Iceberg Ahead: The Effect of Bands and Ridges During Chaos Formation on Europa.

NASA Astrophysics Data System (ADS)

Hedgepeth, J. E.; Schmidt, B. E.

2016-12-01

Europa presents a dynamic and varied surface, but the most enticing component is arguably its chaos structures. With it, the surface and subsurface can interact, but in order to fully understand if this is occurring we have to properly parameterize the surface structural integrity. We consider the Schmidt et al. (2011) method of classifying icebergs by feature type to study what features remained intact in the chaos matrix. In this work we expand on this idea. We hypothesize that the ice that forms ridges and bands exhibit higher structural strengths than plains. Subsequently, this ice is more likely to remain during chaos formation in the form of icebergs. We begin by mapping the surface around Murias chaos and other prominent chaos features. Maps are used to infer what paleo-topographic features existed before chaos formation by using the features surrounding the chaos regions as blueprints for what existed before. We perform a multivariate regression to correlate the amount of icebergs present to the amount of surface that was covered by either bands, plains, or ridges. We find ridges play the biggest role in the production of icebergs with a weighted value of 40%. Bands may play a smaller role (13%), but plains show little to no correlation (5%). Further mapping will better reveal if this trend holds true in other regions. This statistical analysis supports our hypothesis, and further work will better quantify what is occurring. We will address the energy expended in the chaos regions via movement and rotation of icebergs during the formation event and through ice-melt.

Computational complexity of symbolic dynamics at the onset of chaos

NASA Astrophysics Data System (ADS)

Lakdawala, Porus

1996-05-01

In a variety of studies of dynamical systems, the edge of order and chaos has been singled out as a region of complexity. It was suggested by Wolfram, on the basis of qualitative behavior of cellular automata, that the computational basis for modeling this region is the universal Turing machine. In this paper, following a suggestion of Crutchfield, we try to show that the Turing machine model may often be too powerful as a computational model to describe the boundary of order and chaos. In particular we study the region of the first accumulation of period doubling in unimodal and bimodal maps of the interval, from the point of view of language theory. We show that in relation to the ``extended'' Chomsky hierarchy, the relevant computational model in the unimodal case is the nested stack automaton or the related indexed languages, while the bimodal case is modeled by the linear bounded automaton or the related context-sensitive languages.

Disordered wires and quantum chaos in a momentum-space lattice

NASA Astrophysics Data System (ADS)

Meier, Eric; An, Fangzhao; Angonga, Jackson; Gadway, Bryce

2017-04-01

We present two topics: topological wires subjected to disorder and quantum chaos in a spin-J model. These studies are experimentally realized through the use of a momentum-space lattice, in which the dynamics of 87Rb atoms are recorded. In topological wires, a transition to a trivial phase is seen when disorder is applied to either the tunneling strengths or site energies. This transition is detected using both charge-pumping and Hamiltonian-quenching techniques. In the spin-J study we observe the effects of both linear and non-linear spin operations by measuring the linear entropy of the system as well as the out-of-time order correlation function. We further probe the chaotic signatures of the paradigmatic kicked top model.

Conway's Game of Life is a near-critical metastable state in the multiverse of cellular automata.

PubMed

Reia, Sandro M; Kinouchi, Osame

2014-05-01

Conway's cellular automaton Game of Life has been conjectured to be a critical (or quasicritical) dynamical system. This criticality is generally seen as a continuous order-disorder transition in cellular automata (CA) rule space. Life's mean-field return map predicts an absorbing vacuum phase (ρ = 0) and an active phase density, with ρ = 0.37, which contrasts with Life's absorbing states in a square lattice, which have a stationary density of ρ(2D) ≈ 0.03. Here, we study and classify mean-field maps for 6144 outer-totalistic CA and compare them with the corresponding behavior found in the square lattice. We show that the single-site mean-field approach gives qualitative (and even quantitative) predictions for most of them. The transition region in rule space seems to correspond to a nonequilibrium discontinuous absorbing phase transition instead of a continuous order-disorder one. We claim that Life is a quasicritical nucleation process where vacuum phase domains invade the alive phase. Therefore, Life is not at the "border of chaos," but thrives on the "border of extinction."

Conway's game of life is a near-critical metastable state in the multiverse of cellular automata

NASA Astrophysics Data System (ADS)

Reia, Sandro M.; Kinouchi, Osame

2014-05-01

Conway's cellular automaton Game of Life has been conjectured to be a critical (or quasicritical) dynamical system. This criticality is generally seen as a continuous order-disorder transition in cellular automata (CA) rule space. Life's mean-field return map predicts an absorbing vacuum phase (ρ =0) and an active phase density, with ρ =0.37, which contrasts with Life's absorbing states in a square lattice, which have a stationary density of ρ2D≈0.03. Here, we study and classify mean-field maps for 6144 outer-totalistic CA and compare them with the corresponding behavior found in the square lattice. We show that the single-site mean-field approach gives qualitative (and even quantitative) predictions for most of them. The transition region in rule space seems to correspond to a nonequilibrium discontinuous absorbing phase transition instead of a continuous order-disorder one. We claim that Life is a quasicritical nucleation process where vacuum phase domains invade the alive phase. Therefore, Life is not at the "border of chaos," but thrives on the "border of extinction."

Observation and Control of Hamiltonian Chaos in Wave-particle Interaction

NASA Astrophysics Data System (ADS)

Doveil, F.; Elskens, Y.; Ruzzon, A.

2010-11-01

Wave-particle interactions are central in plasma physics. The paradigm beam-plasma system can be advantageously replaced by a traveling wave tube (TWT) to allow their study in a much less noisy environment. This led to detailed analysis of the self-consistent interaction between unstable waves and an either cold or warm electron beam. More recently a test cold beam has been used to observe its interaction with externally excited wave(s). This allowed observing the main features of Hamiltonian chaos and testing a new method to efficiently channel chaotic transport in phase space. To simulate accurately and efficiently the particle dynamics in the TWT and other 1D particle-wave systems, a new symplectic, symmetric, second order numerical algorithm is developed, using particle position as the independent variable, with a fixed spatial step. This contribution reviews : presentation of the TWT and its connection to plasma physics, resonant interaction of a charged particle in electrostatic waves, observation of particle trapping and transition to chaos, test of control of chaos, and description of the simulation algorithm. The velocity distribution function of the electron beam is recorded with a trochoidal energy analyzer at the output of the TWT. An arbitrary waveform generator is used to launch a prescribed spectrum of waves along the 4m long helix of the TWT. The nonlinear synchronization of particles by a single wave, responsible for Landau damping, is observed. We explore the resonant velocity domain associated with a single wave as well as the transition to large scale chaos when the resonant domains of two waves and their secondary resonances overlap. This transition exhibits a devil's staircase behavior when increasing the excitation level in agreement with numerical simulation. A new strategy for control of chaos by building barriers of transport in phase space as well as its robustness is successfully tested. The underlying concepts extend far beyond the field of electron devices and plasma physics.

Activity induces traveling waves, vortices and spatiotemporal chaos in a model actomyosin layer

NASA Astrophysics Data System (ADS)

Ramaswamy, Rajesh; Jülicher, Frank

2016-02-01

Inspired by the actomyosin cortex in biological cells, we investigate the spatiotemporal dynamics of a model describing a contractile active polar fluid sandwiched between two external media. The external media impose frictional forces at the interface with the active fluid. The fluid is driven by a spatially-homogeneous activity measuring the strength of the active stress that is generated by processes consuming a chemical fuel. We observe that as the activity is increased over two orders of magnitude the active polar fluid first shows spontaneous flow transition followed by transition to oscillatory dynamics with traveling waves and traveling vortices in the flow field. In the flow-tumbling regime, the active polar fluid also shows transition to spatiotemporal chaos at sufficiently large activities. These results demonstrate that level of activity alone can be used to tune the operating point of actomyosin layers with qualitatively different spatiotemporal dynamics.

Theoretical analysis of cross-talking signals between counter-streaming electron beams in a vacuum tube oscillator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shin, Y.M.; Ryskin, N.M.; Won, J.H.

The basic theory of cross-talking signals between counter-streaming electron beams in a vacuum tube oscillator consisting of two two-cavity klystron amplifiers reversely coupled through input/output slots is theoretically investigated. Application of Kirchhoff's laws to the coupled equivalent RLC circuit model of the device provides four nonlinear coupled equations, which are the first-order time-delayed differential equations. Analytical solutions obtained through linearization of the equations provide oscillation frequencies and thresholds of four fundamental eigenstates, symmetric/antisymmetric 0/{pi} modes. Time-dependent output signals are numerically analyzed with variation of the beam current, and a self-modulation mechanism and transition to chaos scenario are examined. The oscillatormore » shows a much stronger multistability compared to a delayed feedback klystron oscillator owing to the competitions among more diverse eigenmodes. A fully developed chaos region also appears at a relatively lower beam current, {approx}3.5I{sub st}, compared to typical vacuum tube oscillators (10-100I{sub st}), where I{sub st} is a start-oscillation current.« less

Above Saddle-Point Regions of Order in a Sea of Chaos in the Vibrational Dynamics of KCN.

PubMed

Párraga, H; Arranz, F J; Benito, R M; Borondo, F

2018-04-05

The dynamical characteristics of a region of regular vibrational motion in the sea of chaos above the saddle point corresponding to the linear C-N-K configuration is examined in detail. To explain the origin of this regularity, the associated phase space structures were characterized using suitably defined Poincaré surfaces of section, identifying the different resonances between the stretching and bending modes, as a function of excitation energy. The corresponding topology is elucidated by means of periodic orbit analysis.

Transient chaos - a resolution of breakdown of quantum-classical correspondence in optomechanics.

PubMed

Wang, Guanglei; Lai, Ying-Cheng; Grebogi, Celso

2016-10-17

Recently, the phenomenon of quantum-classical correspondence breakdown was uncovered in optomechanics, where in the classical regime the system exhibits chaos but in the corresponding quantum regime the motion is regular - there appears to be no signature of classical chaos whatsoever in the corresponding quantum system, generating a paradox. We find that transient chaos, besides being a physically meaningful phenomenon by itself, provides a resolution. Using the method of quantum state diffusion to simulate the system dynamics subject to continuous homodyne detection, we uncover transient chaos associated with quantum trajectories. The transient behavior is consistent with chaos in the classical limit, while the long term evolution of the quantum system is regular. Transient chaos thus serves as a bridge for the quantum-classical transition (QCT). Strikingly, as the system transitions from the quantum to the classical regime, the average chaotic transient lifetime increases dramatically (faster than the Ehrenfest time characterizing the QCT for isolated quantum systems). We develop a physical theory to explain the scaling law.

Transient chaos - a resolution of breakdown of quantum-classical correspondence in optomechanics

PubMed Central

Wang, Guanglei; Lai, Ying-Cheng; Grebogi, Celso

2016-01-01

Recently, the phenomenon of quantum-classical correspondence breakdown was uncovered in optomechanics, where in the classical regime the system exhibits chaos but in the corresponding quantum regime the motion is regular - there appears to be no signature of classical chaos whatsoever in the corresponding quantum system, generating a paradox. We find that transient chaos, besides being a physically meaningful phenomenon by itself, provides a resolution. Using the method of quantum state diffusion to simulate the system dynamics subject to continuous homodyne detection, we uncover transient chaos associated with quantum trajectories. The transient behavior is consistent with chaos in the classical limit, while the long term evolution of the quantum system is regular. Transient chaos thus serves as a bridge for the quantum-classical transition (QCT). Strikingly, as the system transitions from the quantum to the classical regime, the average chaotic transient lifetime increases dramatically (faster than the Ehrenfest time characterizing the QCT for isolated quantum systems). We develop a physical theory to explain the scaling law. PMID:27748418

Comparative Analysis of Light-Harvesting Antennae and State Transition in chlorina and cpSRP Mutants.

PubMed

Wang, Peng; Grimm, Bernhard

2016-11-01

State transitions in photosynthesis provide for the dynamic allocation of a mobile fraction of light-harvesting complex II (LHCII) to photosystem II (PSII) in state I and to photosystem I (PSI) in state II. In the state I-to-state II transition, LHCII is phosphorylated by STN7 and associates with PSI to favor absorption cross-section of PSI. Here, we used Arabidopsis (Arabidopsis thaliana) mutants with defects in chlorophyll (Chl) b biosynthesis or in the chloroplast signal recognition particle (cpSRP) machinery to study the flexible formation of PS-LHC supercomplexes. Intriguingly, we found that impaired Chl b biosynthesis in chlorina1-2 (ch1-2) led to preferentially stabilized LHCI rather than LHCII, while the contents of both LHCI and LHCII were equally depressed in the cpSRP43-deficient mutant (chaos). In view of recent findings on the modified state transitions in LHCI-deficient mutants (Benson et al., 2015), the ch1-2 and chaos mutants were used to assess the influence of varying LHCI/LHCII antenna size on state transitions. Under state II conditions, LHCII-PSI supercomplexes were not formed in both ch1-2 and chaos plants. LHCII phosphorylation was drastically reduced in ch1-2, and the inactivation of STN7 correlates with the lack of state transitions. In contrast, phosphorylated LHCII in chaos was observed to be exclusively associated with PSII complexes, indicating a lack of mobile LHCII in chaos Thus, the comparative analysis of ch1-2 and chaos mutants provides new evidence for the flexible organization of LHCs and enhances our understanding of the reversible allocation of LHCII to the two photosystems. © 2016 American Society of Plant Biologists. All Rights Reserved.

Comparative Analysis of Light-Harvesting Antennae and State Transition in chlorina and cpSRP Mutants1[OPEN

PubMed Central

Wang, Peng

2016-01-01

State transitions in photosynthesis provide for the dynamic allocation of a mobile fraction of light-harvesting complex II (LHCII) to photosystem II (PSII) in state I and to photosystem I (PSI) in state II. In the state I-to-state II transition, LHCII is phosphorylated by STN7 and associates with PSI to favor absorption cross-section of PSI. Here, we used Arabidopsis (Arabidopsis thaliana) mutants with defects in chlorophyll (Chl) b biosynthesis or in the chloroplast signal recognition particle (cpSRP) machinery to study the flexible formation of PS-LHC supercomplexes. Intriguingly, we found that impaired Chl b biosynthesis in chlorina1-2 (ch1-2) led to preferentially stabilized LHCI rather than LHCII, while the contents of both LHCI and LHCII were equally depressed in the cpSRP43-deficient mutant (chaos). In view of recent findings on the modified state transitions in LHCI-deficient mutants (Benson et al., 2015), the ch1-2 and chaos mutants were used to assess the influence of varying LHCI/LHCII antenna size on state transitions. Under state II conditions, LHCII-PSI supercomplexes were not formed in both ch1-2 and chaos plants. LHCII phosphorylation was drastically reduced in ch1-2, and the inactivation of STN7 correlates with the lack of state transitions. In contrast, phosphorylated LHCII in chaos was observed to be exclusively associated with PSII complexes, indicating a lack of mobile LHCII in chaos. Thus, the comparative analysis of ch1-2 and chaos mutants provides new evidence for the flexible organization of LHCs and enhances our understanding of the reversible allocation of LHCII to the two photosystems. PMID:27663408

Weak and strong chaos in Fermi-Pasta-Ulam models and beyond.

PubMed

Pettini, Marco; Casetti, Lapo; Cerruti-Sola, Monica; Franzosi, Roberto; Cohen, E G D

2005-03-01

We briefly review some of the most relevant results that our group obtained in the past, while investigating the dynamics of the Fermi-Pasta-Ulam (FPU) models. The first result is the numerical evidence of the existence of two different kinds of transitions in the dynamics of the FPU models: (i) A stochasticity threshold (ST), characterized by a value of the energy per degree of freedom below which the overwhelming majority of the phase space trajectories are regular (vanishing Lyapunov exponents). It tends to vanish as the number N of degrees of freedom is increased. (ii) A strong stochasticity threshold (SST), characterized by a value of the energy per degree of freedom at which a crossover appears between two different power laws of the energy dependence of the largest Lyapunov exponent, which phenomenologically corresponds to the transition between weak and strong chaotic regimes. It is stable with N. The second result is the development of a Riemannian geometric theory to explain the origin of Hamiltonian chaos. Starting this theory has been motivated by the inadequacy of the approach based on homoclinic intersections to explain the origin of chaos in systems of arbitrarily large N, or arbitrarily far from quasi-integrability, or displaying a transition between weak and strong chaos. Finally, the third result stems from the search for the transition between weak and strong chaos in systems other than FPU. Actually, we found that a very sharp SST appears as the dynamical counterpart of a thermodynamic phase transition, which in turn has led, in the light of the Riemannian theory of chaos, to the development of a topological theory of phase transitions.

Weak and strong chaos in Fermi-Pasta-Ulam models and beyond

NASA Astrophysics Data System (ADS)

Pettini, Marco; Casetti, Lapo; Cerruti-Sola, Monica; Franzosi, Roberto; Cohen, E. G. D.

2005-03-01

We briefly review some of the most relevant results that our group obtained in the past, while investigating the dynamics of the Fermi-Pasta-Ulam (FPU) models. The first result is the numerical evidence of the existence of two different kinds of transitions in the dynamics of the FPU models: (i) A stochasticity threshold (ST), characterized by a value of the energy per degree of freedom below which the overwhelming majority of the phase space trajectories are regular (vanishing Lyapunov exponents). It tends to vanish as the number N of degrees of freedom is increased. (ii) A strong stochasticity threshold (SST), characterized by a value of the energy per degree of freedom at which a crossover appears between two different power laws of the energy dependence of the largest Lyapunov exponent, which phenomenologically corresponds to the transition between weak and strong chaotic regimes. It is stable with N. The second result is the development of a Riemannian geometric theory to explain the origin of Hamiltonian chaos. Starting this theory has been motivated by the inadequacy of the approach based on homoclinic intersections to explain the origin of chaos in systems of arbitrarily large N, or arbitrarily far from quasi-integrability, or displaying a transition between weak and strong chaos. Finally, the third result stems from the search for the transition between weak and strong chaos in systems other than FPU. Actually, we found that a very sharp SST appears as the dynamical counterpart of a thermodynamic phase transition, which in turn has led, in the light of the Riemannian theory of chaos, to the development of a topological theory of phase transitions.

A phase transition induces chaos in a predator-prey ecosystem with a dynamic fitness landscape.

PubMed

Gilpin, William; Feldman, Marcus W

2017-07-01

In many ecosystems, natural selection can occur quickly enough to influence the population dynamics and thus future selection. This suggests the importance of extending classical population dynamics models to include such eco-evolutionary processes. Here, we describe a predator-prey model in which the prey population growth depends on a prey density-dependent fitness landscape. We show that this two-species ecosystem is capable of exhibiting chaos even in the absence of external environmental variation or noise, and that the onset of chaotic dynamics is the result of the fitness landscape reversibly alternating between epochs of stabilizing and disruptive selection. We draw an analogy between the fitness function and the free energy in statistical mechanics, allowing us to use the physical theory of first-order phase transitions to understand the onset of rapid cycling in the chaotic predator-prey dynamics. We use quantitative techniques to study the relevance of our model to observational studies of complex ecosystems, finding that the evolution-driven chaotic dynamics confer community stability at the "edge of chaos" while creating a wide distribution of opportunities for speciation during epochs of disruptive selection-a potential observable signature of chaotic eco-evolutionary dynamics in experimental studies.

Does chaos assist localization or delocalization?

PubMed

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

2014-12-01

We aim at a long-standing contradiction between chaos-assisted tunneling and chaos-related localization study quantum transport of a single particle held in an amplitude-modulated and tilted optical lattice. We find some near-resonant regions crossing chaotic and regular regions in the parameter space, and demonstrate that chaos can heighten velocity of delocalization in the chaos-resonance overlapping regions, while chaos may aid localization in the other chaotic regions. The degree of localization enhances with increasing the distance between parameter points and near-resonant regions. The results could be useful for experimentally manipulating chaos-assisted transport of single particles in optical or solid-state lattices.

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

PubMed

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

2015-12-01

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

Research highlights: June 1990 - May 1991

NASA Technical Reports Server (NTRS)

1991-01-01

Linear instability calculations at MSFC have suggested that the Geophysical Fluid Flow Cell (GFFC) should exhibit classic baroclinic instability at accessible parameter settings. Interest was in the mechanisms of transition to temporal chaos and the evolution of spatio-temporal chaos. In order to understand more about such transitions, high resolution numerical experiments for the physically simplest model of two layer baroclinic instability were conducted. This model has the advantage that the numerical code is exponentially convergent and can be efficiently run for very long times, enabling the study of chaotic attractors without the often devastating effects of low-order trunction found in many previous studies. Numerical algorithms for implementing an empirical orthogonal function (EOF) analysis of the high resolution numerical results were completed. Under conditions of rapid rotation and relatively low differential heating, convection in a spherical shell takes place as columnar banana cells wrapped around the annular gap, but with axes oriented along the axis of rotation; these were clearly evident in the GFFC experiments. The results of recent numerical simulations of columnar convection and future research plans are presented.

Tuning quantum measurements to control chaos.

