Earth's core are investigated using electromagnetic theory, simple magnetic earth models, and numerical experiments with geomagnetic field models. The problem of estimating a steady fluid velocity field near the top of Earth's core which induces the secular variation indicated by broad-scale models of the observed geomagnetic field is examined and solved. In Part 1, the steady surficial core flow estimation problem is solved in the context of the source-free mantle/frozen-flux core model. In the first paper (IA), the theory underlying such estimates is reviewed and some consequences of various kinematic and dynamic flow hypotheses are derived. For a frozen-flux core, fluid downwelling is required to change the mean square normal magnetic flux density averaged over the core-mantle boundary. For surficially geostrophic flow, downwelling implies poleward flow. The solution of the forward steady motional induction problem at the surface of a frozen-flux core is derived and found to be a fine, easily visualized example of deterministic chaos. Geomagnetic effects of statistically steady core surface flow may well dominate secular variation over several decades. Indeed, effects of persistent, if not steady, surficially geostrophic core flow are described which may help explain certain features of the present broad-scale geomagnetic field and perhaps paleomagnetic secular variation.
Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems
Marzouk, Youssef M. Najm, Habib N.
2009-04-01
We consider a Bayesian approach to nonlinear inverse problems in which the unknown quantity is a spatial or temporal field, endowed with a hierarchical Gaussian process prior. Computational challenges in this construction arise from the need for repeated evaluations of the forward model (e.g., in the context of Markov chain Monte Carlo) and are compounded by high dimensionality of the posterior. We address these challenges by introducing truncated Karhunen-Loeve expansions, based on the prior distribution, to efficiently parameterize the unknown field and to specify a stochastic forward problem whose solution captures that of the deterministic forward model over the support of the prior. We seek a solution of this problem using Galerkin projection on a polynomial chaos basis, and use the solution to construct a reduced-dimensionality surrogate posterior density that is inexpensive to evaluate. We demonstrate the formulation on a transient diffusion equation with prescribed source terms, inferring the spatially-varying diffusivity of the medium from limited and noisy data.
Non-monotonic temperature dependence of chaos-assisted diffusion in driven periodic systems
NASA Astrophysics Data System (ADS)
Spiechowicz, J.; Talkner, P.; Hänggi, P.; Łuczka, J.
2016-12-01
The spreading of a cloud of independent Brownian particles typically proceeds more effectively at higher temperatures, as it derives from the commonly known Sutherland-Einstein relation for systems in thermal equilibrium. Here, we report on a non-equilibrium situation in which the diffusion of a periodically driven Brownian particle moving in a periodic potential decreases with increasing temperature within a finite temperature window. We identify as the cause for this non-intuitive behaviour a dominant deterministic mechanism consisting of a few unstable periodic orbits embedded into a chaotic attractor together with thermal noise-induced dynamical changes upon varying temperature. The presented analysis is based on extensive numerical simulations of the corresponding Langevin equation describing the studied setup as well as on a simplified stochastic model formulated in terms of a three-state Markovian process. Because chaos exists in many natural as well as in artificial systems representing abundant areas of contemporary knowledge, the described mechanism may potentially be discovered in plentiful different contexts.
Dynamics of hourly sea level at Hillarys Boat Harbour, Western Australia: a chaos theory perspective
NASA Astrophysics Data System (ADS)
Khatibi, Rahman; Ghorbani, Mohammad Ali; Aalami, Mohammad Taghi; Kocak, Kasim; Makarynskyy, Oleg; Makarynska, Dina; Aalinezhad, Mahdi
2011-11-01
Water level forecasting using recorded time series can provide a local modelling capability to facilitate local proactive management practices. To this end, hourly sea water level time series are investigated. The records collected at the Hillarys Boat Harbour, Western Australia, are investigated over the period of 2000 and 2002. Two modelling techniques are employed: low-dimensional dynamic model, known as the deterministic chaos theory, and genetic programming, GP. The phase space, which describes the evolution of the behaviour of a nonlinear system in time, was reconstructed using the delay-embedding theorem suggested by Takens. The presence of chaotic signals in the data was identified by the phase space reconstruction and correlation dimension methods, and also the predictability into the future was calculated by the largest Lyapunov exponent to be 437 h or 18 days into the future. The intercomparison of results of the local prediction and GP models shows that for this site-specific dataset, the local prediction model has a slight edge over GP. However, rather than recommending one technique over another, the paper promotes a pluralistic modelling culture, whereby different techniques should be tested to gain a specific insight from each of the models. This would enable a consensus to be drawn from a set of results rather than ignoring the individual insights provided by each model.
Mathematical wit and mathematical cognition.
Aberdein, Andrew
2013-04-01
The published works of scientists often conceal the cognitive processes that led to their results. Scholars of mathematical practice must therefore seek out less obvious sources. This article analyzes a widely circulated mathematical joke, comprising a list of spurious proof types. An account is proposed in terms of argumentation schemes: stereotypical patterns of reasoning, which may be accompanied by critical questions itemizing possible lines of defeat. It is argued that humor is associated with risky forms of inference, which are essential to creative mathematics. The components of the joke are explicated by argumentation schemes devised for application to topic-neutral reasoning. These in turn are classified under seven headings: retroduction, citation, intuition, meta-argument, closure, generalization, and definition. Finally, the wider significance of this account for the cognitive science of mathematics is discussed.
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
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.
Extension of spatiotemporal chaos in glow discharge-semiconductor systems
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).].
Controlling spatiotemporal chaos in chains of dissipative Kapitza pendula.