PubMed

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

2017-03-20

Environment-induced decoherence has long been recognised as being of crucial importance in the study of chaos in quantum systems. In particular, the exact form and strength of the system-environment interaction play a major role in the quantum-to-classical transition of chaotic systems. In this work we focus on the effect of varying monitoring strategies, i.e. for a given decoherence model and a fixed environmental coupling, there is still freedom on how to monitor a quantum system. We show here that there is a region between the deep quantum regime and the classical limit where the choice of the monitoring parameter allows one to control the complex behaviour of the system, leading to either the emergence or suppression of chaos. Our work shows that this is a result from the interplay between quantum interference effects induced by the nonlinear dynamics and the effectiveness of the decoherence for different measurement schemes.

Chaos Theory as a Model for Life Transitions Counseling: Nonlinear Dynamics and Life's Changes

ERIC Educational Resources Information Center

Bussolari, Cori J.; Goodell, Judith A.

2009-01-01

Chaos theory is presented for counselors working with clients experiencing life transitions. It is proposed as a model that considers disorder, unpredictability, and lack of control as normal parts of transition processes. Nonlinear constructs from physics are adapted for use in counseling. The model provides a method clients can use to…

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.

Stable photon orbits in stationary axisymmetric electrovacuum spacetimes

NASA Astrophysics Data System (ADS)

Dolan, Sam R.; Shipley, Jake O.

2016-08-01

We investigate the existence and phenomenology of stable photon orbits (SPOs) in stationary axisymmetric electrovacuum spacetimes in four dimensions. First, we review the classification of equatorial circular photon orbits on Kerr-Newman spacetimes in the charge-spin plane. Second, using a Hamiltonian formulation, we show that Reissner-Nordström diholes (a family encompassing the Majumdar-Papapetrou and Weyl-Bach special cases) admit SPOs, in a certain parameter regime that we investigate. Third, we explore the transition from order to chaos for typical SPOs bounded within a toroidal region around a dihole, via a selection of Poincaré sections. Finally, for general axisymmetric stationary spacetimes, we show that the Einstein-Maxwell field equations allow for the existence of SPOs in electro vacuum, but not in pure vacuum.

'Butterfly effect' in porous Bénard convection heated from below

DOE Office of Scientific and Technical Information (OSTI.GOV)

Siri, Z.; Liew, K. Y.; Ibrahim, R. I.

2014-07-10

Transition from steady to chaos for the onset of Bénard convection in porous medium was analyzed. The governing equation is reduced to ordinary differential equation and solved using built in MATLAB ODE45. The transition from steady to chaos take over from a limit cycle followed by homoclinic explosion.

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.

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.

Chaotic Dynamics of a Josephson Junction with a Ratchet Potential and Current-Modulating Damping

NASA Astrophysics Data System (ADS)

Li, Fei; Li, Wenwu; Xu, Lan

2018-06-01

The chaotic dynamics of a Josephson junction with a ratchet potential and current-modulating damping are studied. Under the first-order approximation, we construct the general solution of the first-order equation whose boundedness condition contains the famous Melnikov chaotic criterion. Based on the general solution, the incomputability and unpredictability of the system's chaotic behavior are discussed. For the case beyond perturbation conditions, the evolution of stroboscopic Poincaré sections shows that the system undergoes a quasi-periodic transition to chaos with an increasing intensity of the rf-current. Through a suitable feedback controlling strategy, the chaos can be effectively suppressed and the intensity of the controller can vary in a large range. It is also found that the current between the two separated superconductors increases monotonously in some specific parameter spaces.

Chaotic Dynamics of a Josephson Junction with a Ratchet Potential and Current-Modulating Damping

NASA Astrophysics Data System (ADS)

Li, Fei; Li, Wenwu; Xu, Lan

2018-04-01

The chaotic dynamics of a Josephson junction with a ratchet potential and current-modulating damping are studied. Under the first-order approximation, we construct the general solution of the first-order equation whose boundedness condition contains the famous Melnikov chaotic criterion. Based on the general solution, the incomputability and unpredictability of the system's chaotic behavior are discussed. For the case beyond perturbation conditions, the evolution of stroboscopic Poincaré sections shows that the system undergoes a quasi-periodic transition to chaos with an increasing intensity of the rf-current. Through a suitable feedback controlling strategy, the chaos can be effectively suppressed and the intensity of the controller can vary in a large range. It is also found that the current between the two separated superconductors increases monotonously in some specific parameter spaces.

Chaotic Careers: A Narrative Analysis of Career Transition Themes and Outcomes Using Chaos Theory as a Guiding Metaphor

ERIC Educational Resources Information Center

Peake, Sharon; McDowall, Almuth

2012-01-01

In a rapidly changing world of work, little research exists on mid-career transitions. We investigated these using the open-systems approach of chaos theory as a guiding metaphor and conducted interviews with seven mid-career individuals chosen for their experience of a significant mid-career transition. Four common themes were identified through…

Geometric chaos indicators and computations of the spherical hypertube manifolds of the spatial circular restricted three-body problem

NASA Astrophysics Data System (ADS)

Guzzo, Massimiliano; Lega, Elena

2018-06-01

The circular restricted three-body problem has five relative equilibria L1 ,L2, . . . ,L5. The invariant stable-unstable manifolds of the center manifolds originating at the partially hyperbolic equilibria L1 ,L2 have been identified as the separatrices for the motions which transit between the regions of the phase-space which are internal or external with respect to the two massive bodies. While the stable and unstable manifolds of the planar problem have been extensively studied both theoretically and numerically, the spatial case has not been as deeply investigated. This paper is devoted to the global computation of these manifolds in the spatial case with a suitable finite time chaos indicator. The definition of the chaos indicator is not trivial, since the mandatory use of the regularizing Kustaanheimo-Stiefel variables may introduce discontinuities in the finite time chaos indicators. From the study of such discontinuities, we define geometric chaos indicators which are globally defined and smooth, and whose ridges sharply approximate the stable and unstable manifolds of the center manifolds of L1 ,L2. We illustrate the method for the Sun-Jupiter mass ratio, and represent the topology of the asymptotic manifolds using sections and three-dimensional representations.

A qualitative numerical study of high dimensional dynamical systems

NASA Astrophysics Data System (ADS)

Albers, David James

Since Poincare, the father of modern mathematical dynamical systems, much effort has been exerted to achieve a qualitative understanding of the physical world via a qualitative understanding of the functions we use to model the physical world. In this thesis, we construct a numerical framework suitable for a qualitative, statistical study of dynamical systems using the space of artificial neural networks. We analyze the dynamics along intervals in parameter space, separating the set of neural networks into roughly four regions: the fixed point to the first bifurcation; the route to chaos; the chaotic region; and a transition region between chaos and finite-state neural networks. The study is primarily with respect to high-dimensional dynamical systems. We make the following general conclusions as the dimension of the dynamical system is increased: the probability of the first bifurcation being of type Neimark-Sacker is greater than ninety-percent; the most probable route to chaos is via a cascade of bifurcations of high-period periodic orbits, quasi-periodic orbits, and 2-tori; there exists an interval of parameter space such that hyperbolicity is violated on a countable, Lebesgue measure 0, "increasingly dense" subset; chaos is much more likely to persist with respect to parameter perturbation in the chaotic region of parameter space as the dimension is increased; moreover, as the number of positive Lyapunov exponents is increased, the likelihood that any significant portion of these positive exponents can be perturbed away decreases with increasing dimension. The maximum Kaplan-Yorke dimension and the maximum number of positive Lyapunov exponents increases linearly with dimension. The probability of a dynamical system being chaotic increases exponentially with dimension. The results with respect to the first bifurcation and the route to chaos comment on previous results of Newhouse, Ruelle, Takens, Broer, Chenciner, and Iooss. Moreover, results regarding the high-dimensional chaotic region of parameter space is interpreted and related to the closing lemma of Pugh, the windows conjecture of Barreto, the stable ergodicity theorem of Pugh and Shub, and structural stability theorem of Robbin, Robinson, and Mane.

Large-Scale Chaos and Fluctuations in Active Nematics

NASA Astrophysics Data System (ADS)

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

2014-07-01

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

Propagation of Electrical Excitation in a Ring of Cardiac Cells: A Computer Simulation Study

NASA Technical Reports Server (NTRS)

Kogan, B. Y.; Karplus, W. J.; Karpoukhin, M. G.; Roizen, I. M.; Chudin, E.; Qu, Z.

1996-01-01

The propagation of electrical excitation in a ring of cells described by the Noble, Beeler-Reuter (BR), Luo-Rudy I (LR I), and third-order simplified (TOS) mathematical models is studied using computer simulation. For each of the models it is shown that after transition from steady-state circulation to quasi-periodicity achieved by shortening the ring length (RL), the action potential duration (APD) restitution curve becomes a double-valued function and is located below the original ( that of an isolated cell) APD restitution curve. The distributions of APD and diastolic interval (DI) along a ring for the entire range of RL corresponding to quasi-periodic oscillations remain periodic with the period slightly different from two RLs. The 'S' shape of the original APD restitution curve determines the appearance of the second steady-state circulation region for short RLs. For all the models and the wide variety of their original APD restitution curves, no transition from quasi-periodicity to chaos was observed.

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 Orbits and Stationary States in Chemical Systems * Recursive Proportional-Feedback and Its Use to Control Chaos in an Electrochemical System * Temperature Patterns on Catalytic Surfaces * Meteorology/Oceanography * Nonlinear Evolution of Water Waves: Hilbert's View * Fractal Properties of Isoconcentration Surfaces in a Smoke Plume * Fractal Dimensions of Remotely Sensed Atmospheric Signals * Are Ocean Surface Waves Chaotic? * Dynamical Attractor Reconstruction for a Marine Stratocumulus Cloud

Quantitative kinetic theory of active matter

NASA Astrophysics Data System (ADS)

Ihle, Thomas; Chou, Yen-Liang

2014-03-01

Models of self-driven agents similar to the Vicsek model [Phys. Rev. Lett. 75 (1995) 1226] are studied by means of kinetic theory. In these models, particles try to align their travel directions with the average direction of their neighbours. At strong alignment a globally ordered state of collective motion forms. An Enskog-like kinetic theory is derived from the exact Chapman-Kolmogorov equation in phase space using Boltzmann's mean-field approximation of molecular chaos. The kinetic equation is solved numerically by a nonlocal Lattice-Boltzmann-like algorithm. Steep soliton-like waves are observed that lead to an abrupt jump of the global order parameter if the noise level is changed. The shape of the wave is shown to follow a novel scaling law and to quantitatively agree within 3 % with agent-based simulations at large particle speeds. This provides a mean-field mechanism to change the second-order character of the flocking transition to first order. Diagrammatic techniques are used to investigate small particle speeds, where the mean-field assumption of Molecular Chaos is invalid and where correlation effects need to be included.

Bifurcations and chaos in convection taking non-Fourier heat-flux

NASA Astrophysics Data System (ADS)

Layek, G. C.; Pati, N. C.

2017-11-01

In this Letter, we report the influences of thermal time-lag on the onset of convection, its bifurcations and chaos of a horizontal layer of Boussinesq fluid heated underneath taking non-Fourier Cattaneo-Christov hyperbolic model for heat propagation. A five-dimensional nonlinear system is obtained for a low-order Galerkin expansion, and it reduces to Lorenz system for Cattaneo number tending to zero. The linear stability agreed with existing results that depend on Cattaneo number C. It also gives a threshold Cattaneo number, CT, above which only oscillatory solutions can persist. The oscillatory solutions branch terminates at the subcritical steady branch with a heteroclinic loop connecting a pair of saddle points for subcritical steady-state solutions. For subcritical onset of convection two stable solutions coexist, that is, hysteresis phenomenon occurs at this stage. The steady solution undergoes a Hopf bifurcation and is of subcritical type for small value of C, while it becomes supercritical for moderate Cattaneo number. The system goes through period-doubling/noisy period-doubling transition to chaos depending on the control parameters. There after the system exhibits Shil'nikov chaos via homoclinic explosion. The complexity of spiral strange attractor is analyzed using fractal dimension and return map.

Stretched exponential dynamics of coupled logistic maps on a small-world network

NASA Astrophysics Data System (ADS)

Mahajan, Ashwini V.; Gade, Prashant M.

2018-02-01

We investigate the dynamic phase transition from partially or fully arrested state to spatiotemporal chaos in coupled logistic maps on a small-world network. Persistence of local variables in a coarse grained sense acts as an excellent order parameter to study this transition. We investigate the phase diagram by varying coupling strength and small-world rewiring probability p of nonlocal connections. The persistent region is a compact region bounded by two critical lines where band-merging crisis occurs. On one critical line, the persistent sites shows a nonexponential (stretched exponential) decay for all p while for another one, it shows crossover from nonexponential to exponential behavior as p → 1 . With an effectively antiferromagnetic coupling, coupling to two neighbors on either side leads to exchange frustration. Apart from exchange frustration, non-bipartite topology and nonlocal couplings in a small-world network could be a reason for anomalous relaxation. The distribution of trap times in asymptotic regime has a long tail as well. The dependence of temporal evolution of persistence on initial conditions is studied and a scaling form for persistence after waiting time is proposed. We present a simple possible model for this behavior.

Creating order from chaos: part II: tactical planning for mass casualty and disaster response at definitive care facilities.

PubMed

Baker, Michael S

2007-03-01

Current events highlight the need for disaster preparedness. We have seen tsunamis, hurricanes, terrorism, and combat in the news every night. There are many variables in a disaster, such as damage to facilities, loss of critical staff members, and overwhelming numbers of casualties. Each medical treatment facility should have a plan for everything from caring for staff members to getting the laundry done and providing enhanced security or mortuary services. Communication and agreements with local, regional, and federal agencies are vital. Then we must train and drill to shape the tools to impose order on chaos and to provide the most care to the greatest number.

Relative Time-scale for Channeling Events Within Chaotic Terrains, Margaritifer Sinus, Mars

NASA Technical Reports Server (NTRS)

Janke, D.

1985-01-01

A relative time scale for ordering channel and chaos forming events was constructed for areas within the Margaritifer Sinus region of Mars. Transection and superposition relationships of channels, chaotic terrain, and the surfaces surrounding them were used to create the relative time scale; crater density studies were not used. Channels and chaos in contact with one another were treated as systems. These systems were in turn treated both separately (in order to understand internal relationships) and as members of the suite of Martian erosional forms (in order to produce a combined, master time scale). Channeling events associated with chaotic terrain development occurred over an extended geomorphic period. The channels can be divided into three convenient groups: those that pre-date intercrater plains development post-plains, pre-chasma systems; and those associated with the development of the Vallis Marineris chasmata. No correlations with cyclic climatic changes, major geologic events in other regions on Mars, or triggering phenomena (for example, specific impact events) were found.

Discovery of Dozy Chaos and Discovery of Quanta: Analogy Being in Science and Perhaps in Human Progress

NASA Astrophysics Data System (ADS)

Egorov, Vladimir V.

The concept of a dozy chaos in the theory of quantum transitions and its applications are discussed in a historical context. Conjectured that dozy chaos is of primary importance to the dynamic self-organization of any living organism and concentrated in its brain. A hypothesis of the physical origin of cancer is put forward. Surmised that dozy chaos is the physical origin of life and driving force of its evolution.

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 and its critical properties depend on the shape of the single-neuron nonlinear input-output transfer function, near firing threshold. In particular, for nonlinear transfer functions with a sharp rise near threshold, the transition to chaos disappears in the limit of a large network; instead, the system exhibits chaotic fluctuations even for small synaptic gain. Finally, we investigate transition to chaos in network models with spiking dynamics. We show that when synaptic time constants are slow relative to the mean inverse firing rates, the network undergoes a transition from fast spiking fluctuations with constant rates to a state where the firing rates exhibit chaotic fluctuations, similar to the transition predicted by rate-based dynamics. Systems with finite synaptic time constants and firing rates exhibit a smooth transition from a regime dominated by stationary firing rates to a regime of slow rate fluctuations. This smooth crossover obeys scaling properties, similar to crossover phenomena in statistical mechanics. The theoretical results are supported by computer simulations of several neuronal architectures and dynamics. Consequences for cortical circuit dynamics are discussed. These results advance our understanding of the properties of intrinsic dynamics in realistic neuronal networks and their functional consequences.

FROM ORDER TO CHAOS IN EARTH SATELLITE ORBITS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gkolias, Ioannis; Gachet, Fabien; Daquin, Jérôme

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,more » 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.« less

Transition from complete synchronization to spatio-temporal chaos in coupled chaotic systems with nonhyperbolic and hyperbolic attractors

NASA Astrophysics Data System (ADS)

Rybalova, Elena; Semenova, Nadezhda; Strelkova, Galina; Anishchenko, Vadim

2017-06-01

We study the transition from coherence (complete synchronization) to incoherence (spatio-temporal chaos) in ensembles of nonlocally coupled chaotic maps with nonhyperbolic and hyperbolic attractors. As basic models of a partial element we use the Henon map and the Lozi map. We show that the transition to incoherence in a ring of coupled Henon maps occurs through the appearance of phase and amplitude chimera states. An ensemble of coupled Lozi maps demonstrates the coherence-incoherence transition via solitary states and no chimera states are observed in this case.

Observation of Hamiltonian chaos and its control in wave particle interaction

NASA Astrophysics Data System (ADS)

Doveil, F.; Macor, A.; Aïssi, A.

2007-12-01

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

Chaos enhancing tunneling in a coupled Bose-Einstein condensate with a double driving.

PubMed

Rong, Shiguang; Hai, Wenhua; Xie, Qiongtao; Zhu, Qianquan

2009-09-01

We study the effects of chaotic dynamics on atomic tunneling between two weakly coupled Bose-Einstein condensates driven by a double-frequency periodic field. Under the Melnikov's chaos criterion, we divide the parameter space into three parts of different types, regular region, low-chaoticity region, and high-chaoticity region, and give the accurate boundaries between the different regions. It is found that the atomic tunneling can be enhanced in the presence of chaos. Particularly, in the high-chaoticity regions, the chaos-induced inversion of the population imbalance is observed numerically.

Investigating a link between large and small-scale chaos features on Europa

NASA Astrophysics Data System (ADS)

Tognetti, L.; Rhoden, A.; Nelson, D. M.

2017-12-01

Chaos is one of the most recognizable, and studied, features on Europa's surface. Most models of chaos formation invoke liquid water at shallow depths within the ice shell; the liquid destabilizes the overlying ice layer, breaking it into mobile rafts and destroying pre-existing terrain. This class of model has been applied to both large-scale chaos like Conamara and small-scale features (i.e. microchaos), which are typically <10 km in diameter. Currently unknown, however, is whether both large-scale and small-scale features are produced together, e.g. through a network of smaller sills linked to a larger liquid water pocket. If microchaos features do form as satellites of large-scale chaos features, we would expect a drop off in the number density of microchaos with increasing distance from the large chaos feature; the trend should not be observed in regions without large-scale chaos features. Here, we test the hypothesis that large chaos features create "satellite" systems of smaller chaos features. Either outcome will help us better understand the relationship between large-scale chaos and microchaos. We focus first on regions surrounding the large chaos features Conamara and Murias (e.g. the Mitten). We map all chaos features within 90,000 sq km of the main chaos feature and assign each one a ranking (High Confidence, Probable, or Low Confidence) based on the observed characteristics of each feature. In particular, we look for a distinct boundary, loss of preexisting terrain, the existence of rafts or blocks, and the overall smoothness of the feature. We also note features that are chaos-like but lack sufficient characteristics to be classified as chaos. We then apply the same criteria to map microchaos features in regions of similar area ( 90,000 sq km) that lack large chaos features. By plotting the distribution of microchaos with distance from the center point of the large chaos feature or the mapping region (for the cases without a large feature), we determine whether there is a distinct signature linking large-scale chaos features with nearby microchaos. We discuss the implications of these results on the process of chaos formation and the extent of liquid water within Europa's ice shell.

Chaos and Chaos Control of the Frenkel-Kontorova Model with Dichotomous Noise

NASA Astrophysics Data System (ADS)

Lei, Youming; Zheng, Fan; Shao, Xizhen

Chaos and chaos control of the Frenkel-Kontorova (FK) model with dichotomous noise are studied theoretically and numerically. The threshold conditions for the onset of chaos in the FK model are firstly derived by applying the random Melnikov method with a mean-square criterion to the soliton equation, which is a fundamental topological mode of the FK model and accounts for its nonlinear phenomena. We found that dichotomous noise can induce stochastic chaos in the FK model, and the threshold of noise amplitude for the onset of chaos increases with the increase of its transition rate. Then the analytical criterion of chaos control is obtained by means of the time-delay feedback method. Since the time-delay feedback control raises the threshold of noise amplitude for the onset of chaos, chaos in the FK model is effectively suppressed. Through numerical simulations including the mean top Lyapunov exponent and the safe basin, we demonstrate the validity of the analytical predictions of chaos. Furthermore, time histories and phase portraits are utilized to verify the effectiveness of the proposed control.

Stochastic sensitivity analysis of the variability of dynamics and transition to chaos in the business cycles model

NASA Astrophysics Data System (ADS)

Bashkirtseva, Irina; Ryashko, Lev; Ryazanova, Tatyana

2018-01-01

A problem of mathematical modeling of complex stochastic processes in macroeconomics is discussed. For the description of dynamics of income and capital stock, the well-known Kaldor model of business cycles is used as a basic example. The aim of the paper is to give an overview of the variety of stochastic phenomena which occur in Kaldor model forced by additive and parametric random noise. We study a generation of small- and large-amplitude stochastic oscillations, and their mixed-mode intermittency. To analyze these phenomena, we suggest a constructive approach combining the study of the peculiarities of deterministic phase portrait, and stochastic sensitivity of attractors. We show how parametric noise can stabilize the unstable equilibrium and transform dynamics of Kaldor system from order to chaos.

Crises, noise, and tipping in the Hassell population model

NASA Astrophysics Data System (ADS)

Bashkirtseva, Irina

2018-03-01

We consider a problem of the analysis of the noise-induced tipping in population systems. To study this phenomenon, we use Hassell-type system with Allee effect as a conceptual model. A mathematical investigation of the tipping is connected with the analysis of the crisis bifurcations, both boundary and interior. In the parametric study of the abrupt changes in dynamics related to the noise-induced extinction and transition from order to chaos, the stochastic sensitivity function technique and confidence domains are used. The effectiveness of the suggested approach to detect early warnings of critical stochastic transitions is demonstrated.

Dynamical Epidemic Suppression Using Stochastic Prediction and Control

DTIC Science & Technology

2004-10-28

initial probability density function (PDF), p: D C R2 -- R, is defined by the stochastic Frobenius - Perron For deterministic systems, normal methods of...induced chaos. To analyze the qualitative change, we apply the technique of the stochastic Frobenius - Perron operator [L. Billings et al., Phys. Rev. Lett...transition matrix describing the probability of transport from one region of phase space to another, which approximates the stochastic Frobenius - Perron

Magnetic chaos healing in the helical reversed-field pinch: indications from the volume-preserving field line tracing code NEMATO

NASA Astrophysics Data System (ADS)

Bonfiglio, D.; Veranda, M.; Cappello, S.; Chacón, L.; Spizzo, G.

2010-11-01

The emergence of a self-organized reversed-field pinch (RFP) helical regime, first shown by 3D MHD numerical simulations, has been highlighted in the RFX-mod experiment at high current operation (IP above 1 MA). In fact, a quasi-stationary helical configuration spontaneously appears, characterized by strong internal electron transport barriers. In such regime electron temperature and density become, to a very good approximation, functions of the helical flux coordinate related to the dominant helical magnetic component. In addition, this regime is diagnosed to be associated with the topological transition to a single-helical-axis (SHAx) state, achieved after the expulsion of the separatrix of the dominant mode's magnetic island. The SHAx state is theoretically predicted to be resilient to the magnetic chaos induced by secondary modes. In this paper, we present initial results of the volume-preserving field line tracing code NEMATO [Finn J M and Chacón L 2005 Phys. Plasmas 12 054503] applied to study the magnetic topology resulting from 3D MHD simulations of the RFP. First, a successful 2D verification test of the code is shown, then, initial application to a systematic study of chaos healing in the helical RFP is discussed. The separatrix disappearance is confirmed to play an essential role for chaos healing. The triggering effect of a reversed magnetic shear for the formation of ordered surfaces within magnetic chaos is also diagnosed.

Magnetic chaos healing in hte helical reversed-field pinch: indications from the volume-preserving field line tracing code NEMATO

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bonfiglio, Daniele; Veranda, M.; Cappello, Susanna

2010-01-01

The emergence of a self-organized reversed-field pinch (RFP) helical regime, first shown by 3D MHD numerical simulations, has been highlighted in the RFX-mod experiment at high current operation (IP above 1 MA). In fact, a quasi-stationary helical configuration spontaneously appears, characterized by strong internal electron transport barriers. In such regime electron temperature and density become, to a very good approximation, functions of the helical flux coordinate related to the dominant helical magnetic component. In addition, this regime is diagnosed to be associated with the topological transition to a single-helical-axis (SHAx) state, achieved after the expulsion of the separatrix of themore » dominant mode's magnetic island. The SHAx state is theoretically predicted to be resilient to the magnetic chaos induced by secondary modes. In this paper, we present initial results of the volume-preserving field line tracing code nemato [Finn J M and Chacon L 2005 Phys. Plasmas 12 054503] applied to study the magnetic topology resulting from 3D MHD simulations of the RFP. First, a successful 2D verification test of the code is shown, then, initial application to a systematic study of chaos healing in the helical RFP is discussed. The separatrix disappearance is confirmed to play an essential role for chaos healing. The triggering effect of a reversed magnetic shear for the formation of ordered surfaces within magnetic chaos is also diagnosed.« less

Regular and irregular patterns of self-localized excitation in arrays of coupled phase oscillators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wolfrum, Matthias; Omel'chenko, Oleh E.; Sieber, Jan

We study a system of phase oscillators with nonlocal coupling in a ring that supports self-organized patterns of coherence and incoherence, called chimera states. Introducing a global feedback loop, connecting the phase lag to the order parameter, we can observe chimera states also for systems with a small number of oscillators. Numerical simulations show a huge variety of regular and irregular patterns composed of localized phase slipping events of single oscillators. Using methods of classical finite dimensional chaos and bifurcation theory, we can identify the emergence of chaotic chimera states as a result of transitions to chaos via period doublingmore » cascades, torus breakup, and intermittency. We can explain the observed phenomena by a mechanism of self-modulated excitability in a discrete excitable medium.« less

Chaotic dynamics of flexible beams driven by external white noise

NASA Astrophysics Data System (ADS)

Awrejcewicz, J.; Krysko, A. V.; Papkova, I. V.; Zakharov, V. M.; Erofeev, N. P.; Krylova, E. Yu.; Mrozowski, J.; Krysko, V. A.

2016-10-01

Mathematical models of continuous structural members (beams, plates and shells) subjected to an external additive white noise are studied. The structural members are considered as systems with infinite number of degrees of freedom. We show that in mechanical structural systems external noise can not only lead to quantitative changes in the system dynamics (that is obvious), but also cause the qualitative, and sometimes surprising changes in the vibration regimes. Furthermore, we show that scenarios of the transition from regular to chaotic regimes quantified by Fast Fourier Transform (FFT) can lead to erroneous conclusions, and a support of the wavelet analysis is needed. We have detected and illustrated the modifications of classical three scenarios of transition from regular vibrations to deterministic chaos. The carried out numerical experiment shows that the white noise lowers the threshold for transition into spatio-temporal chaotic dynamics. A transition into chaos via the proposed modified scenarios developed in this work is sensitive to small noise and significantly reduces occurrence of periodic vibrations. Increase of noise intensity yields decrease of the duration of the laminar signal range, i.e., time between two successive turbulent bursts decreases. Scenario of transition into chaos of the studied mechanical structures essentially depends on the control parameters, and it can be different in different zones of the constructed charts (control parameter planes). Furthermore, we found an interesting phenomenon, when increase of the noise intensity yields surprisingly the vibrational characteristics with a lack of noisy effect (chaos is destroyed by noise and windows of periodicity appear).

Foraging at the Edge of Chaos: Internal Clock versus External Forcing

NASA Astrophysics Data System (ADS)

Nicolis, S. C.; Fernández, J.; Pérez-Penichet, C.; Noda, C.; Tejera, F.; Ramos, O.; Sumpter, D. J. T.; Altshuler, E.

2013-06-01

Activity rhythms in animal groups arise both from external changes in the environment, as well as from internal group dynamics. These cycles are reminiscent of physical and chemical systems with quasiperiodic and even chaotic behavior resulting from “autocatalytic” mechanisms. We use nonlinear differential equations to model how the coupling between the self-excitatory interactions of individuals and external forcing can produce four different types of activity rhythms: quasiperiodic, chaotic, phase locked, and displaying over or under shooting. At the transition between quasiperiodic and chaotic regimes, activity cycles are asymmetrical, with rapid activity increases and slower decreases and a phase shift between external forcing and activity. We find similar activity patterns in ant colonies in response to varying temperature during the day. Thus foraging ants operate in a region of quasiperiodicity close to a cascade of transitions leading to chaos. The model suggests that a wide range of temporal structures and irregularities seen in the activity of animal and human groups might be accounted for by the coupling between collectively generated internal clocks and external forcings.

Route to chaos in porous-medium thermal convection

NASA Astrophysics Data System (ADS)

Kimura, S.; Schubert, G.; Straus, J. M.

1986-05-01

The transition to chaos in two-dimensional single-cell time-dependent convection in a square cross section of porous material saturated with fluid and heated from below is investigated theoretically by means of pseudospectral numerical simulations. The results are presented graphically and discussed in terms of the time-averaged Nusselt number, the oscillation mechanism, and similarities to Hele-Shaw convection. As the Rayleigh number (R) increases, the system is found to proceed from the steady state to a simply periodic state, a quasi-periodic state with two basic frequencies, a second simply periodic state, and finally to chaos. The transitions occur at R = 4 pi squared, 380-400, 500-520, 560-570, and 850-1000. The intermediate and chaotic regimes are characterized in detail.

Nature of the narrow optical band in H*-aggregates: Dozy-chaos–exciton coupling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Egorov, Vladimir V., E-mail: egorov@photonics.ru

2014-07-15

Dozy chaos emerges as a combined effect of the collective chaotic motion of electrons and nuclei, and their chaotic electromagnetic interactions in the transient state of molecules experiencing quantum transitions. Following earlier discussions of the well-known Brönsted relations for proton-transfer reactions; the temperature-dependent electron transfer in Langmuir–Blodgett films; the shape of the optical bands of polymethine dye monomers, their dimers, and J-aggregates, this paper reports one more application of the dozy-chaos theory of molecular quantum transitions. The qualitative and quantitative explanations for shape of a narrow and blue-shifted optical absorption band in H{sup *}-aggregates is given on the basis ofmore » the dozy-chaos theory by taking into account the dozy-chaos–exciton coupling effect. It is emphasized that in the H{sup *}-aggregate chromophore (dimer of cyclic bis-thiacarbocyanines) there is a competition between two Frenkel exciton transitions through the chaotic reorganization motion of nuclear environment. As a result, the highly organized quantum transition to the upper exciton state becomes an exciton-induced source of dozy chaos for the low organized transition to the lower exciton state. This manifests itself in appearing the narrow peak and broad wing in the optical spectrum pattern of H{sup *}-aggregates. A similar enhancement in the H{sup *}-effect caused by the strengthening of the exciton coupling in H{sup *}-dimers, which could be achieved by synthesizing tertiary and quarternary thiacarbocyanine monomers, is predicted.« less

[Shedding light on chaos theory].

PubMed

Chou, Shieu-Ming

2004-06-01

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

Chaos Theory as a Planning Tool for Community-Based Educational Experiences for Health Students.

ERIC Educational Resources Information Center

Velde, Beth P.; Greer, Annette G.; Lynch, Deirdre C.; Escott-Stump, Sylvia

2002-01-01

Chaos theory, which attempts to understand underlying order where none is apparent, was applied to an interdisciplinary rural health training program for health professionals. Similar programs should anticipate systemic flux between order and chaos and pay attention to information flow, degree of diversity, richness of connectivity, contained…

Chaos-chaos transition of left hemisphere EEGs during standard tasks of Waterloo-Stanford Group Scale of hypnotic susceptibility.

PubMed

Yargholi, Elahe'; Nasrabadi, Ali Motie

2015-01-01

A recent study, recurrence quantification analysis of EEG signals during standard tasks of Waterloo-Stanford Group Scale of hypnotic susceptibility investigated recurrence quantifiers (RQs) of hypnotic electroencephalograph (EEG) signals recorded after hypnotic induction while subjects were doing standard tasks of Waterloo-Stanford Group Scale (WSGS) of hypnotic susceptibility to distinguish subjects of different hypnotizability levels. Following the same analysis, the current study determines the capability of different RQs to distinguish subjects of low, medium and high hypnotizability level and studies the influence of hypnotizability level on underlying dynamic of tasks. Besides, EEG channels were sorted according to the number of their RQs, which differed significantly among subjects of different hypnotizability levels. Another valuable result was determination of major brain regions in observing significant differences in various task types (ideomotors, hallucination, challenge and memory).

Topographic variations in chaos on Europa: Implications for diapiric formation

NASA Technical Reports Server (NTRS)

Schenk, Paul M.; Pappalardo, Robert T.

2004-01-01

Disrupted terrain, or chaos, on Europa, might have formed through melting of a floating ice shell from a subsurface ocean [Cam et al., 1998; Greenberg et al., 19991, or breakup by diapirs rising from the warm lower portion of the ice shell [Head and Pappalardo, 1999; Collins et al., 20001. Each model makes specific and testable predictions for topographic expression within chaos and relative to surrounding terrains on local and regional scales. High-resolution stereo-controlled photoclinometric topography indicates that chaos topography, including the archetypal Conamara Chaos region, is uneven and commonly higher than surrounding plains by up to 250 m. Elevated and undulating topography is more consistent with diapiric uplift of deep material in a relatively thick ice shell, rather than melt-through and refreezing of regionally or globally thin ice by a subsurface ocean. Vertical and horizontal scales of topographic doming in Conamara Chaos are consistent with a total ice shell thickness >15 km. Contact between Europa's ocean and surface may most likely be indirectly via diapirism or convection.

Topographic variations in chaos on Europa: Implications for diapiric formation

NASA Astrophysics Data System (ADS)

Schenk, Paul M.; Pappalardo, Robert T.

2004-08-01

Disrupted terrain, or chaos, on Europa, might have formed through melting of a floating ice shell from a subsurface ocean [Carr et al., 1998; Greenberg et al., 1999], or breakup by diapirs rising from the warm lower portion of the ice shell [Head and Pappalardo, 1999; Collins et al., 2000]. Each model makes specific and testable predictions for topographic expression within chaos and relative to surrounding terrains on local and regional scales. High-resolution stereo-controlled photoclinometric topography indicates that chaos topography, including the archetypal Conamara Chaos region, is uneven and commonly higher than surrounding plains by up to 250 m. Elevated and undulating topography is more consistent with diapiric uplift of deep material in a relatively thick ice shell, rather than melt-through and refreezing of regionally or globally thin ice by a subsurface ocean. Vertical and horizontal scales of topographic doming in Conamara Chaos are consistent with a total ice shell thickness >15 km. Contact between Europa's ocean and surface may most likely be indirectly via diapirism or convection.

Strategic Assessment 1995. U.S. Security Challenges in Transition

DTIC Science & Technology

1995-01-01

as decreasing order of impact , line. Many states in this category run the they are: risk of backsliding into political chaos and Economic/political...investment needs ahead of wor- The sad results of such intra-state ten- ries about the long-term impact of current sions can be seen in many places. Violent...step down and allow duly elected Panama. Kenya . government to return to power, 25 September 94: Operation DISTANT 11 December 92-May 93: RESTORE HOPE

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.

Scrambling in the quantum Lifshitz model

NASA Astrophysics Data System (ADS)

Plamadeala, Eugeniu; Fradkin, Eduardo

2018-06-01

We study signatures of chaos in the quantum Lifshitz model through out-of-time ordered correlators (OTOC) of current operators. This model is a free scalar field theory with dynamical critical exponent z  =  2. It describes the quantum phase transition in 2D systems, such as quantum dimer models, between a phase with a uniform ground state to another one with spontaneously broken translation invariance. At the lowest temperatures the chaotic dynamics are dominated by a marginally irrelevant operator which induces a temperature dependent stiffness term. The numerical computations of OTOC exhibit a non-zero Lyapunov exponent (LE) in a wide range of temperatures and interaction strengths. The LE (in units of temperature) is a weakly temperature-dependent function; it vanishes at weak interaction and saturates for strong interaction. The Butterfly velocity increases monotonically with interaction strength in the studied region while remaining smaller than the interaction-induced velocity/stiffness.

The Capabilities of Chaos and Complexity

PubMed Central

Abel, David L.

2009-01-01

To what degree could chaos and complexity have organized a Peptide or RNA World of crude yet necessarily integrated protometabolism? How far could such protolife evolve in the absence of a heritable linear digital symbol system that could mutate, instruct, regulate, optimize and maintain metabolic homeostasis? To address these questions, chaos, complexity, self-ordered states, and organization must all be carefully defined and distinguished. In addition their cause-and-effect relationships and mechanisms of action must be delineated. Are there any formal (non physical, abstract, conceptual, algorithmic) components to chaos, complexity, self-ordering and organization, or are they entirely physicodynamic (physical, mass/energy interaction alone)? Chaos and complexity can produce some fascinating self-ordered phenomena. But can spontaneous chaos and complexity steer events and processes toward pragmatic benefit, select function over non function, optimize algorithms, integrate circuits, produce computational halting, organize processes into formal systems, control and regulate existing systems toward greater efficiency? The question is pursued of whether there might be some yet-to-be discovered new law of biology that will elucidate the derivation of prescriptive information and control. “System” will be rigorously defined. Can a low-informational rapid succession of Prigogine’s dissipative structures self-order into bona fide organization? PMID:19333445

Periodic and chaotic psychological stress variations as predicted by a social support buffered response model

NASA Astrophysics Data System (ADS)

Field, Richard J.; Gallas, Jason A. C.; Schuldberg, David

2017-08-01

Recent work has introduced social dynamic models of people's stress-related processes, some including amelioration of stress symptoms by support from others. The effects of support may be ;direct;, depending only on the level of support, or ;buffering;, depending on the product of the level of support and level of stress. We focus here on the nonlinear buffering term and use a model involving three variables (and 12 control parameters), including stress as perceived by the individual, physical and psychological symptoms, and currently active social support. This model is quantified by a set of three nonlinear differential equations governing its stationary-state stability, temporal evolution (sometimes oscillatory), and how each variable affects the others. Chaos may appear with periodic forcing of an environmental stress parameter. Here we explore this model carefully as the strength and amplitude of this forcing, and an important psychological parameter relating to self-kindling in the stress response, are varied. Three significant observations are made: 1. There exist many complex but orderly regions of periodicity and chaos, 2. there are nested regions of increasing number of peaks per cycle that may cascade to chaos, and 3. there are areas where more than one state, e.g., a period-2 oscillation and chaos, coexist for the same parameters; which one is reached depends on initial conditions.

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

ERIC Educational Resources Information Center

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

2005-01-01

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

Information processing in echo state networks at the edge of chaos.

PubMed

Boedecker, Joschka; Obst, Oliver; Lizier, Joseph T; Mayer, N Michael; Asada, Minoru

2012-09-01

We investigate information processing in randomly connected recurrent neural networks. It has been shown previously that the computational capabilities of these networks are maximized when the recurrent layer is close to the border between a stable and an unstable dynamics regime, the so called edge of chaos. The reasons, however, for this maximized performance are not completely understood. We adopt an information-theoretical framework and are for the first time able to quantify the computational capabilities between elements of these networks directly as they undergo the phase transition to chaos. Specifically, we present evidence that both information transfer and storage in the recurrent layer are maximized close to this phase transition, providing an explanation for why guiding the recurrent layer toward the edge of chaos is computationally useful. As a consequence, our study suggests self-organized ways of improving performance in recurrent neural networks, driven by input data. Moreover, the networks we study share important features with biological systems such as feedback connections and online computation on input streams. A key example is the cerebral cortex, which was shown to also operate close to the edge of chaos. Consequently, the behavior of model systems as studied here is likely to shed light on reasons why biological systems are tuned into this specific regime.

Dynamical phases of the Hindmarsh-Rose neuronal model: studies of the transition from bursting to spiking chaos.

PubMed

Innocenti, Giacomo; Morelli, Alice; Genesio, Roberto; Torcini, Alessandro

2007-12-01

The dynamical phases of the Hindmarsh-Rose neuronal model are analyzed in detail by varying the external current I. For increasing current values, the model exhibits a peculiar cascade of nonchaotic and chaotic period-adding bifurcations leading the system from the silent regime to a chaotic state dominated by bursting events. At higher I-values, this phase is substituted by a regime of continuous chaotic spiking and finally via an inverse period doubling cascade the system returns to silence. The analysis is focused on the transition between the two chaotic phases displayed by the model: one dominated by spiking dynamics and the other by bursts. At the transition an abrupt shrinking of the attractor size associated with a sharp peak in the maximal Lyapunov exponent is observable. However, the transition appears to be continuous and smoothed out over a finite current interval, where bursts and spikes coexist. The beginning of the transition (from the bursting side) is signaled from a structural modification in the interspike interval return map. This change in the map shape is associated with the disappearance of the family of solutions responsible for the onset of the bursting chaos. The successive passage from bursting to spiking chaos is associated with a progressive pruning of unstable long-lasting bursts.

Towards a definition of life.