Chacón, R; Marcheggiani, L
2010-07-01
The control of chaos (suppression and enhancement) of a damped pendulum subjected to two perpendicular periodic excitations of its pivot (one chaos inducing and the other chaos controlling) is investigated. Analytical (Melnikov analysis) and numerical (Lyapunov exponents) results show that the initial phase difference between the two excitations plays a fundamental role in the control scenario. We demonstrate the effectiveness of the method in suppressing spatiotemporal chaos of chains of identical chaotic coupled pendula where homogeneous regularization is obtained under localized control on a minimal number of pendula. Additionally, we demonstrate the robustness of the control scenario against changes in the coupling function. In particular, synchronization-induced homogeneous regularization of chaotic chains can be highly enhanced by considering time-varying couplings instead of stationary couplings.
Quasiperiodicity route to chaos in cardiac conduction model
NASA Astrophysics Data System (ADS)
Quiroz-Juárez, M. A.; Vázquez-Medina, R.; Ryzhii, E.; Ryzhii, M.; Aragón, J. L.
2017-01-01
It has been suggested that cardiac arrhythmias are instances of chaos. In particular that the ventricular fibrillation is a form of spatio-temporal chaos that arises from normal rhythm through a quasi-periodicity or Ruelle-Takens-Newhouse route to chaos. In this work, we modify the heterogeneous oscillator model of cardiac conduction system proposed in Ref. [Ryzhii E, Ryzhii M. A heterogeneous coupled oscillator model for simulation of ECG signals. Comput Meth Prog Bio 2014;117(1):40-49. doi:10.1016/j.cmpb.2014.04.009.], by including an ectopic pacemaker that stimulates the ventricular muscle to model arrhythmias. With this modification, the transition from normal rhythm to ventricular fibrillation is controlled by a single parameter. We show that this transition follows the so-called torus of quasi-periodic route to chaos, as verified by using numerical tools such as power spectrum and largest Lyapunov exponent.
Numerical and experimental exploration of phase control of chaos.
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.
Extension of spatiotemporal chaos in glow discharge-semiconductor systems.
Akhmet, Marat; Rafatov, Ismail; Fen, Mehmet Onur
2014-12-01
Generation of chaos in response systems is discovered numerically through specially designed unidirectional coupling of two glow discharge-semiconductor systems. By utilizing the auxiliary system approach, [H. D. I. Abarbanel, N. F. Rulkov, and M. M. Sushchik, Phys. Rev. E 53, 4528-4535 (1996)] it is verified that the phenomenon is not a chaos synchronization. Simulations demonstrate various aspects of the chaos appearance in both drive and response systems. Chaotic control is through the external circuit equation and governs the electrical potential on the boundary. The expandability of the theory to collectives of glow discharge systems is discussed, and this increases the potential of applications of the results. Moreover, the research completes the previous discussion of the chaos appearance in a glow discharge-semiconductor system [D. D. Šijačić U. Ebert, and I. Rafatov, Phys. Rev. E 70, 056220 (2004).].
Inducing chaos by resonant perturbations: theory and experiment.
Lai, Ying-Cheng; Kandangath, Anil; Krishnamoorthy, Satish; Gaudet, John A; de Moura, Alessandro P S
2005-06-03
We propose a scheme to induce chaos in nonlinear oscillators that either are by themselves incapable of exhibiting chaos or are far away from parameter regions of chaotic behaviors. Our idea is to make use of small, judiciously chosen perturbations in the form of weak periodic signals with time-varying frequency and phase, and to drive the system into a hierarchy of nonlinear resonant states and eventually into chaos. We demonstrate this method by using numerical examples and a laboratory experiment with a Duffing type of electronic circuit driven by a phase-locked loop. The phase-locked loop can track the instantaneous frequency and phase of the Duffing circuit and deliver resonant perturbations to generate robust chaos.
Computational chaos in massively parallel neural networks
NASA Technical Reports Server (NTRS)
Barhen, Jacob; Gulati, Sandeep
1989-01-01
A fundamental issue which directly impacts the scalability of current theoretical neural network models to massively parallel embodiments, in both software as well as hardware, is the inherent and unavoidable concurrent asynchronicity of emerging fine-grained computational ensembles and the possible emergence of chaotic manifestations. Previous analyses attributed dynamical instability to the topology of the interconnection matrix, to parasitic components or to propagation delays. However, researchers have observed the existence of emergent computational chaos in a concurrently asynchronous framework, independent of the network topology. Researcher present a methodology enabling the effective asynchronous operation of large-scale neural networks. Necessary and sufficient conditions guaranteeing concurrent asynchronous convergence are established in terms of contracting operators. Lyapunov exponents are computed formally to characterize the underlying nonlinear dynamics. Simulation results are presented to illustrate network convergence to the correct results, even in the presence of large delays.
Control of neural chaos by synaptic noise.
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.
Chaos, fractals, and our concept of disease.
Varela, Manuel; Ruiz-Esteban, Raul; Mestre de Juan, Maria Jose
2010-01-01
The classic anatomo-clinic paradigm based on clinical syndromes is fraught with problems. Nevertheless, for multiple reasons, clinicians are reluctant to embrace a more pathophysiological approach, even though this is the prevalent paradigm under "which basic sciences work. In recent decades, nonlinear dynamics ("chaos theory") and fractal geometry have provided powerful new tools to analyze physiological systems. However, these tools are embedded in the pathophysiological perspective and are not easily translated to our classic syndromes. This article comments on the problems raised by the conventional anatomo-clinic paradigm and reviews three areas in which the influence of nonlinear dynamics and fractal geometry can be especially prominent: disease as a loss of complexity, the idea of homeostasis, and fractals in pathology.
Adaptive functional systems: learning with chaos.
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.
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).
Chaos computing in terms of periodic orbits.
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.