PubMed

Macklem, Peter T; Seely, Andrew

2010-01-01

This article offers a new definition of life as a "self-contained, self-regulating, self-organizing, self-reproducing, interconnected, open thermodynamic network of component parts which performs work, existing in a complex regime which combines stability and adaptability in the phase transition between order and chaos, as a plant, animal, fungus, or microbe." Open thermodynamic networks, which create and maintain order and are used by all organisms to perform work, import energy from and export entropy into the environment. Intra- and extracellular interconnected networks also confer order. Although life obeys the laws of physics and chemistry, the design of living organisms is not determined by these laws, but by Darwinian selection of the fittest designs. Over a short range of normalized energy consumption, open thermodynamic systems change from deeply ordered to chaotic, and life is found in this phase transition, where a dynamic balance between stability and adaptability allows for homeokinesis. Organisms and cells move within the phase transition with changes in metabolic rate. Seeds, spores and cryo-preserved tissue are well within the ordered regime, while health probably cannot be maintained with displacements into the chaotic regime. Understanding life in these terms may provide new insights into what constitutes health and lead to new theories of disease.

Universality in quantum chaos and the one-parameter scaling theory.

PubMed

García-García, Antonio M; Wang, Jiao

2008-02-22

The one-parameter scaling theory is adapted to the context of quantum chaos. We define a generalized dimensionless conductance, g, semiclassically and then study Anderson localization corrections by renormalization group techniques. This analysis permits a characterization of the universality classes associated to a metal (g-->infinity), an insulator (g-->0), and the metal-insulator transition (g-->g(c)) in quantum chaos provided that the classical phase space is not mixed. According to our results the universality class related to the metallic limit includes all the systems in which the Bohigas-Giannoni-Schmit conjecture holds but automatically excludes those in which dynamical localization effects are important. The universality class related to the metal-insulator transition is characterized by classical superdiffusion or a fractal spectrum in low dimensions (d < or = 2). Several examples are discussed in detail.

Chaos in driven Alfvén systems: unstable periodic orbits and chaotic saddles

NASA Astrophysics Data System (ADS)

Chian, A. C.-L.; Santana, W. M.; Rempel, E. L.; Borotto, F. A.; Hada, T.; Kamide, Y.

2007-01-01

The chaotic dynamics of Alfvén waves in space plasmas governed by the derivative nonlinear Schrödinger equation, in the low-dimensional limit described by stationary spatial solutions, is studied. A bifurcation diagram is constructed, by varying the driver amplitude, to identify a number of nonlinear dynamical processes including saddle-node bifurcation, boundary crisis, and interior crisis. The roles played by unstable periodic orbits and chaotic saddles in these transitions are analyzed, and the conversion from a chaotic saddle to a chaotic attractor in these dynamical processes is demonstrated. In particular, the phenomenon of gap-filling in the chaotic transition from weak chaos to strong chaos via an interior crisis is investigated. A coupling unstable periodic orbit created by an explosion, within the gaps of the chaotic saddles embedded in a chaotic attractor following an interior crisis, is found numerically. The gap-filling unstable periodic orbits are responsible for coupling the banded chaotic saddle (BCS) to the surrounding chaotic saddle (SCS), leading to crisis-induced intermittency. The physical relevance of chaos for Alfvén intermittent turbulence observed in the solar wind is discussed.

Synchronization transition in neuronal networks composed of chaotic or non-chaotic oscillators.

PubMed

Xu, Kesheng; Maidana, Jean Paul; Castro, Samy; Orio, Patricio

2018-05-30

Chaotic dynamics has been shown in the dynamics of neurons and neural networks, in experimental data and numerical simulations. Theoretical studies have proposed an underlying role of chaos in neural systems. Nevertheless, whether chaotic neural oscillators make a significant contribution to network behaviour and whether the dynamical richness of neural networks is sensitive to the dynamics of isolated neurons, still remain open questions. We investigated synchronization transitions in heterogeneous neural networks of neurons connected by electrical coupling in a small world topology. The nodes in our model are oscillatory neurons that - when isolated - can exhibit either chaotic or non-chaotic behaviour, depending on conductance parameters. We found that the heterogeneity of firing rates and firing patterns make a greater contribution than chaos to the steepness of the synchronization transition curve. We also show that chaotic dynamics of the isolated neurons do not always make a visible difference in the transition to full synchrony. Moreover, macroscopic chaos is observed regardless of the dynamics nature of the neurons. However, performing a Functional Connectivity Dynamics analysis, we show that chaotic nodes can promote what is known as multi-stable behaviour, where the network dynamically switches between a number of different semi-synchronized, metastable states.

Detecting a pronounced delocalized state in third-harmonic generation phenomenon; a quantum chaos approach

NASA Astrophysics Data System (ADS)

Behnia, S.; Ziaei, J.; Khodavirdizadeh, M.

2018-06-01

Nonlinear optics (NLO) deserves special attention in new optical devices, making it possible to generate coherent light more efficiently. Among the various NLO phenomena the third-harmonic generation (THG) is at the core of the effective operating mechanism of broadband wavelength conversion, in all-optical devices. Here, we aim to understand how the third-order susceptibility and the electric field may be effectively effect on the localization properties of the light in the THG process when included in a two-mode cavity coherently perturbed by a classical field. We address a stable-unstable transition due to the combination effect of the aforementioned factors. We report a reliable evidence confirming the appearance of chaos in THG under suitable conditions. By tracing the signatures of adjacent-spectral-spacing-ratio (ASSR) distribution and participation ratio, we also find a critical point (ɛc ,κc) =(3 . 1 , 0 . 35) for which a pronounced delocalized response is seen. This study may have profound findings for practical devices, and ushers in new opportunities for practical exploitation of the electric field and the third-order susceptibility effect in nonlinear optical devices.

Transitions in eigenvalue and wavefunction structure in (1+2) -body random matrix ensembles with spin.

PubMed

Vyas, Manan; Kota, V K B; Chavda, N D

2010-03-01

Finite interacting Fermi systems with a mean-field and a chaos generating two-body interaction are modeled by one plus two-body embedded Gaussian orthogonal ensemble of random matrices with spin degree of freedom [called EGOE(1+2)-s]. Numerical calculations are used to demonstrate that, as lambda , the strength of the interaction (measured in the units of the average spacing of the single-particle levels defining the mean-field), increases, generically there is Poisson to GOE transition in level fluctuations, Breit-Wigner to Gaussian transition in strength functions (also called local density of states) and also a duality region where information entropy will be the same in both the mean-field and interaction defined basis. Spin dependence of the transition points lambda_{c} , lambdaF, and lambdad , respectively, is described using the propagator for the spectral variances and the formula for the propagator is derived. We further establish that the duality region corresponds to a region of thermalization. For this purpose we compared the single-particle entropy defined by the occupancies of the single-particle orbitals with thermodynamic entropy and information entropy for various lambda values and they are very close to each other at lambda=lambdad.

Fluid elasticity and the transition to chaos in thermal convection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Khayat, R.E.

1995-01-01

The influence of fluid elasticity on the onset of aperiodic or chaotic motion of an upper-convected Maxwellian fluid is examined in the context of the Rayleigh-Benard thermal convection problem. A truncated Fourier representation of the flow and temperature fields leads to a four-dimensional dynamical system that constitutes a generalization of the classical Lorenz system for Newtonian fluids. It is found that, to the order of the present truncation and above a critical value of the Deborah number De[sup [ital c

The Importance of Chaos and Lenticulae on Europa for the JIMO Mission

NASA Technical Reports Server (NTRS)

Spaun, Nicole A.

2003-01-01

The Galileo Solid State Imaging (SSI) experiment provided high-resolution images of Europa's surface allowing identification of surface features barely distinguishable at Voyager's resolution. SSI revealed the visible pitting on Europa's surface to be due to large disrupted features, chaos, and smaller sub-circular patches, lenticulae. Chaos features contain a hummocky matrix material and commonly contain dislocated blocks of ridged plains. Lenticulae are morphologically interrelated and can be divided into three classes: domes, spots, and micro-chaos. Domes are broad, upwarped features that generally do not disrupt the texture of the ridged plains. Spots are areas of low albedo that are generally smooth in texture compared to other units. Micro-chaos are disrupted features with a hummocky matrix material, resembling that observed within chaos regions. Chaos and lenticulae are ubiquitous in the SSI regional map observations, which average approximately 200 meters per pixel (m/pxl) in resolution, and appear in several of the ultra-high resolution, i.e., better than 50 m/pxl, images of Europa as well. SSI also provided a number of multi-spectral observations of chaos and lenticulae. Using this dataset we have undertaken a thorough study of the morphology, size, spacing, stratigraphy, and color of chaos and lenticulae to determine their properties and evaluate models of their formation. Geological mapping indicates that chaos and micro-chaos have a similar internal morphology of in-situ degradation suggesting that a similar process was operating during their formation. The size distribution denotes a dominant size of 4-8 km in diameter for features containing hummocky material (i.e., chaos and micro-chaos). Results indicate a dominant spacing of 15 - 36 km apart. Chaos and lenticulae are generally among the youngest features stratigraphically observed on the surface, suggesting a recent change in resurfacing style. Also, the reddish non-icy materials on Europa's surface have high concentrations in many chaos and lenticulae features. Nonetheless, a complete global map of the distribution of chaos and lenticulae is not possible with the SSI dataset. Only <20% of the surface has been imaged at 200 m/pxl or better resolution, mostly of the near-equatorial regions. Color and ultra-high-res images have much less surface coverage. Thus we suggest that full global imaging of Europa at 200 m/pxl or better resolution, preferably in multi-spectral wavelengths, should be a high priority for the JIMO mission.

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…

Transition Time: Make It a Learning Time.

ERIC Educational Resources Information Center

Baker, Betty Ruth

Teacher selection and planning of appropriate transition activities for preschool age children is discussed in this paper. Teachers are encouraged to use transition time to provide an opportunity for imaginative and creative thinking and to avoid tedious waiting and chaos. Transition activities can be used as a teaching technique to prepare…

Stochastic Estimation via Polynomial Chaos

DTIC Science & Technology

2015-10-01

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

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.

Conditions for order and chaos in the dynamics of a trapped Bose-Einstein condensate in coordinate and energy space

NASA Astrophysics Data System (ADS)

Sakhel, Roger R.; Sakhel, Asaad R.; Ghassib, Humam B.; Balaz, Antun

2016-03-01

We investigate numerically conditions for order and chaos in the dynamics of an interacting Bose-Einstein condensate (BEC) confined by an external trap cut off by a hard-wall box potential. The BEC is stirred by a laser to induce excitations manifesting as irregular spatial and energy oscillations of the trapped cloud. Adding laser stirring to the external trap results in an effective time-varying trapping frequency in connection with the dynamically changing combined external+laser potential trap. The resulting dynamics are analyzed by plotting their trajectories in coordinate phase space and in energy space. The Lyapunov exponents are computed to confirm the existence of chaos in the latter space. Quantum effects and trap anharmonicity are demonstrated to generate chaos in energy space, thus confirming its presence and implicating either quantum effects or trap anharmonicity as its generator. The presence of chaos in energy space does not necessarily translate into chaos in coordinate space. In general, a dynamic trapping frequency is found to promote chaos in a trapped BEC. An apparent means to suppress chaos in a trapped BEC is achieved by increasing the characteristic scale of the external trap with respect to the condensate size.

PHYSICAL EFFECTS OCCURRING DURING GENERATION AND AMPLIFICATION OF LASER RADIATION: Dynamic chaos in a laser with a bleachable filter and dimensionality

NASA Astrophysics Data System (ADS)

Samson, A. M.; Kotomtseva, L. A.; Grigor'eva, E. V.

1989-02-01

A theoretical study of the dynamics of a laser with a bleachable filter revealed chaotic lasing regimes and ranges of bistable states of parameters close to those found in reality. It is shown how a transition to chaos occurs as a result of period-doubling bifurcation. A study is reported of the degree of chaos and of the structure of the resultant strange attractor by calculation of its fractal dimensionality and of the Lyapunov indices.

More Lessons From Complexity

NASA Astrophysics Data System (ADS)

Puente, C. E.

2002-12-01

The last few decades have witnessed the development of a host of ideas aimed at understanding and predicting nature's ever present complexity. It is shown that such a work provides, through its detailed study of order and disorder, a suitable framework for visualizing the dynamics and consequences of mankind's ever present divisive traits. Specifically, this article explains how recent universal results pertaining to the transition from order to chaos via a cascade of bifurcations point us to a serene state, symbolized by the convergence to the origin in the root of a Feigenbaum's tree, in which we all may achieve our inherently desired condition of justice and peace.

Mesoscopic chaos mediated by Drude electron-hole plasma in silicon optomechanical oscillators

PubMed Central

Wu, Jiagui; Huang, Shu-Wei; Huang, Yongjun; Zhou, Hao; Yang, Jinghui; Liu, Jia-Ming; Yu, Mingbin; Lo, Guoqiang; Kwong, Dim-Lee; Duan, Shukai; Wei Wong, Chee

2017-01-01

Chaos has revolutionized the field of nonlinear science and stimulated foundational studies from neural networks, extreme event statistics, to physics of electron transport. Recent studies in cavity optomechanics provide a new platform to uncover quintessential architectures of chaos generation and the underlying physics. Here, we report the generation of dynamical chaos in silicon-based monolithic optomechanical oscillators, enabled by the strong and coupled nonlinearities of two-photon absorption induced Drude electron–hole plasma. Deterministic chaotic oscillation is achieved, and statistical and entropic characterization quantifies the chaos complexity at 60 fJ intracavity energies. The correlation dimension D2 is determined at 1.67 for the chaotic attractor, along with a maximal Lyapunov exponent rate of about 2.94 times the fundamental optomechanical oscillation for fast adjacent trajectory divergence. Nonlinear dynamical maps demonstrate the subharmonics, bifurcations and stable regimes, along with distinct transitional routes into chaos. This provides a CMOS-compatible and scalable architecture for understanding complex dynamics on the mesoscopic scale. PMID:28598426

Dynamic Analysis and Adaptive Sliding Mode Controller for a Chaotic Fractional Incommensurate Order Financial System

NASA Astrophysics Data System (ADS)

Hajipour, Ahmad; Tavakoli, Hamidreza

2017-12-01

In this study, the dynamic behavior and chaos control of a chaotic fractional incommensurate-order financial system are investigated. Using well-known tools of nonlinear theory, i.e. Lyapunov exponents, phase diagrams and bifurcation diagrams, we observe some interesting phenomena, e.g. antimonotonicity, crisis phenomena and route to chaos through a period doubling sequence. Adopting largest Lyapunov exponent criteria, we find that the system yields chaos at the lowest order of 2.15. Next, in order to globally stabilize the chaotic fractional incommensurate order financial system with uncertain dynamics, an adaptive fractional sliding mode controller is designed. Numerical simulations are used to demonstrate the effectiveness of the proposed control method.

Understanding the Chaotic Behavior of Field Lines using the Simple Map

NASA Astrophysics Data System (ADS)

Saralkar, R.; White, C.; Ali, H.; Punjabi, A.

1998-11-01

The Simple Map is given by x_n+1=x_n-ky_n(1-y_n), y_n+1=y_n+kx_n+1. Different initial values of x and y create different surfaces. We can see at what point the order begins to fade, at what point the surface breaks up and islands form, and at what point chaos occurs. The outer surfaces are chaotic as expected because the plasma is nearing the X-point in the tokamak, where the order begins to break up. We are specifically investigating two areas of the Simple Map. First we want to see what ther surfaces look like if they are magnified near the X-point. We are looking for self-similar structures in which order can be found in chaos, and chaos can be found in order. Our second investigation deals with how neighboring field lines separate in the chaotic region. We are expecting to see the distance between two close points drastically increase as we near the X-point. Reshama Saralkar and Cedric White are HU CFRT 1998 Summer Fusion High School Workshop Participants from the NASA SHARP PLUS Program. RS attends Watkins Mill High School in Gaithersburg, MD. CW attends Gwynn Park High School in Brandywine,MD. They are mentored by Dr. Ali and Dr. Punjabi of HU CFRT. 1. Punjabi et al, Phys Rev Lett 69 3322 (1992) 2. Punjabi et al, J Plasma Phys 52 91 (1994)

Bistability and chaos in the Taylor-Green dynamo.

PubMed

Yadav, Rakesh K; Verma, Mahendra K; Wahi, Pankaj

2012-03-01

Using direct numerical simulations, we study dynamo action under Taylor-Green forcing for a magnetic Prandtl number of 0.5. We observe bistability with weak- and strong-magnetic-field branches. Both the dynamo branches undergo subcritical dynamo transition. We also observe a host of dynamo states including constant, periodic, quasiperiodic, and chaotic magnetic fields. One of the chaotic states originates through a quasiperiodic route with phase locking, while the other chaotic attractor appears to follow the Newhouse-Ruelle-Takens route to chaos. We also observe intermittent transitions between quasiperiodic and chaotic states for a given Taylor-Green forcing.

The onset of chaos in orbital pilot-wave dynamics.

PubMed

Tambasco, Lucas D; Harris, Daniel M; Oza, Anand U; Rosales, Rodolfo R; Bush, John W M

2016-10-01

We present the results of a numerical investigation of the emergence of chaos in the orbital dynamics of droplets walking on a vertically vibrating fluid bath and acted upon by one of the three different external forces, specifically, Coriolis, Coulomb, or linear spring forces. As the vibrational forcing of the bath is increased progressively, circular orbits destabilize into wobbling orbits and eventually chaotic trajectories. We demonstrate that the route to chaos depends on the form of the external force. When acted upon by Coriolis or Coulomb forces, the droplet's orbital motion becomes chaotic through a period-doubling cascade. In the presence of a central harmonic potential, the transition to chaos follows a path reminiscent of the Ruelle-Takens-Newhouse scenario.

Dynamics analysis of fractional order Yu-Wang system

NASA Astrophysics Data System (ADS)

Bhalekar, Sachin

2013-10-01

Fractional order version of a dynamical system introduced by Yu and Wang (Engineering, Technology & Applied Science Research, 2, (2012) 209-215) is discussed in this article. The basic dynamical properties of the system are studied. Minimum effective dimension 0.942329 for the existence of chaos in the proposed system is obtained using the analytical result. For chaos detection, we have calculated maximum Lyapunov exponents for various values of fractional order. Feedback control method is then used to control chaos in the system. Further, the system is synchronized with itself and with fractional order financial system using active control technique. Modified Adams-Bashforth-Moulton algorithm is used for numerical simulations.

Signatures of chaos in the Brillouin zone.

PubMed

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

2017-10-01

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

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

ERIC Educational Resources Information Center

Pryor, Robert; Bright, Jim

2004-01-01

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

Confirmatory Factor Analysis of the Malay Version of the Confusion, Hubbub and Order Scale (CHAOS-6) among Myocardial Infarction Survivors in a Malaysian Cardiac Healthcare Facility.

PubMed

Ganasegeran, Kurubaran; Selvaraj, Kamaraj; Rashid, Abdul

2017-08-01

The six item Confusion, Hubbub and Order Scale (CHAOS-6) has been validated as a reliable tool to measure levels of household disorder. We aimed to investigate the goodness of fit and reliability of a new Malay version of the CHAOS-6. The original English version of the CHAOS-6 underwent forward-backward translation into the Malay language. The finalised Malay version was administered to 105 myocardial infarction survivors in a Malaysian cardiac health facility. We performed confirmatory factor analyses (CFAs) using structural equation modelling. A path diagram and fit statistics were yielded to determine the Malay version's validity. Composite reliability was tested to determine the scale's reliability. All 105 myocardial infarction survivors participated in the study. The CFA yielded a six-item, one-factor model with excellent fit statistics. Composite reliability for the single factor CHAOS-6 was 0.65, confirming that the scale is reliable for Malay speakers. The Malay version of the CHAOS-6 was reliable and showed the best fit statistics for our study sample. We thus offer a simple, brief, validated, reliable and novel instrument to measure chaos, the Skala Kecelaruan, Keriuhan & Tertib Terubahsuai (CHAOS-6) , for the Malaysian population.

Confirmatory Factor Analysis of the Malay Version of the Confusion, Hubbub and Order Scale (CHAOS-6) among Myocardial Infarction Survivors in a Malaysian Cardiac Healthcare Facility

PubMed Central

Ganasegeran, Kurubaran; Selvaraj, Kamaraj; Rashid, Abdul

2017-01-01

Background The six item Confusion, Hubbub and Order Scale (CHAOS-6) has been validated as a reliable tool to measure levels of household disorder. We aimed to investigate the goodness of fit and reliability of a new Malay version of the CHAOS-6. Methods The original English version of the CHAOS-6 underwent forward-backward translation into the Malay language. The finalised Malay version was administered to 105 myocardial infarction survivors in a Malaysian cardiac health facility. We performed confirmatory factor analyses (CFAs) using structural equation modelling. A path diagram and fit statistics were yielded to determine the Malay version’s validity. Composite reliability was tested to determine the scale’s reliability. Results All 105 myocardial infarction survivors participated in the study. The CFA yielded a six-item, one-factor model with excellent fit statistics. Composite reliability for the single factor CHAOS-6 was 0.65, confirming that the scale is reliable for Malay speakers. Conclusion The Malay version of the CHAOS-6 was reliable and showed the best fit statistics for our study sample. We thus offer a simple, brief, validated, reliable and novel instrument to measure chaos, the Skala Kecelaruan, Keriuhan & Tertib Terubahsuai (CHAOS-6), for the Malaysian population. PMID:28951688

Geometric and dynamic perspectives on phase-coherent and noncoherent chaos.

PubMed

Zou, Yong; Donner, Reik V; Kurths, Jürgen

2012-03-01

Statistically distinguishing between phase-coherent and noncoherent chaotic dynamics from time series is a contemporary problem in nonlinear sciences. In this work, we propose different measures based on recurrence properties of recorded trajectories, which characterize the underlying systems from both geometric and dynamic viewpoints. The potentials of the individual measures for discriminating phase-coherent and noncoherent chaotic oscillations are discussed. A detailed numerical analysis is performed for the chaotic Rössler system, which displays both types of chaos as one control parameter is varied, and the Mackey-Glass system as an example of a time-delay system with noncoherent chaos. Our results demonstrate that especially geometric measures from recurrence network analysis are well suited for tracing transitions between spiral- and screw-type chaos, a common route from phase-coherent to noncoherent chaos also found in other nonlinear oscillators. A detailed explanation of the observed behavior in terms of attractor geometry is given.

A Resonance Overlap Criterion for the Onset of Chaos in Systems of Two Eccentric Planets

NASA Astrophysics Data System (ADS)

Hadden, Sam; Lithwick, Yoram

2018-04-01

I will desrcribe a new analytic criterion to predict the onset of chaos in systems consisting of two massive, eccentric planets. Given a planet pair's spacing and masses, the criterion predicts the eccentricities at which the onset of large-scale chaos occurs. The onset of chaos is predicted based on overlap of mean motion resonances as in Wisdom (1980)'s pioneering work. Whereas Wisdom's work was limited to the overlap of first-order resonance and therefore to nearly circular planets, we account for resonances of all orders. This allows us to consider resonance overlap for planets with arbitrary eccentricities (up to orbit-crossing). Our results show excellent agreement with numerical simulations.

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

NASA Technical Reports Server (NTRS)

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

2003-01-01

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

Phase-Space Transport of Stochastic Chaos in Population Dynamics of Virus Spread

NASA Astrophysics Data System (ADS)

Billings, Lora; Bollt, Erik M.; Schwartz, Ira B.

2002-06-01

A general way to classify stochastic chaos is presented and applied to population dynamics models. A stochastic dynamical theory is used to develop an algorithmic tool to measure the transport across basin boundaries and predict the most probable regions of transport created by noise. The results of this tool are illustrated on a model of virus spread in a large population, where transport regions reveal how noise completes the necessary manifold intersections for the creation of emerging stochastic chaos.

From Fears of Entropy to Comfort in Chaos: "Arcadia," "The Waste Land," "Numb3rs," and Man's Relationship with Science

ERIC Educational Resources Information Center

Miller, Kristen

2007-01-01

Through the use of some purposeful anachronisms, Tom Stoppard uses his 1993 play "Arcadia" to explore the effects on man's psyche of the transition from Newton's Laws to the laws of thermodynamics and from thermodynamics to chaos theory. However, remarkably similar reactions to these changes are also reflected in works from the actual time periods…

Methods of Stochastic Analysis of Complex Regimes in the 3D Hindmarsh-Rose Neuron Model

NASA Astrophysics Data System (ADS)

Bashkirtseva, Irina; Ryashko, Lev; Slepukhina, Evdokia

A problem of the stochastic nonlinear analysis of neuronal activity is studied by the example of the Hindmarsh-Rose (HR) model. For the parametric region of tonic spiking oscillations, it is shown that random noise transforms the spiking dynamic regime into the bursting one. This stochastic phenomenon is specified by qualitative changes in distributions of random trajectories and interspike intervals (ISIs). For a quantitative analysis of the noise-induced bursting, we suggest a constructive semi-analytical approach based on the stochastic sensitivity function (SSF) technique and the method of confidence domains that allows us to describe geometrically a distribution of random states around the deterministic attractors. Using this approach, we develop a new algorithm for estimation of critical values for the noise intensity corresponding to the qualitative changes in stochastic dynamics. We show that the obtained estimations are in good agreement with the numerical results. An interplay between noise-induced bursting and transitions from order to chaos is discussed.

A phase transition induces chaos in a predator-prey ecosystem with a dynamic fitness landscape

PubMed Central

2017-01-01

In many ecosystems, natural selection can occur quickly enough to influence the population dynamics and thus future selection. This suggests the importance of extending classical population dynamics models to include such eco-evolutionary processes. Here, we describe a predator-prey model in which the prey population growth depends on a prey density-dependent fitness landscape. We show that this two-species ecosystem is capable of exhibiting chaos even in the absence of external environmental variation or noise, and that the onset of chaotic dynamics is the result of the fitness landscape reversibly alternating between epochs of stabilizing and disruptive selection. We draw an analogy between the fitness function and the free energy in statistical mechanics, allowing us to use the physical theory of first-order phase transitions to understand the onset of rapid cycling in the chaotic predator-prey dynamics. We use quantitative techniques to study the relevance of our model to observational studies of complex ecosystems, finding that the evolution-driven chaotic dynamics confer community stability at the “edge of chaos” while creating a wide distribution of opportunities for speciation during epochs of disruptive selection—a potential observable signature of chaotic eco-evolutionary dynamics in experimental studies. PMID:28678792

Transition to chaos of a vertical collapsible tube conveying air flow

NASA Astrophysics Data System (ADS)

Castillo Flores, F.; Cros, A.

2009-05-01

"Sky dancers", the large collapsible tubes used as advertising, are studied in this work through a simple experimental device. Our study is devoted to the nonlinear dynamics of this system and to its transition to chaos. Firstly, we have shown that after a collapse occurs, the air fills the tube at a different speed rate from the flow velocity. Secondly, the temporal intermittency is studied as the flow rate is increased. A statistical analysis shows that the chaotic times maintain roughly the same value by increasing air speed. On the other hand, laminar times become shorter, until the system reaches a completely chaotic state.

Chaos, Complexity, Learning, and the Learning Organization: Towards a Chaordic Enterprise

ERIC Educational Resources Information Center

van Eijnatten, Frans M.; Putnik, Goran D.

2004-01-01

In order to set the stage for this special issue, the prime concepts are defined: i.e. "chaos," "complexity," "learning" (individual and organizational), "learning organization," and "chaordic enterprise". Also, several chaos-and-complexity-related definitions of learning and learning organizations are provided. Next, the guest editors' main…

Geological History of the Tyre Region of Europa: A Regional Perspective on Europan Surface Features and Ice Thickness

NASA Technical Reports Server (NTRS)

Kadel, Steven D.; Chuang, Frank C.; Greeley, Ronald; Moore, Jeffrey M.

2000-01-01

Galileo images of the Tyre Macula region of Europa at regional (170 m/pixel) and local (approx. 40 m/pixel) scales allow mapping and understanding of surface processes and landforms. Ridged plains, doublet and complex ridges, shallow pits, domes, "chaos" areas. impact structures, tilted blocks and massifs, and young fracture systems indicate a complex history of surface deformation on Europa. Regional and local morphologies of the Tyre region of Europa suggest that an impactor penetrated through several kilometers of water ice tc a mobile layer below. The surface morphology was initially dominated by formation of ridged plains, followed by development of ridge bands and doublet ridges, with chaos and fracture formation dominating the latter part of the geologic history of the Tyre region. Two distinct types of chaos have been identified which, along with upwarped dome materials, appear to represent a continuum of features (domes-play chaos-knobby chaos) resulting from increasing degree of surface disruption associated with local lithospheric heating and thinning. Local and regional stratigraphic relationships, block heights, and the morphology of the Tyre impact structure suggest the presence of low-viscosity ice or liquid water beneath a thin (severa1 kilometers) surface ice shell at the time of the impact. The very low impact crater density on the surface of Europa suggests that this thin shell has either formed or been thoroughly resurfaced in the very recent past.

Chaos and complexity by design

DOE PAGES

Roberts, Daniel A.; Yoshida, Beni

2017-04-20

We study the relationship between quantum chaos and pseudorandomness by developing probes of unitary design. A natural probe of randomness is the “frame poten-tial,” which is minimized by unitary k-designs and measures the 2-norm distance between the Haar random unitary ensemble and another ensemble. A natural probe of quantum chaos is out-of-time-order (OTO) four-point correlation functions. We also show that the norm squared of a generalization of out-of-time-order 2k-point correlators is proportional to the kth frame potential, providing a quantitative connection between chaos and pseudorandomness. In addition, we prove that these 2k-point correlators for Pauli operators completely determine the k-foldmore » channel of an ensemble of unitary operators. Finally, we use a counting argument to obtain a lower bound on the quantum circuit complexity in terms of the frame potential. This provides a direct link between chaos, complexity, and randomness.« less

Children's ideas about the solar system and the chaos in learning science

NASA Astrophysics Data System (ADS)

Sharp, John G.; Kuerbis, Paul

2006-01-01

Findings from a quasi-experimental study of children's ideas about the solar system and how these ideas changed in response to a 10-week intervention period of formal astronomy teaching at a single primary school in England are presented in detail. Initial interviews with all of the 9- to 11-year-olds involved revealed a relatively poorly developed prior knowledge base, and this was reflected in the predominantly intuitive and transitional nature of the different mental models expressed and used when answering questions and completing tasks. Following intervention, progression was evident in many different forms and this could be described and measured both qualitatively and quantitatively. The routes and pathways toward scientific conceptualization were often direct, and most changes could be attributed largely to the processes of weak and radical knowledge restructuring. Together with the retention of newly formed ideas over time, learning outcomes were considered particularly encouraging. In order to explain findings more fully, evidence is presented which lends some support to the notion of chaos in cognition.

Death and revival of chaos.

PubMed

Kaszás, Bálint; Feudel, Ulrike; Tél, Tamás

2016-12-01

We investigate the death and revival of chaos under the impact of a monotonous time-dependent forcing that changes its strength with a non-negligible rate. Starting on a chaotic attractor it is found that the complexity of the dynamics remains very pronounced even when the driving amplitude has decayed to rather small values. When after the death of chaos the strength of the forcing is increased again with the same rate of change, chaos is found to revive but with a different history. This leads to the appearance of a hysteresis in the complexity of the dynamics. To characterize these dynamics, the concept of snapshot attractors is used, and the corresponding ensemble approach proves to be superior to a single trajectory description, that turns out to be nonrepresentative. The death (revival) of chaos is manifested in a drop (jump) of the standard deviation of one of the phase-space coordinates of the ensemble; the details of this chaos-nonchaos transition depend on the ratio of the characteristic times of the amplitude change and of the internal dynamics. It is demonstrated that chaos cannot die out as long as underlying transient chaos is present in the parameter space. As a condition for a "quasistatically slow" switch-off, we derive an inequality which cannot be fulfilled in practice over extended parameter ranges where transient chaos is present. These observations need to be taken into account when discussing the implications of "climate change scenarios" in any nonlinear dynamical system.

Chaos as the hub of systems dynamics. The part I-The attitude control of spacecraft by involving in the heteroclinic chaos

NASA Astrophysics Data System (ADS)

Doroshin, Anton V.

2018-06-01

In this work the chaos in dynamical systems is considered as a positive aspect of dynamical behavior which can be applied to change systems dynamical parameters and, moreover, to change systems qualitative properties. From this point of view, the chaos can be characterized as a hub for the system dynamical regimes, because it allows to interconnect separated zones of the phase space of the system, and to fulfill the jump into the desirable phase space zone. The concretized aim of this part of the research is to focus on developing the attitude control method for magnetized gyrostat-satellites, which uses the passage through the intentionally generated heteroclinic chaos. The attitude dynamics of the satellite/spacecraft in this case represents the series of transitions from the initial dynamical regime into the chaotic heteroclinic regime with the subsequent exit to the final target dynamical regime with desirable parameters of the attitude dynamics.

Defects and spatiotemporal disorder in a pattern of falling liquid columns

NASA Astrophysics Data System (ADS)

Brunet, Philippe; Limat, Laurent

2004-10-01

Disordered regimes of a one-dimensional pattern of liquid columns hanging below an overflowing circular dish are investigated experimentally. The interaction of two basic dynamical modes (oscillations and drift) combined with the occurrence of defects (birth of new columns, disappearances by coalescences of two columns) leads to spatiotemporal chaos. When the flow rate is progressively increased, a continuous transition between transient and permanent chaos is pointed into evidence. We introduce the rate of defects as the sole relevant quantity to quantify this “turbulence” without ambiguity. Statistics on both transient and endlessly chaotic regimes enable to define a critical flow rate around which exponents are extracted. Comparisons are drawn with other interfacial pattern-forming systems, where transition towards chaos follows similar steps. Qualitatively, careful examinations of the global dynamics show that the contamination processes are nonlocal and involve the propagation of blocks of elementary laminar states (such as propagative domains or local oscillations), emitted near the defects, which turn out to be essential ingredients of this self-sustained disorder.

Origins of Chaos in Autonomous Boolean Networks

NASA Astrophysics Data System (ADS)

Socolar, Joshua; Cavalcante, Hugo; Gauthier, Daniel; Zhang, Rui

2010-03-01

Networks with nodes consisting of ideal Boolean logic gates are known to display either steady states, periodic behavior, or an ultraviolet catastrophe where the number of logic-transition events circulating in the network per unit time grows as a power-law. In an experiment, non-ideal behavior of the logic gates prevents the ultraviolet catastrophe and may lead to deterministic chaos. We identify certain non-ideal features of real logic gates that enable chaos in experimental networks. We find that short-pulse rejection and the asymmetry between the logic states tends to engender periodic behavior. On the other hand, a memory effect termed ``degradation'' can generate chaos. Our results strongly suggest that deterministic chaos can be expected in a large class of experimental Boolean-like networks. Such devices may find application in a variety of technologies requiring fast complex waveforms or flat power spectra. The non-ideal effects identified here also have implications for the statistics of attractors in large complex networks.

Shape and size distribution of chaos areas on Europa

NASA Astrophysics Data System (ADS)

Mikell, T.; Cox, R.

2008-12-01

Chaos terrain is ubiquitous on Europa's surface, but not randomly distributed. The global distribution of chaos areas shows a significant concentration between 30° N and S latitude, decreasing dramatically at higher latitudes. The low-latitude clustering is not an artifact of recognizability, as there is a greater proportion of images with high solar incidence angle (low light) at higher latitudes. Clustering is especially marked in context of the few but vast regional chaos tracts (>15,000 km2) that occupy a substantial proportion of the equatorial region: i.e. the low latitudes have not only greater numbers but much greater areal chaos coverage. Apex-antapex asymmetry is difficult to evaluate because the Galileo longitudinal coverage is so poor; but comparison of the image swaths that follow great circles across the leading and trailing hemispheres respectively shows greater numbers of chaos areas on the leading side. In spite of the equatorial location of a few vast chaos tracts, there is no apparent relationship between chaos area size and latitude. Chaos area outlines vary from smoothly circular to extremely jagged: the irregularity index ranges from 2- 270% (based on the ratio between measured chaos area perimeter and the circumference of a circle of equal area). There is a range of shapes in all size brackets, but smaller chaos areas on average have simpler, more equidimensional shapes, and edge complexity increases for larger chaos areas. Chaos areas of ~10 km equivalent circle diameter (ECD) have outlines that are 4-90% irregular, ones ~50 km ECD are 15-180% and those >100 km ECD are 35-270% irregular. In general, chaos areas with higher irregularity indices also have a higher raft:matrix ratio. These results, while preliminary, are consistent with experimental evidence suggesting an impact origin for some chaos terrain on Europa. In particular, the relationship between shape and size parallels the results of impact experiments into ice over water, in which lower-energy impacts produce small, circular bullet-holes with few or no rafts; and higher-energy impacts generate wide-field fragmentation of the ice, producing large and highly irregular openings with abundant floating crustal blocks.

Application of Chaos Theory to 1/f Noise

DTIC Science & Technology

1988-02-12

recently, we lacked the mathematical sophistication to analyze chaotic behavior. However, that situation is changing rapidly. We are now beginning to...along with nonlinear coupling between dependent variables. Linked with the notion of chaos is a mathematical construct known as a "strange attractor". 11...flow 12 S as the Reynolds number, Re, is increased above some critical value. We can observe this transition in the mathematics by watching the

Transition from Poissonian to Gaussian-orthogonal-ensemble level statistics in a modified Artin's billiard

NASA Astrophysics Data System (ADS)

Csordás, A.; Graham, R.; Szépfalusy, P.; Vattay, G.

1994-01-01

One wall of an Artin's billiard on the Poincaré half-plane is replaced by a one-parameter (cp) family of nongeodetic walls. A brief description of the classical phase space of this system is given. In the quantum domain, the continuous and gradual transition from the Poisson-like to Gaussian-orthogonal-ensemble (GOE) level statistics due to the small perturbations breaking the symmetry responsible for the ``arithmetic chaos'' at cp=1 is studied. Another GOE-->Poisson transition due to the mixed phase space for large perturbations is also investigated. A satisfactory description of the intermediate level statistics by the Brody distribution was found in both cases. The study supports the existence of a scaling region around cp=1. A finite-size scaling relation for the Brody parameter as a function of 1-cp and the number of levels considered can be established.

Electric fields yield chaos in microflows

PubMed Central

Posner, Jonathan D.; Pérez, Carlos L.; Santiago, Juan G.

2012-01-01

We present an investigation of chaotic dynamics of a low Reynolds number electrokinetic flow. Electrokinetic flows arise due to couplings of electric fields and electric double layers. In these flows, applied (steady) electric fields can couple with ionic conductivity gradients outside electric double layers to produce flow instabilities. The threshold of these instabilities is controlled by an electric Rayleigh number, Rae. As Rae increases monotonically, we show here flow dynamics can transition from steady state to a time-dependent periodic state and then to an aperiodic, chaotic state. Interestingly, further monotonic increase of Rae shows a transition back to a well-ordered state, followed by a second transition to a chaotic state. Temporal power spectra and time-delay phase maps of low dimensional attractors graphically depict the sequence between periodic and chaotic states. To our knowledge, this is a unique report of a low Reynolds number flow with such a sequence of periodic-to-aperiodic transitions. Also unique is a report of strange attractors triggered and sustained through electric fluid body forces. PMID:22908251

Chaos M-ary modulation and demodulation method based on Hamilton oscillator and its application in communication.

PubMed

Fu, Yongqing; Li, Xingyuan; Li, Yanan; Yang, Wei; Song, Hailiang

2013-03-01

Chaotic communication has aroused general interests in recent years, but its communication effect is not ideal with the restriction of chaos synchronization. In this paper a new chaos M-ary digital modulation and demodulation method is proposed. By using region controllable characteristics of spatiotemporal chaos Hamilton map in phase plane and chaos unique characteristic, which is sensitive to initial value, zone mapping method is proposed. It establishes the map relationship between M-ary digital information and the region of Hamilton map phase plane, thus the M-ary information chaos modulation is realized. In addition, zone partition demodulation method is proposed based on the structure characteristic of Hamilton modulated information, which separates M-ary information from phase trajectory of chaotic Hamilton map, and the theory analysis of zone partition demodulator's boundary range is given. Finally, the communication system based on the two methods is constructed on the personal computer. The simulation shows that in high speed transmission communications and with no chaos synchronization circumstance, the proposed chaotic M-ary modulation and demodulation method has outperformed some conventional M-ary modulation methods, such as quadrature phase shift keying and M-ary pulse amplitude modulation in bit error rate. Besides, it has performance improvement in bandwidth efficiency, transmission efficiency and anti-noise performance, and the system complexity is low and chaos signal is easy to generate.

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

ERIC Educational Resources Information Center

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

2005-01-01

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

Quasiperiodicity and chaos in cardiac fibrillation.

PubMed Central

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

Quasiperiodicity and chaos in cardiac fibrillation.

PubMed

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

1997-01-15

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.

Chaos, Hubbub, and Order Scale and Health Risk Behaviors in Adolescents in Los Angeles.

PubMed

Chatterjee, Avik; Gillman, Matthew W; Wong, Mitchell D

2015-12-01

To determine the relationship between household chaos and substance use, sexual activity, and violence-related risk behaviors in adolescents. We analyzed cross-sectional data among 929 high-school students in Los Angeles who completed a 90-minute interview that assessed health behaviors and household chaos with the 14-question Chaos, Hubbub, and Order Scale (CHAOS). Using the generalized estimating equation and adjusting for personal, parental, and family covariates, we examined associations of CHAOS score with substance use, sexual activity, and violent behavior outcome variables. We also examined the role of depression and school engagement as mediators. Mean (SD) age of the 929 students was 16.4 (1.3) years, 516 (55%) were female, and 780 (84%) were Latino. After adjustment, compared with students with CHAOS score 0, those students with the greatest scores (5-14) had ORs of 3.1 (95% CI 1.1-8.7) for smoking, 2.6 (95% CI 1.6-4.4) for drinking, 6.1 (95% CI 1.8-21) for substance use at school, and 1.9 (95% CI 1.1-3.3) for fighting in the past 12 months. Associations between CHAOS score and sexual risk and other violent behaviors were not significant. Depression and school engagement attenuated the associations. In this group of adolescents, greatest CHAOS score was associated with increased odds of risky health behaviors, with depression and school engagement as potential mediators. In the future, CHAOS score could be measured to assess risk for such behaviors or be a target for intervention to reduce chances of engaging in these behaviors. Copyright © 2015 Elsevier Inc. All rights reserved.

Quasiperiodic instability and chaos in the bad-cavity laser with modulated inversion: Numerical analysis of a Toda oscillator system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ogawa, T.

The exact equivalence between a bad-cavity laser with modulated inversion and a nonlinear oscillator in a Toda potential driven by an external modulation is presented. The dynamical properties of the laser system are investigated in detail by analyzing a Toda oscillator system. The temporal characteristics of the bad-cavity laser under strong modulation are analyzed extensively by numerically investigating the simpler Toda system as a function of two control parameters: the dc component of the population inversion and the modulation amplitude. The system exhibits two kinds of optical chaos: One is the quasiperiodic chaos in the region of the intermediate modulationmore » amplitude and the other is the intermittent kicked chaos in the region of strong modulation and large dc component of the pumping. The former is well described by a one-dimensional discrete map with a singular invariant probability measure. There are two types of onset of the chaos: quasiperiodic instability (continuous path to chaos) and catastrophic crisis (discontinuous path). The period-doubling cascade of bifurcation is also observed. The simple discrete model of the Toda system is presented to obtain analytically the one-dimensional map function and to understand the effect of the asymmetric potential curvature on yielding chaos.« less

A bound on chaos

DOE PAGES

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

2016-08-17

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

Invoking the muse: Dada's chaos.

PubMed

Rosen, Diane

2014-07-01

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

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.

Recurrence-plot-based measures of complexity and their application to heart-rate-variability data.

PubMed

Marwan, Norbert; Wessel, Niels; Meyerfeldt, Udo; Schirdewan, Alexander; Kurths, Jürgen

2002-08-01

The knowledge of transitions between regular, laminar or chaotic behaviors is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there are several nonlinear methods that, however, require rather long time observations. To overcome these difficulties, we propose measures of complexity based on vertical structures in recurrence plots and apply them to the logistic map as well as to heart-rate-variability data. For the logistic map these measures enable us not only to detect transitions between chaotic and periodic states, but also to identify laminar states, i.e., chaos-chaos transitions. The traditional recurrence quantification analysis fails to detect the latter transitions. Applying our measures to the heart-rate-variability data, we are able to detect and quantify the laminar phases before a life-threatening cardiac arrhythmia occurs thereby facilitating a prediction of such an event. Our findings could be of importance for the therapy of malignant cardiac arrhythmias.

Dynamical transitions in large systems of mean field-coupled Landau-Stuart oscillators: Extensive chaos and cluster states.

PubMed

Ku, Wai Lim; Girvan, Michelle; Ott, Edward

2015-12-01

In this paper, we study dynamical systems in which a large number N of identical Landau-Stuart oscillators are globally coupled via a mean-field. Previously, it has been observed that this type of system can exhibit a variety of different dynamical behaviors. These behaviors include time periodic cluster states in which each oscillator is in one of a small number of groups for which all oscillators in each group have the same state which is different from group to group, as well as a behavior in which all oscillators have different states and the macroscopic dynamics of the mean field is chaotic. We argue that this second type of behavior is "extensive" in the sense that the chaotic attractor in the full phase space of the system has a fractal dimension that scales linearly with N and that the number of positive Lyapunov exponents of the attractor also scales linearly with N. An important focus of this paper is the transition between cluster states and extensive chaos as the system is subjected to slow adiabatic parameter change. We observe discontinuous transitions between the cluster states (which correspond to low dimensional dynamics) and the extensively chaotic states. Furthermore, examining the cluster state, as the system approaches the discontinuous transition to extensive chaos, we find that the oscillator population distribution between the clusters continually evolves so that the cluster state is always marginally stable. This behavior is used to reveal the mechanism of the discontinuous transition. We also apply the Kaplan-Yorke formula to study the fractal structure of the extensively chaotic attractors.

Dynamical transitions in large systems of mean field-coupled Landau-Stuart oscillators: Extensive chaos and cluster states

NASA Astrophysics Data System (ADS)

Ku, Wai Lim; Girvan, Michelle; Ott, Edward

2015-12-01

In this paper, we study dynamical systems in which a large number N of identical Landau-Stuart oscillators are globally coupled via a mean-field. Previously, it has been observed that this type of system can exhibit a variety of different dynamical behaviors. These behaviors include time periodic cluster states in which each oscillator is in one of a small number of groups for which all oscillators in each group have the same state which is different from group to group, as well as a behavior in which all oscillators have different states and the macroscopic dynamics of the mean field is chaotic. We argue that this second type of behavior is "extensive" in the sense that the chaotic attractor in the full phase space of the system has a fractal dimension that scales linearly with N and that the number of positive Lyapunov exponents of the attractor also scales linearly with N. An important focus of this paper is the transition between cluster states and extensive chaos as the system is subjected to slow adiabatic parameter change. We observe discontinuous transitions between the cluster states (which correspond to low dimensional dynamics) and the extensively chaotic states. Furthermore, examining the cluster state, as the system approaches the discontinuous transition to extensive chaos, we find that the oscillator population distribution between the clusters continually evolves so that the cluster state is always marginally stable. This behavior is used to reveal the mechanism of the discontinuous transition. We also apply the Kaplan-Yorke formula to study the fractal structure of the extensively chaotic attractors.

On the motion of classical three-body system with consideration of quantum fluctuations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gevorkyan, A. S., E-mail: g-ashot@sci.am

2017-03-15

We obtained the systemof stochastic differential equations which describes the classicalmotion of the three-body system under influence of quantum fluctuations. Using SDEs, for the joint probability distribution of the total momentum of bodies system were obtained the partial differential equation of the second order. It is shown, that the equation for the probability distribution is solved jointly by classical equations, which in turn are responsible for the topological peculiarities of tubes of quantum currents, transitions between asymptotic channels and, respectively for arising of quantum chaos.

Some new surprises in chaos.

PubMed

Bunimovich, Leonid A; Vela-Arevalo, Luz V

2015-09-01

"Chaos is found in greatest abundance wherever order is being sought.It always defeats order, because it is better organized"Terry PratchettA brief review is presented of some recent findings in the theory of chaotic dynamics. We also prove a statement that could be naturally considered as a dual one to the Poincaré theorem on recurrences. Numerical results demonstrate that some parts of the phase space of chaotic systems are more likely to be visited earlier than other parts. A new class of chaotic focusing billiards is discussed that clearly violates the main condition considered to be necessary for chaos in focusing billiards.

Chaos in the fractional order logistic delay system: Circuit realization and synchronization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baskonus, Haci Mehmet; Hammouch, Zakia; Mekkaoui, Toufik

2016-06-08

In this paper, we present a numerical study and a circuit design to prove existence of chaos in the fractional order Logistic delay system. In addition, we investigate an active control synchronization scheme in this system. Numerical and cicruit simulations show the effectiveness and feasibility of this method.

Photonic integrated circuits unveil crisis-induced intermittency.

PubMed

Karsaklian Dal Bosco, Andreas; Akizawa, Yasuhiro; Kanno, Kazutaka; Uchida, Atsushi; Harayama, Takahisa; Yoshimura, Kazuyuki

2016-09-19

We experimentally investigate an intermittent route to chaos in a photonic integrated circuit consisting of a semiconductor laser with time-delayed optical feedback from a short external cavity. The transition from a period-doubling dynamics to a fully-developed chaos reveals a stage intermittently exhibiting these two dynamics. We unveil the bifurcation mechanism underlying this route to chaos by using the Lang-Kobayashi model and demonstrate that the process is based on a phenomenon of attractor expansion initiated by a particular distribution of the local Lyapunov exponents. We emphasize on the crucial importance of the distribution of the steady-state solutions introduced by the time-delayed feedback on the existence of this intermittent dynamics.

Anti-control of chaos of single time-scale brushless DC motor.

PubMed

Ge, Zheng-Ming; Chang, Ching-Ming; Chen, Yen-Sheng

2006-09-15

Anti-control of chaos of single time-scale brushless DC motors is studied in this paper. In order to analyse a variety of periodic and chaotic phenomena, we employ several numerical techniques such as phase portraits, bifurcation diagrams and Lyapunov exponents. Anti-control of chaos can be achieved by adding an external constant term or an external periodic term.

Chaos in charged AdS black hole extended phase space

NASA Astrophysics Data System (ADS)

Chabab, M.; El Moumni, H.; Iraoui, S.; Masmar, K.; Zhizeh, S.

2018-06-01

We present an analytical study of chaos in a charged black hole in the extended phase space in the context of the Poincare-Melnikov theory. Along with some background on dynamical systems, we compute the relevant Melnikov function and find its zeros. Then we analyse these zeros either to identify the temporal chaos in the spinodal region, or to observe spatial chaos in the small/large black hole equilibrium configuration. As a byproduct, we derive a constraint on the Black hole' charge required to produce chaotic behaviour. To the best of our knowledge, this is the first endeavour to understand the correlation between chaos and phase picture in black holes.

Noise-induced shifts in the population model with a weak Allee effect

NASA Astrophysics Data System (ADS)

Bashkirtseva, Irina; Ryashko, Lev

2018-02-01

We consider the Truscott-Brindley system of interacting phyto- and zooplankton populations with a weak Allee effect. We add a random noise to the parameter of the prey carrying capacity, and study how the noise affects the dynamic behavior of this nonlinear prey-predator model. Phenomena of the stochastic excitement and noise-induced shifts in zones of the Andronov-Hopf bifurcation and Canard explosion are analyzed on the base of the direct numerical simulation and stochastic sensitivity functions technique. A relationship of these phenomena with transitions between order and chaos is discussed.

Wave Number Selection for Incompressible Parallel Jet Flows Periodic in Space

NASA Technical Reports Server (NTRS)

Miles, Jeffrey Hilton

1997-01-01

The temporal instability of a spatially periodic parallel flow of an incompressible inviscid fluid for various jet velocity profiles is studied numerically using Floquet Analysis. The transition matrix at the end of a period is evaluated by direct numerical integration. For verification, a method based on approximating a continuous function by a series of step functions was used. Unstable solutions were found only over a limited range of wave numbers and have a band type structure. The results obtained are analogous to the behavior observed in systems exhibiting complexity at the edge of order and chaos.

Overexpression of DOSOC1, an ortholog of Arabidopsis SOC1, promotes flowering in the orchid Dendrobium Chao Parya Smile.

PubMed

Ding, Lihua; Wang, Yanwen; Yu, Hao

2013-04-01

SUPPRESSOR OF OVEREXPRESSION OF CONSTANS1 (SOC1) encodes a MADS-box protein that plays an essential role in integrating multiple flowering signals to regulate the transition from vegetative to reproductive development in the model plant Arabidopsis. Although SOC1-like genes have been isolated in various angiosperms, its orthologs in Orchidaceae, one of the largest families of flowering plants, are so far unknown. To investigate the regulatory mechanisms of flowering time control in orchids, we isolated a SOC1-like gene, DOSOC1, from Dendrobium Chao Praya Smile. DOSOC1 was highly expressed in reproductive organs, including inflorescence apices, pedicels, floral buds and open flowers. Its expression significantly increased in whole plantlets during the transition from vegetative to reproductive development, which usually occurred after 8 weeks of culture in Dendrobium Chao Praya Smile. In the shoot apex at the floral transitional stage, DOSOC1 was particularly expressed in emerging floral meristems. Overexpression of DOSOC1 in wild-type Arabidopsis plants resulted in early flowering, which was coupled with the up-regulation of two other flowering promoters, AGAMOUS-LIKE 24 and LEAFY. In addition, overexpression of DOSOC1 was able partially to complement the late-flowering phenotype of Arabidopsis soc1-2 loss-of-function mutants. Furthermore, we successfully created seven 35S:DOSOC1 transgenic Dendrobium orchid lines, which consistently exhibited earlier flowering than wild-type orchids. Our results suggest that SOC1-like genes play an evolutionarily conserved role in promoting flowering in the Orchidaceae family, and that DOSOC1 isolated from Dendrobium Chao Praya Smile could serve as an important target for genetic manipulation of flowering time in orchids.

Many-Body Quantum Chaos and Entanglement in a Quantum Ratchet

NASA Astrophysics Data System (ADS)

Valdez, Marc Andrew; Shchedrin, Gavriil; Heimsoth, Martin; Creffield, Charles E.; Sols, Fernando; Carr, Lincoln D.

2018-06-01

We uncover signatures of quantum chaos in the many-body dynamics of a Bose-Einstein condensate-based quantum ratchet in a toroidal trap. We propose measures including entanglement, condensate depletion, and spreading over a fixed basis in many-body Hilbert space, which quantitatively identify the region in which quantum chaotic many-body dynamics occurs, where random matrix theory is limited or inaccessible. With these tools, we show that many-body quantum chaos is neither highly entangled nor delocalized in the Hilbert space, contrary to conventionally expected signatures of quantum chaos.

Many-Body Quantum Chaos and Entanglement in a Quantum Ratchet.

PubMed

Valdez, Marc Andrew; Shchedrin, Gavriil; Heimsoth, Martin; Creffield, Charles E; Sols, Fernando; Carr, Lincoln D

2018-06-08

We uncover signatures of quantum chaos in the many-body dynamics of a Bose-Einstein condensate-based quantum ratchet in a toroidal trap. We propose measures including entanglement, condensate depletion, and spreading over a fixed basis in many-body Hilbert space, which quantitatively identify the region in which quantum chaotic many-body dynamics occurs, where random matrix theory is limited or inaccessible. With these tools, we show that many-body quantum chaos is neither highly entangled nor delocalized in the Hilbert space, contrary to conventionally expected signatures of quantum chaos.

THE CONSISTENCY OF AMEBA CYTOPLASM AND ITS BEARING ON THE MECHANISM OF AMEBOID MOVEMENT

PubMed Central

Allen, Robert D.

1960-01-01

Three species of common, free-living amebae, Amoeba proteus, Amoeba dubia, and Chaos chaos were directly observed and photographed while exposed to a range of centrifugal accelerations in two types of centrifuge microscopes. Cytoplasmic inclusions in all three species are displaced discontinuously (at a variable velocity) in apparently all parts of the cell, suggesting non-Newtonian behavior and/or heterogeneous consistency. The ectoplasm of all species shows the highest yield point of any region in the cell; the posterior ectoplasm is less rigid than that in the anterior part of the cell. The axial part of the endoplasm shows evidence of structure (a sharp viscosity transition if not a true yield point) by its: (a) resistance to the displacement of particles carried in that region of the cell, (b) hindrance to the passage through the cell of inclusions displaced from other regions, and its (c) support without visible back-slip of inclusion being resuspended in the axial endoplasm in a centripetal direction at accelerations as high as 170 g. At this acceleration, each crystal "weighs" the equivalent reduced weight of seven times its volume in gold at 1 g. The only regions of the normal, moving cell which show clear evidence of low apparent viscosity are the "shear zone" (see Fig. 8) and the "recruitment zone." Possible reasons for low apparent viscosity in these regions are discussed. A new scheme of ameba "structure" is presented on the basis of the combined results of velocity profile analysis and the present centrifugation study. PMID:13682546

Understanding the Role of Chaos Theory in Military Decision Making

DTIC Science & Technology

2009-01-01

Because chaos is bounded, planners can create allowances for system noise. The existence of strange and normal chaotic attractors helps explain why... strange and normal chaotic attractors helps explain why system turbulence is uneven or concentrated around specific solution regions. Finally, the...give better understanding of the implications of chaos: sensitivity to initial conditions, strange attractors , and constants of motion. By showing the

Short-time Lyapunov exponent analysis and the transition to chaos in Taylor-Couette flow

NASA Technical Reports Server (NTRS)

Vastano, John A.; Moser, Robert D.

1991-01-01

The physical mechanism driving the weakly chaotic Taylor-Couette flow is investigated using the short-time Liapunov exponent analysis. In this procedure, the transition from quasi-periodicity to chaos is studied using direct numerical 3D simulations of axially periodic Taylor-Couette flow, and a partial Liapunov exponent spectrum for the flow is computed by simultaneously advancing the full solution and a set of perturbations. It is shown that the short-time Liapunov exponent analysis yields more information on the exponents and dimension than that obtained from the common Liapunov exponent calculations. Results show that the chaotic state studied here is caused by a Kelvin-Helmholtz-type instability of the outflow boundary jet of Taylor vortices.

Transition to chaos in an open unforced 2D flow

NASA Technical Reports Server (NTRS)

Pulliam, Thomas H.; Vastano, John A.

1993-01-01

The present numerical study of unsteady, low Reynolds number flow past a 2D airfoil attempts to ascertain the bifurcation sequence leading from simple periodic to complex aperiodic flow with rising Reynolds number, as well as to characterize the degree of chaos present in the aperiodic flow and assess the role of numerics in the modification and control of the observed bifurcation scenario. The ARC2D Navier-Stokes code is used in an unsteady time-accurate mode for most of these computations. The system undergoes a period-doubling bifurcation to chaos as the Reynolds number is increased from 800 to 1600; its chaotic attractors are characterized by estimates of the fractal dimension and partial Liapunov exponent spectra.

Photonic generation of polarization-resolved wideband chaos with time-delay concealment in three-cascaded vertical-cavity surface-emitting lasers.

PubMed

Liu, Huijie; Li, Nianqiang; Zhao, Qingchun

2015-05-10

Optical chaos generated by chaotic lasers has been widely used in several important applications, such as chaos-based communications and high-speed random-number generators. However, these applications are susceptible to degradation by the presence of time-delay (TD) signature identified from the chaotic output. Here we propose to achieve the concealment of TD signature, along with the enhancement of chaos bandwidth, in three-cascaded vertical-cavity surface-emitting lasers (VCSELs). The cascaded system is composed of an external-cavity master VCSEL, a solitary intermediate VCSEL, and a solitary slave VCSEL. Through mapping the evolutions of TD signature and chaos bandwidth in the parameter space of the injection strength and frequency detuning, photonic generation of polarization-resolved wideband chaos with TD concealment is numerically demonstrated for wide regions of the injection parameters.

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)

The security energy encryption in wireless power transfer

NASA Astrophysics Data System (ADS)

Sadzali, M. N.; Ali, A.; Azizan, M. M.; Albreem, M. A. M.

2017-09-01

This paper presents a concept of security in wireless power transfer (WPT) by applying chaos theory. Chaos theory is applied as a security system in order to safeguard the transfer of energy from a transmitter to the intended receiver. The energy encryption of the wireless power transfer utilizes chaos theory to generate the possibility of a logistic map for the chaotic security key. The simulation for energy encryption wireless power transfer system was conducted by using MATLAB and Simulink. By employing chaos theory, the chaotic key ensures the transmission of energy from transmitter to its intended receiver.

Evolutionary behaviour, trade-offs and cyclic and chaotic population dynamics.

PubMed

Hoyle, Andy; Bowers, Roger G; White, Andy

2011-05-01

Many studies of the evolution of life-history traits assume that the underlying population dynamical attractor is stable point equilibrium. However, evolutionary outcomes can change significantly in different circumstances. We present an analysis based on adaptive dynamics of a discrete-time demographic model involving a trade-off whose shape is also an important determinant of evolutionary behaviour. We derive an explicit expression for the fitness in the cyclic region and consequently present an adaptive dynamic analysis which is algebraic. We do this fully in the region of 2-cycles and (using a symbolic package) almost fully for 4-cycles. Simulations illustrate and verify our results. With equilibrium population dynamics, trade-offs with accelerating costs produce a continuously stable strategy (CSS) whereas trade-offs with decelerating costs produce a non-ES repellor. The transition to 2-cycles produces a discontinuous change: the appearance of an intermediate region in which branching points occur. The size of this region decreases as we move through the region of 2-cycles. There is a further discontinuous fall in the size of the branching region during the transition to 4-cycles. We extend our results numerically and with simulations to higher-period cycles and chaos. Simulations show that chaotic population dynamics can evolve from equilibrium and vice-versa.

Dynamical transitions in large systems of mean field-coupled Landau-Stuart oscillators: Extensive chaos and cluster states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ku, Wai Lim; Girvan, Michelle; Ott, Edward

In this paper, we study dynamical systems in which a large number N of identical Landau-Stuart oscillators are globally coupled via a mean-field. Previously, it has been observed that this type of system can exhibit a variety of different dynamical behaviors. These behaviors include time periodic cluster states in which each oscillator is in one of a small number of groups for which all oscillators in each group have the same state which is different from group to group, as well as a behavior in which all oscillators have different states and the macroscopic dynamics of the mean field ismore » chaotic. We argue that this second type of behavior is “extensive” in the sense that the chaotic attractor in the full phase space of the system has a fractal dimension that scales linearly with N and that the number of positive Lyapunov exponents of the attractor also scales linearly with N. An important focus of this paper is the transition between cluster states and extensive chaos as the system is subjected to slow adiabatic parameter change. We observe discontinuous transitions between the cluster states (which correspond to low dimensional dynamics) and the extensively chaotic states. Furthermore, examining the cluster state, as the system approaches the discontinuous transition to extensive chaos, we find that the oscillator population distribution between the clusters continually evolves so that the cluster state is always marginally stable. This behavior is used to reveal the mechanism of the discontinuous transition. We also apply the Kaplan-Yorke formula to study the fractal structure of the extensively chaotic attractors.« less

Timing of chaotic terrain formation in Argadnel Regio, Europa, and implications for geological history

NASA Astrophysics Data System (ADS)

Parro, Laura M.; Ruiz, Javier; Pappalardo, Robert T.

2016-10-01

Chaos terrains are among the most prominent landforms of Europa, and are generally among the youngest features recorded on the surface. Chaos units were formed by to endogenic activity, maybe related to solid-state convection and thermal diapirism in the ice shell, perhaps aided by melting of salt-rich ice bodies below the surface. In this work, we analyze the different units of chaotic terrain in a portion of Argadnel Regio, a region located on the anti-Jovian hemisphere of Europa, and their possible timing in the general stratigraphic framework of this satellite. Two different chaos units can be differentiated, based on surface texture, morphology, and cross-cutting relationships with other units, and from interpretations based on pre-existing surface restoration through elimination of a low albedo band. The existence of two stratigraphically different chaos units implies that conditions for chaos formation occurred during more than a single discreet time on Europa, at least in Argadnel Regio, and perhaps in other places. The existence of older chaos units on Europa might be related to convective episodes possibly favored by local conditions in the icy shell, such as variations in grain size, abundance of non-water ice-components, or regional thickness of the brittle lithosphere or the entire ice shell.

The Importance of Why: An Intelligence Approach for a Multi-Polar World

DTIC Science & Technology

2016-04-04

December 27, 2015). 12. 2 Jupiter Scientific, “Definitions of Important Terms in Chaos Theory ,” Jupiter Scientific website, http...Important Terms in Chaos Theory .” Linearizing a system is approximating a nonlinear system through the application of linear system model. 25...Complexity Theory to Anticipate Strategic Surprise,” 24. 16 M. Mitchell Waldrop, Complexity: The Emerging Science at the Edge of Order and Chaos (New

Detection of Gray Crystalline Hematite in the Aureum and Iani Chaos Layered Terrains

NASA Astrophysics Data System (ADS)

Glotch, T. D.; Rogers, D.; Christensen, P. R.

2005-12-01

Using the TES and THEMIS datasets, small hematite-rich deposits have been discovered in Aureum and Iani Chaos. The newly discovered hematite-rich deposits share several similarities with the deposit in Aram Chaos [1], including the occurrence of hematite in a friable layered unit, and the presence of a light-toned caprock. The presence of these units over a distance of several hundred kilometers in the equatorial latitudes of Mars may point to a preferred global mechanism for hematite formation. However, it is unclear how, if at all, these units are related to the hematite- and sulfate-rich unit in Meridiani Planum, which is substantially larger and older (by as much as 1 Ga) than the layered units seen in the equatorial chaotic terrains. Though the caprock units in Aram Chaos and Aureum Chaos are similar, the corresponding unit in Iani Chaos is morphologically different, exhibiting less of a cliff-forming erosional pattern. The hematite-rich units in Aram and Aureum Chaos lie stratigraphically below the light-toned caprock units. In Iani Chaos, the hematite deposit is coincident with the light-toned unit. Data returned from the Mars Express OMEGA instrument have shown the presence of hydrated sulfates in the hematite-rich units associated with Aram and Iani Chaos, although to date, no sulfate detection has been reported in Aureum Chaos [2]. The sequence of caprock and hematite units in Aram, Aureum, and Iani Chaos probably did not form coincidentally as part of an extensive regional layer, but instead formed by similar, but not identical, processes in their respective chaotic terrains. The presence of these units in chaotic terrains, which have been hypothesized to form by subsidence after the release of subsurface water, indicate that these units may have been deposited in an aqueous environment. By analogy to Meridiani Planum, later subsurface aqueous activity in the region of the chaotic terrains may have provided the necessary diagenetic conditions for the formation of hematite within the layered units. [1] Glotch and Christensen, J. Geophys. Res., in press. [2] Gendrin et al., 2005, Science, 307 p. 1587-1590

Experimental identification of a comb-shaped chaotic region in multiple parameter spaces simulated by the Hindmarsh—Rose neuron model

NASA Astrophysics Data System (ADS)

Jia, Bing

2014-03-01

A comb-shaped chaotic region has been simulated in multiple two-dimensional parameter spaces using the Hindmarsh—Rose (HR) neuron model in many recent studies, which can interpret almost all of the previously simulated bifurcation processes with chaos in neural firing patterns. In the present paper, a comb-shaped chaotic region in a two-dimensional parameter space was reproduced, which presented different processes of period-adding bifurcations with chaos with changing one parameter and fixed the other parameter at different levels. In the biological experiments, different period-adding bifurcation scenarios with chaos by decreasing the extra-cellular calcium concentration were observed from some neural pacemakers at different levels of extra-cellular 4-aminopyridine concentration and from other pacemakers at different levels of extra-cellular caesium concentration. By using the nonlinear time series analysis method, the deterministic dynamics of the experimental chaotic firings were investigated. The period-adding bifurcations with chaos observed in the experiments resembled those simulated in the comb-shaped chaotic region using the HR model. The experimental results show that period-adding bifurcations with chaos are preserved in different two-dimensional parameter spaces, which provides evidence of the existence of the comb-shaped chaotic region and a demonstration of the simulation results in different two-dimensional parameter spaces in the HR neuron model. The results also present relationships between different firing patterns in two-dimensional parameter spaces.

Chaos as an intermittently forced linear system.

PubMed

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

2017-05-30

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

Melnikov's criteria, parametric control of chaos, and stationary chaos occurrence in systems with asymmetric potential subjected to multiscale type excitation.

PubMed

Kwuimy, C A Kitio; Nataraj, C; Litak, G

2011-12-01

We consider the problems of chaos and parametric control in nonlinear systems under an asymmetric potential subjected to a multiscale type excitation. The lower bound line for horseshoes chaos is analyzed using the Melnikov's criterion for a transition to permanent or transient nonperiodic motions, complement by the fractal or regular shape of the basin of attraction. Numerical simulations based on the basins of attraction, bifurcation diagrams, Poincaré sections, Lyapunov exponents, and phase portraits are used to show how stationary dissipative chaos occurs in the system. Our attention is focussed on the effects of the asymmetric potential term and the driven frequency. It is shown that the threshold amplitude ∣γ(c)∣ of the excitation decreases for small values of the driven frequency ω and increases for large values of ω. This threshold value decreases with the asymmetric parameter α and becomes constant for sufficiently large values of α. γ(c) has its maximum value for asymmetric load in comparison with the symmetric load. Finally, we apply the Melnikov theorem to the controlled system to explore the gain control parameter dependencies.

Symmetric Fold/Super-Hopf Bursting, Chaos and Mixed-Mode Oscillations in Pernarowski Model of Pancreatic Beta-Cells

NASA Astrophysics Data System (ADS)

Fallah, Haniyeh

Pancreatic beta-cells produce insulin to regularize the blood glucose level. Bursting is important in beta cells due to its relation to the release of insulin. Pernarowski model is a simple polynomial model of beta-cell activities indicating bursting oscillations in these cells. This paper presents bursting behaviors of symmetric type in this model. In addition, it is shown that the current system exhibits the phenomenon of period doubling cascades of canards which is a route to chaos. Canards are also observed symmetrically near folds of slow manifold which results in a chaotic transition between n and n + 1 spikes symmetric bursting. Furthermore, mixed-mode oscillations (MMOs) and combination of symmetric bursting together with MMOs are illustrated during the transition between symmetric bursting and continuous spiking.

A period-doubling cascade precedes chaos for planar maps.

PubMed

Sander, Evelyn; Yorke, James A

2013-09-01

A period-doubling cascade is often seen in numerical studies of those smooth (one-parameter families of) maps for which as the parameter is varied, the map transitions from one without chaos to one with chaos. Our emphasis in this paper is on establishing the existence of such a cascade for many maps with phase space dimension 2. We use continuation methods to show the following: under certain general assumptions, if at one parameter there are only finitely many periodic orbits, and at another parameter value there is chaos, then between those two parameter values there must be a cascade. We investigate only families that are generic in the sense that all periodic orbit bifurcations are generic. Our method of proof in showing there is one cascade is to show there must be infinitely many cascades. We discuss in detail two-dimensional families like those which arise as a time-2π maps for the Duffing equation and the forced damped pendulum equation.

Self-organization of chaos in mythology from a scientific point of view

NASA Astrophysics Data System (ADS)

Melker, Alexander I.

2007-04-01

In this contribution ancient Greek myths describing world's creation are analyzed as if they were a scientific paper. The 'paper' divided into the following parts: initial and boundary conditions, self-organization of chaos, world lines of self-organization, conclusion. It is shown that the self-organization of chaos consists of several stages during which two motive forces (attractive and repulsive) are generated, and totally disordered chaos transforms into partially ordered. It is found that there are five world lines of self-organization: water, light, cosmos-weather, water-fire, and State evolution.

Chaotic electron diffusion through stochastic webs enhances current flow in superlattices.

PubMed

Fromhold, T M; Patanè, A; Bujkiewicz, S; Wilkinson, P B; Fowler, D; Sherwood, D; Stapleton, S P; Krokhin, A A; Eaves, L; Henini, M; Sankeshwar, N S; Sheard, F W

2004-04-15

Understanding how complex systems respond to change is of fundamental importance in the natural sciences. There is particular interest in systems whose classical newtonian motion becomes chaotic as an applied perturbation grows. The transition to chaos usually occurs by the gradual destruction of stable orbits in parameter space, in accordance with the Kolmogorov-Arnold-Moser (KAM) theorem--a cornerstone of nonlinear dynamics that explains, for example, gaps in the asteroid belt. By contrast, 'non-KAM' chaos switches on and off abruptly at critical values of the perturbation frequency. This type of dynamics has wide-ranging implications in the theory of plasma physics, tokamak fusion, turbulence, ion traps, and quasicrystals. Here we realize non-KAM chaos experimentally by exploiting the quantum properties of electrons in the periodic potential of a semiconductor superlattice with an applied voltage and magnetic field. The onset of chaos at discrete voltages is observed as a large increase in the current flow due to the creation of unbound electron orbits, which propagate through intricate web patterns in phase space. Non-KAM chaos therefore provides a mechanism for controlling the electrical conductivity of a condensed matter device: its extreme sensitivity could find applications in quantum electronics and photonics.

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.

Interactions between neural networks: a mechanism for tuning chaos and oscillations.

PubMed

Wang, Lipo

2007-06-01

We show that chaos and oscillations in a higher-order binary neural network can be tuned effectively using interactions between neural networks. Our results suggest that network interactions may be useful as a means of adjusting the level of dynamic activities in systems that employ chaos and oscillations for information processing, or as a means of suppressing oscillatory behaviors in systems that require stability.

Memory effects, transient growth, and wave breakup in a model of paced atrium

NASA Astrophysics Data System (ADS)

Garzón, Alejandro; Grigoriev, Roman O.

2017-09-01

The mechanisms underlying cardiac fibrillation have been investigated for over a century, but we are still finding surprising results that change our view of this phenomenon. The present study focuses on the transition from normal rhythm to spiral wave chaos associated with a gradual increase in the pacing rate. While some of our findings are consistent with existing experimental, numerical, and theoretical studies of this problem, one result appears to contradict the accepted picture. Specifically we show that, in a two-dimensional model of paced homogeneous atrial tissue, transition from discordant alternans to conduction block, wave breakup, reentry, and spiral wave chaos is associated with the transient growth of finite amplitude disturbances rather than a conventional instability. It is mathematically very similar to subcritical, or bypass, transition from laminar fluid flow to turbulence, which allows many of the tools developed in the context of fluid turbulence to be used for improving our understanding of cardiac arrhythmias.

Generation of chaotic radiation in a driven traveling wave tube amplifier with time-delayed feedback

NASA Astrophysics Data System (ADS)

Marchewka, Chad; Larsen, Paul; Bhattacharjee, Sudeep; Booske, John; Sengele, Sean; Ryskin, Nikita; Titov, Vladimir

2006-01-01

The application of chaos in communications and radar offers new and interesting possibilities. This article describes investigations on the generation of chaos in a traveling wave tube (TWT) amplifier and the experimental parameters responsible for sustaining stable chaos. Chaos is generated in a TWT amplifier when it is made to operate in a highly nonlinear regime by recirculating a fraction of the TWT output power back to the input in a delayed feedback configuration. A driver wave provides a constant external force to the system making it behave like a forced nonlinear oscillator. The effects of the feedback bandwidth, intensity, and phase are described. The study illuminates the different transitions to chaos and the effect of parameters such as the frequency and intensity of the driver wave. The detuning frequency, i.e., difference frequency between the driver wave and the natural oscillation of the system, has been identified as being an important physical parameter for controlling evolution to chaos. Among the observed routes to chaos, besides the more common period doubling, a new route called loss of frequency locking occurs when the driving frequency is adjacent to a natural oscillation mode. The feedback bandwidth controls the nonlinear dynamics of the system, particularly the number of natural oscillation modes. A computational model has been developed to simulate the experiments and reasonably good agreement is obtained between them. Experiments are described that demonstrate the feasibility of chaotic communications using two TWTs, where one is operated as a driven chaotic oscillator and the other as a time-delayed, open-loop amplifier.

A PRELIMINARY STUDY ON THE FRACTAL PHENOMENON: “DISCONNECTED+ DISCONNECTED=CONNECTED”

NASA Astrophysics Data System (ADS)

Wang, Da; Liu, Shutang; Zhao, Yang

The well-known Parrondo’s paradox: “losing+losing=winning” [G. P. Harmer and D. Abbott, Parrondo’s paradox, Stat. Sci. 14 (2009) 206-213.] indicated that two games with negative gains can generate a new game with positive gain. By extending the Parrondo’s philosophy into chaos research, it was shown that the periodic alteration of two chaotic dynamics results in an ordered dynamics, that is the phenomenon: “chaos+chaos=order” [J. Almeida, D. Peralta-Salas and M. Romera, Can two chaotic systems give rise to order, Physica D 200 124-132 (2005)]. This paper further extends these researches into fractal research by proposing that two disconnected Julia sets can originate a new connected Julia set via alternating order. This new parrondian paradoxical phenomenon can be stated in the Parrondo’s terms as “disconnected+disconnected=connected”.

Defect chaos of oscillating hexagons in rotating convection

PubMed

Echebarria; Riecke

2000-05-22

Using coupled Ginzburg-Landau equations, the dynamics of hexagonal patterns with broken chiral symmetry are investigated, as they appear in rotating non-Boussinesq or surface-tension-driven convection. We find that close to the secondary Hopf bifurcation to oscillating hexagons the dynamics are well described by a single complex Ginzburg-Landau equation (CGLE) coupled to the phases of the hexagonal pattern. At the band center these equations reduce to the usual CGLE and the system exhibits defect chaos. Away from the band center a transition to a frozen vortex state is found.

Improved Adaptive LSB Steganography Based on Chaos and Genetic Algorithm

NASA Astrophysics Data System (ADS)

Yu, Lifang; Zhao, Yao; Ni, Rongrong; Li, Ting

2010-12-01

We propose a novel steganographic method in JPEG images with high performance. Firstly, we propose improved adaptive LSB steganography, which can achieve high capacity while preserving the first-order statistics. Secondly, in order to minimize visual degradation of the stego image, we shuffle bits-order of the message based on chaos whose parameters are selected by the genetic algorithm. Shuffling message's bits-order provides us with a new way to improve the performance of steganography. Experimental results show that our method outperforms classical steganographic methods in image quality, while preserving characteristics of histogram and providing high capacity.

Chaos-Assisted Quantum Tunneling and Delocalization Caused by Resonance or Near-Resonance

NASA Astrophysics Data System (ADS)

Liang, Danfu; Zhang, Jiawei; Zhang, Xili

2018-05-01

We investigate the quantum transport of a single particle trapped in a tilted optical lattice modulated with periodical delta kicks, and attempt to figure out the relationship between chaos and delocalization or quantum tunneling. We illustrate some resonant parameter lines existing in both chaotic and regular parameter regions, and discover the velocity of delocalization of particle tends to faster in the resonant line as well as the lines in which the lattice tilt is an integral multiple n of tilt driving frequency in chaotic region. While the degree of localization is linked to the distance between parameter points and resonant lines. Those useful results can be experimentally applied to control chaos-assisted transport of single particle held in optical lattices.

Interactions between neural networks: a mechanism for tuning chaos and oscillations

PubMed Central

2007-01-01

We show that chaos and oscillations in a higher-order binary neural network can be tuned effectively using interactions between neural networks. Our results suggest that network interactions may be useful as a means of adjusting the level of dynamic activities in systems that employ chaos and oscillations for information processing, or as a means of suppressing oscillatory behaviors in systems that require stability. PMID:19003511

Sensitivity of Chaos Measures in Detecting Stress in the Focusing Control Mechanism of the Short-Sighted Eye.

PubMed

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

2017-08-01

When fixating on a stationary object, the power of the eye's lens fluctuates. Studies have suggested that changes in these so-called microfluctuations in accommodation may be a factor in the onset and progression of short-sightedness. Like many physiological signals, the fluctuations in the power of the lens exhibit chaotic behaviour. A breakdown or reduction in chaos in physiological systems indicates stress to the system or pathology. The purpose of this study was to determine whether the chaos in fluctuations of the power of the lens changes with refractive error, i.e. how short-sighted a subject is, and/or accommodative demand, i.e. the effective distance of the object that is being viewed. Six emmetropes (EMMs, non-short-sighted), six early-onset myopes (EOMs, onset of short-sightedness before the age of 15), and six late-onset myopes (LOMs, onset of short-sightedness after the age of 15) took part in the study. Accommodative microfluctuations were measured at 22 Hz using an SRW-5000 autorefractor at accommodative demands of 1 D (dioptres), 2 D, and 3 D. Chaos theory analysis was used to determine the embedding lag, embedding dimension, limit of predictability, and Lyapunov exponent. Topological transitivity was also tested for. For comparison, the power spectrum and standard deviation were calculated for each time record. The EMMs had a statistically significant higher Lyapunov exponent than the LOMs ([Formula: see text] vs. [Formula: see text]) and a lower embedding dimension than the LOMs ([Formula: see text] vs. [Formula: see text]). There was insufficient evidence (non-significant p value) of a difference between EOMs and EMMs or EOMs and LOMs. The majority of time records were topologically transitive. There was insufficient evidence of accommodative demand having an effect. Power spectrum analysis and assessment of the standard deviation of the fluctuations failed to discern differences based on refractive error. Chaos differences in accommodation microfluctuations indicate that the control system for LOMs is under stress in comparison to EMMs. Chaos theory analysis is a more sensitive marker of changes in accommodation microfluctuations than traditional analysis methods.

Manifestation of resonance-related chaos in coupled Josephson junctions

NASA Astrophysics Data System (ADS)

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

2012-11-01

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

Applying Chaos Theory to Careers: Attraction and Attractors

ERIC Educational Resources Information Center

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

2007-01-01

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

Transition between order and chaos in a composite disk galaxy model with a massive nucleus and a dark matter halo

NASA Astrophysics Data System (ADS)

Caranicolas, Nicolaos D.; Zotos, Euaggelos E.

2013-02-01

We investigate the transition from regular to chaotic motion in a composite galaxy model with a disk-halo, a massive dense nucleus and a dark halo component. We obtain relationships connecting the critical value of the mass of the nucleus or the critical value of the angular momentum Lzc, with the mass Mh of the dark halo, where the transition from regular motion to chaos occurs. We also present 3D diagrams connecting the mass of nucleus the energy and the percentage of stars that can show chaotic motion. The fraction of the chaotic orbits observed in the (r,pr) phase plane, as a function of the mass of the dark halo is also computed. We use a semi-numerical method, that is a combination of theoretical and numerical procedure. The theoretical results obtained using the version 8.0 of the Mathematica package, while all the numerical calculations were made using a Bulirsch-Stöer FORTRAN routine in double precision. The results can be obtained in semi-numerical or numerical form and give good description for the connection of the physical quantities entering the model and the transition between regular and chaotic motion. We observe that the mass of the dark halo, the mass of the dense nucleus and the Lz component of the angular momentum, are important physical quantities, as they are linked to the regular or chaotic character of orbits in disk galaxies described by the model. Our numerical experiments suggest, that the amount of the dark matter plays an important role in disk galaxies represented by the model, as the mass of the halo affects, not only the regular or chaotic nature of motion but it is also connected with the existence of the different families of regular orbits. Comparison of the present results with earlier work is also presented.

Synchronisation of chaos and its applications

NASA Astrophysics Data System (ADS)

Eroglu, Deniz; Lamb, Jeroen S. W.; Pereira, Tiago

2017-07-01

Dynamical networks are important models for the behaviour of complex systems, modelling physical, biological and societal systems, including the brain, food webs, epidemic disease in populations, power grids and many other. Such dynamical networks can exhibit behaviour in which deterministic chaos, exhibiting unpredictability and disorder, coexists with synchronisation, a classical paradigm of order. We survey the main theory behind complete, generalised and phase synchronisation phenomena in simple as well as complex networks and discuss applications to secure communications, parameter estimation and the anticipation of chaos.

Four dimensional chaos and intermittency in a mesoscopic model of the electroencephalogram.

PubMed

Dafilis, Mathew P; Frascoli, Federico; Cadusch, Peter J; Liley, David T J

2013-06-01

The occurrence of so-called four dimensional chaos in dynamical systems represented by coupled, nonlinear, ordinary differential equations is rarely reported in the literature. In this paper, we present evidence that Liley's mesoscopic theory of the electroencephalogram (EEG), which has been used to describe brain activity in a variety of clinically relevant contexts, possesses a chaotic attractor with a Kaplan-Yorke dimension significantly larger than three. This accounts for simple, high order chaos for a physiologically admissible parameter set. Whilst the Lyapunov spectrum of the attractor has only one positive exponent, the contracting dimensions are such that the integer part of the Kaplan-Yorke dimension is three, thus giving rise to four dimensional chaos. A one-parameter bifurcation analysis with respect to the parameter corresponding to extracortical input is conducted, with results indicating that the origin of chaos is due to an inverse period doubling cascade. Hence, in the vicinity of the high order, strange attractor, the model is shown to display intermittent behavior, with random alternations between oscillatory and chaotic regimes. This phenomenon represents a possible dynamical justification of some of the typical features of clinically established EEG traces, which can arise in the case of burst suppression in anesthesia and epileptic encephalopathies in early infancy.

The Smaller Alignment Index (SALI) applied in a study of stellar orbits in barred galaxies potential models using the LP-VIcode

NASA Astrophysics Data System (ADS)

Caritá, Lucas Antonio; Rodrigues, Irapuan; Puerari, Ivânio; Schiavo, Luiz Eduardo Camargo Aranha

2018-04-01

The Smaller Alignment Index (SALI) is a mathematical tool, not yet conventional, for chaos detection in the phase space of Hamiltonian Dynamical Systems. The SALI values has temporal behaviors very specific to ordered or chaotic motions, what makes the distinction between order and chaos easily observable in these systems. In this paper, this method will be applied to the stability study of stellar orbits immersed in gravitational potential of barred galaxies, since the motion of a test particle in a rotating barred galaxy model is given by a Hamiltonian function. Extracting four parameter sets from the Manos and Athanassoula (2011) work and elaborating a different initial conditions set for each case, we were able to introduce another point of view of their stability study for two degrees of freedom. We have also introduced two new extreme models that corroborates with the conclusions that more axisymmetric bars create an environment with less chaos and that more massive bars create an environment with more chaos. Separate studies were carried out for prograde and retrograde orbits that showed that the retrograde orbits seem more conducive to chaos. To perform all the orbits integrations we used the LP-VIcode program.

Lagrangian turbulence: Structures and mixing in admissible model flows

NASA Astrophysics Data System (ADS)

Ottino, Julio M.

1991-12-01

The goal of our research was to bridge the gap between modern ideas from dynamical systems and chaos and more traditional approaches to turbulence. In order to reach this objective we conducted theoretical and computational work on two systems: (1) a perturbed-Kelvin cat eyes flow, and (2) prototype solutions of the Navier-Stokes equations near solid walls. The main results obtained are two-fold: we have been able to produce flows capable of producing complex distributions of vorticity, and we have been able to construct flowfields, based on solutions of the Navier-Stokes equations, which are capable of displaying both Eulerian and Lagrangian turbulence. These results exemplify typical mechanisms of mixing enhancement in transitional flows.

Adaptive Schools in a Quantum Universe.

ERIC Educational Resources Information Center

Garmston, Robert; Wellman, Bruce

1995-01-01

Information from quantum mechanics, chaos theory, fractal geometry, and the new biology can help educators rethink school-improvement approaches. Chaos and order exist simultaneously. Adaptability, the central operating principle of successful organizations, stems from five human energy fields: efficacy, flexibility, craftsmanship, consciousness,…

Devaney chaos plus shadowing implies distributional chaos.

PubMed

Li, Jian; Li, Jie; Tu, Siming

2016-09-01

We explore connections among the regional proximal relation, the asymptotic relation, and the distal relation for a topological dynamical system with the shadowing property and show that if a Devaney chaotic system has the shadowing property then it is distributionally chaotic.

Stability-to-instability transition in the structure of large-scale networks

NASA Astrophysics Data System (ADS)

Hu, Dandan; Ronhovde, Peter; Nussinov, Zohar

2012-12-01

We examine phase transitions between the “easy,” “hard,” and “unsolvable” phases when attempting to identify structure in large complex networks (“community detection”) in the presence of disorder induced by network “noise” (spurious links that obscure structure), heat bath temperature T, and system size N. The partition of a graph into q optimally disjoint subgraphs or “communities” inherently requires Potts-type variables. In earlier work [Philos. Mag.1478-643510.1080/14786435.2011.616547 92, 406 (2012)], when examining power law and other networks (and general associated Potts models), we illustrated that transitions in the computational complexity of the community detection problem typically correspond to spin-glass-type transitions (and transitions to chaotic dynamics in mechanical analogs) at both high and low temperatures and/or noise. The computationally “hard” phase exhibits spin-glass type behavior including memory effects. The region over which the hard phase extends in the noise and temperature phase diagram decreases as N increases while holding the average number of nodes per community fixed. This suggests that in the thermodynamic limit a direct sharp transition may occur between the easy and unsolvable phases. When present, transitions at low temperature or low noise correspond to entropy driven (or “order by disorder”) annealing effects, wherein stability may initially increase as temperature or noise is increased before becoming unsolvable at sufficiently high temperature or noise. Additional transitions between contending viable solutions (such as those at different natural scales) are also possible. Identifying community structure via a dynamical approach where “chaotic-type” transitions were found earlier. The correspondence between the spin-glass-type complexity transitions and transitions into chaos in dynamical analogs might extend to other hard computational problems. In this work, we examine large networks (with a power law distribution in cluster size) that have a large number of communities (q≫1). We infer that large systems at a constant ratio of q to the number of nodes N asymptotically tend towards insolvability in the limit of large N for any positive T. The asymptotic behavior of temperatures below which structure identification might be possible, T×=O[1/lnq], decreases slowly, so for practical system sizes, there remains an accessible, and generally easy, global solvable phase at low temperature. We further employ multivariate Tutte polynomials to show that increasing q emulates increasing T for a general Potts model, leading to a similar stability region at low T. Given the relation between Tutte and Jones polynomials, our results further suggest a link between the above complexity transitions and transitions associated with random knots.

Devaney chaos, Li-Yorke chaos, and multi-dimensional Li-Yorke chaos for topological dynamics

NASA Astrophysics Data System (ADS)

Dai, Xiongping; Tang, Xinjia

2017-11-01

Let π : T × X → X, written T↷π X, be a topological semiflow/flow on a uniform space X with T a multiplicative topological semigroup/group not necessarily discrete. We then prove: If T↷π X is non-minimal topologically transitive with dense almost periodic points, then it is sensitive to initial conditions. As a result of this, Devaney chaos ⇒ Sensitivity to initial conditions, for this very general setting. Let R+↷π X be a C0-semiflow on a Polish space; then we show: If R+↷π X is topologically transitive with at least one periodic point p and there is a dense orbit with no nonempty interior, then it is multi-dimensional Li-Yorke chaotic; that is, there is a uncountable set Θ ⊆ X such that for any k ≥ 2 and any distinct points x1 , … ,xk ∈ Θ, one can find two time sequences sn → ∞ ,tn → ∞ with Moreover, let X be a non-singleton Polish space; then we prove: Any weakly-mixing C0-semiflow R+↷π X is densely multi-dimensional Li-Yorke chaotic. Any minimal weakly-mixing topological flow T↷π X with T abelian is densely multi-dimensional Li-Yorke chaotic. Any weakly-mixing topological flow T↷π X is densely Li-Yorke chaotic. We in addition construct a completely Li-Yorke chaotic minimal SL (2 , R)-acting flow on the compact metric space R ∪ { ∞ }. Our various chaotic dynamics are sensitive to the choices of the topology of the phase semigroup/group T.

Evolution of secondary whirls in thermoconvective vortices: Strengthening, weakening, and disappearance in the route to chaos

NASA Astrophysics Data System (ADS)

Castaño, D.; Navarro, M. C.; Herrero, H.

2016-01-01

The appearance, evolution, and disappearance of periodic and quasiperiodic dynamics of fluid flows in a cylindrical annulus locally heated from below are analyzed using nonlinear simulations. The results reveal a route of the transition from a steady axisymmetric vertical vortex to a chaotic flow. The chaotic flow regime is reached after a sequence of successive supercritical Hopf bifurcations to periodic, quasiperiodic, and chaotic flow regimes. A scenario similar to the Ruelle-Takens-Newhouse scenario is verified in this convective flow. In the transition to chaos we find the appearance of subvortices embedded in the primary axisymmetric vortex, flows where the subvortical structure strengthens and weakens, that almost disappears before reforming again, leading to a more disorganized flow to a final chaotic regime. Results are remarkable as they connect to observations describing formation, weakening, and virtual disappearance before revival of subvortices in some atmospheric swirls such as dust devils.

The role of emotions in spatial prisoner's dilemma game with voluntary participation

NASA Astrophysics Data System (ADS)

Wang, Lu; Ye, Shun-Qiang; Cheong, Kang Hao; Bao, Wei; Xie, Neng-gang

2018-01-01

This paper develops an extended emotional model in the voluntary prisoner's dilemma game. It fills a gap in the traditional imitation mechanism by assuming that players do not simply imitate pure strategies, but imitate the emotional profiles of one another instead. The relationship between emotional profiles and strategy are constructed and Monte Carlo simulations are performed on a square lattice. Simulation results reveal that with an increase in the temptation parameter T (1 ⩽ T ⩽ 2), the order-chaos-order transition occurs. When T is around 1.2, we find that a bifurcation occurs. From a social system perspective, as T increases, the system changes from a benign one (respect for the 'successful' people and sympathy towards the weak one) to one that is of vicious nature (that is, bully the weak and fear the strong).

Encounters with neighbours : current developments of concepts based on recurrence plots and their applications

NASA Astrophysics Data System (ADS)

Marwan, Norbert

2003-09-01

In this work, different aspects and applications of the recurrence plot analysis are presented. First, a comprehensive overview of recurrence plots and their quantification possibilities is given. New measures of complexity are defined by using geometrical structures of recurrence plots. These measures are capable to find chaos-chaos transitions in processes. Furthermore, a bivariate extension to cross recurrence plots is studied. Cross recurrence plots exhibit characteristic structures which can be used for the study of differences between two processes or for the alignment and search for matching sequences of two data series. The selected applications of the introduced techniques to various kind of data demonstrate their ability. Analysis of recurrence plots can be adopted to the specific problem and thus opens a wide field of potential applications. Regarding the quantification of recurrence plots, chaos-chaos transitions can be found in heart rate variability data before the onset of life threatening cardiac arrhythmias. This may be of importance for the therapy of such cardiac arrhythmias. The quantification of recurrence plots allows to study transitions in brain during cognitive experiments on the base of single trials. Traditionally, for the finding of these transitions the averaging of a collection of single trials is needed. Using cross recurrence plots, the existence of an El Niño/Southern Oscillation-like oscillation is traced in northwestern Argentina 34,000 yrs. ago. In further applications to geological data, cross recurrence plots are used for time scale alignment of different borehole data and for dating a geological profile with a reference data set. Additional examples from molecular biology and speech recognition emphasize the suitability of cross recurrence plots. Diese Arbeit beschäftigt sich mit verschiedenen Aspekten und Anwendungen von Recurrence Plots. Nach einer Übersicht über Methoden, die auf Recurrence Plots basieren, werden neue Komplexitätsmaße eingeführt, die geometrische Strukturen in den Recurrence Plots beschreiben. Diese neuen Maße erlauben die Identifikation von Chaos-Chaos-Übergängen in dynamischen Prozessen. In einem weiteren Schritt werden Cross Recurrence Plots eingeführt, mit denen zwei verschiedene Prozesse untersucht werden. Diese bivariate Analyse ermöglicht die Bewertung von Unterschieden zwischen zwei Prozessen oder das Anpassen der Zeitskalen von zwei Zeitreihen. Diese Technik kann auch genutzt werden, um ähnliche Abschnitte in zwei verschiedenen Datenreihen zu finden. Im Anschluß werden diese neuen Entwicklungen auf Daten verschiedener Art angewendet. Methoden, die auf Recurrence Plots basieren, können an die speziellen Probleme angepaßt werden, so daß viele weitere Anwendungen möglich sind. Durch die Anwendung der neu eingeführten Komplexitätsmaße können Chaos-Chaos-Übergänge in Herzschlagdaten vor dem Auftreten einer lebensbedrohlichen Herzrhythmusstörung festgestellt werden, was für die Entwicklung neuer Therapien dieser Herzrhythmusstörungen von Bedeutung sein könnte. In einem weiteren Beispiel, in dem EEG-Daten aus einem kognitiv orientierten Experiment untersucht werden, ermöglichen diese Komplexitätsmaße das Erkennen von spezifischen Reaktionen im Gehirn bereits in Einzeltests. Normalerweise können diese Reaktionen erst durch die Auswertung von vielen Einzeltests erkannt werden. Mit der Hilfe von Cross Recurrence Plots wird die Existenz einer klimatischen Zirkulation, die der heutigen El Niño/ Southern Oscillation sehr ähnlich ist, im Nordwesten Argentiniens vor etwa 34000 Jahren nachgewiesen. Außerdem können mit Cross Recurrence Plots die Zeitskalen verschiedener Bohrlochdaten aufeinander abgeglichen werden. Diese Methode kann auch dazu genutzt werden, ein geologisches Profil mit Hilfe eines Referenzprofiles mit bekannter Zeitskala zu datieren. Weitere Beispiele aus den Gebieten der Molekularbiologie und der Spracherkennung unterstreichen das Potential dieser Methode.

Onset of chaos in a single-phase power electronic inverter.

PubMed

Avrutin, Viktor; Mosekilde, Erik; Zhusubaliyev, Zhanybai T; Gardini, Laura

2015-04-01

Supported by experiments on a power electronic DC/AC converter, this paper considers an unusual transition from the domain of stable periodic dynamics (corresponding to the desired mode of operation) to chaotic dynamics. The behavior of the converter is studied by means of a 1D stroboscopic map derived from a non-autonomous ordinary differential equation with discontinuous right-hand side. By construction, this stroboscopic map has a high number of border points. It is shown that the onset of chaos occurs stepwise, via irregular cascades of different border collisions, some of which lead to bifurcations while others do not.

Docosapentaenoic acid (DPA) is a critical determinant of cubic membrane formation in amoeba Chaos mitochondria.

PubMed

Deng, Yuru; Almsherqi, Zakaria A; Shui, Guanghou; Wenk, Markus R; Kohlwein, Sepp D

2009-09-01

Very long-chain polyunsaturated fatty acids (VLC-PUFAs), such as docosahexaenoic acid (DHA) and docosapentaenoic acid (DPA), have recently made it to the realm of "magical molecules" based on their multiple presumably beneficial effects in biological systems, making these PUFAs particularly interesting in biomedicine. Their specific biological functions, however, remain enigmatic. Here we provide evidence derived from studies in the amoeba Chaos that indicates a structural role for omega-6 DPA in cell membrane organization, which may help to explain the multiple diverse effects of VLC-PUFA in healthy and diseased states. Amoeba Chaos mitochondria undergo a remarkable and reversible morphological transition into cubic morphology on starvation. This morphological transition is reflected in major changes in fatty acid and lipid composition, as determined by gas liquid chromatography and mass spectrometry, in particular by a drastic increase in C22:5 modified phosphatidylcholine plasmalogen, phosphatidylethanolamine plasmalogen, and phosphatidylinositol species. Liposomes produced in vitro from lipids of starved amoeba cells show a high propensity to form hexagonal tubular and cubic morphologies. Addition of omega-6 DPA, but not of omega-3 DPA, to the cell culture also induced mitochondrial membrane transformation into cubic morphology in fed cells, demonstrating for the first time an important structural role of omega-6 DPA-containing lipids in cell membrane organization.

Recurrent flow analysis in spatiotemporally chaotic 2-dimensional Kolmogorov flow

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lucas, Dan, E-mail: dan.lucas@ucd.ie; Kerswell, Rich R., E-mail: r.r.kerswell@bris.ac.uk

2015-04-15

Motivated by recent success in the dynamical systems approach to transitional flow, we study the efficiency and effectiveness of extracting simple invariant sets (recurrent flows) directly from chaotic/turbulent flows and the potential of these sets for providing predictions of certain statistics of the flow. Two-dimensional Kolmogorov flow (the 2D Navier-Stokes equations with a sinusoidal body force) is studied both over a square [0, 2π]{sup 2} torus and a rectangular torus extended in the forcing direction. In the former case, an order of magnitude more recurrent flows are found than previously [G. J. Chandler and R. R. Kerswell, “Invariant recurrent solutionsmore » embedded in a turbulent two-dimensional Kolmogorov flow,” J. Fluid Mech. 722, 554–595 (2013)] and shown to give improved predictions for the dissipation and energy pdfs of the chaos via periodic orbit theory. Analysis of the recurrent flows shows that the energy is largely trapped in the smallest wavenumbers through a combination of the inverse cascade process and a feature of the advective nonlinearity in 2D. Over the extended torus at low forcing amplitudes, some extracted states mimic the statistics of the spatially localised chaos present surprisingly well recalling the findings of Kawahara and Kida [“Periodic motion embedded in plane Couette turbulence: Regeneration cycle and burst,” J. Fluid Mech. 449, 291 (2001)] in low-Reynolds-number plane Couette flow. At higher forcing amplitudes, however, success is limited highlighting the increased dimensionality of the chaos and the need for larger data sets. Algorithmic developments to improve the extraction procedure are discussed.« less

Improvement and empirical research on chaos control by theory of "chaos + chaos = order".

PubMed

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.

Spontaneous Symmetry Breaking of Domain Walls in Phase-Competing Regions

NASA Astrophysics Data System (ADS)

Ishizuka, Hiroaki; Yamada, Yasusada; Nagaosa, Naoto

2018-05-01

In this study, we investigate the nature of domain walls in an ordered phase in the phase-competing region of two Ising-type order parameters. We consider a two-component ϕ4 theory and show that the domain wall of the ground-state (primary) order parameter shows a second-order phase transition associated with the secondary order parameter of the competing phase; the effective theory of the phase transition is given by the Landau theory of an Ising-type phase transition. We find that the phase boundary of this phase transition is different from the spinodal line of the competing order. The phase transition is detected experimentally by the divergence of the susceptibility corresponding to the secondary order when the temperature is quenched to introduce the domain walls.

Chaos in a restricted problem of rotation of a rigid body with a fixed point

NASA Astrophysics Data System (ADS)

Borisov, A. V.; Kilin, A. A.; Mamaev, I. S.

2008-06-01

In this paper, we consider the transition to chaos in the phase portrait of a restricted problem of rotation of a rigid body with a fixed point. Two interrelated mechanisms responsible for chaotization are indicated: (1) the growth of the homoclinic structure and (2) the development of cascades of period doubling bifurcations. On the zero level of the area integral, an adiabatic behavior of the system (as the energy tends to zero) is noted. Meander tori induced by the break of the torsion property of the mapping are found.

Bifurcation and chaos of a new discrete fractional-order logistic map

NASA Astrophysics Data System (ADS)

Ji, YuanDong; Lai, Li; Zhong, SuChuan; Zhang, Lu

2018-04-01

The fractional-order discrete maps with chaotic behaviors based on the theory of ;fractional difference; are proposed in recent years. In this paper, instead of using fractional difference, a new fractionalized logistic map is proposed based on the numerical algorithm of fractional differentiation definition. The bifurcation diagrams of this map with various differential orders are given by numerical simulation. The simulation results show that the fractional-order logistic map derived in this manner holds rich dynamical behaviors because of its memory effect. In addition, new types of behaviors of bifurcation and chaos are found, which are different from those of the integer-order and the previous fractional-order logistic maps.

Chaos minimization in DC-DC boost converter using circuit parameter optimization

NASA Astrophysics Data System (ADS)

Sudhakar, N.; Natarajan, Rajasekar; Gourav, Kumar; Padmavathi, P.

2017-11-01

DC-DC converters are prone to several types of nonlinear phenomena including bifurcation, quasi periodicity, intermittency and chaos. These undesirable effects must be controlled for periodic operation of the converter to ensure the stability. In this paper an effective solution to control of chaos in solar fed DC-DC boost converter is proposed. Controlling of chaos is significantly achieved using optimal circuit parameters obtained through Bacterial Foraging Optimization Algorithm. The optimization renders the suitable parameters in minimum computational time. The obtained results are compared with the operation of traditional boost converter. Further the obtained results with BFA optimized parameter ensures the operations of the converter are within the controllable region. To elaborate the study of bifurcation analysis with optimized and unoptimized parameters are also presented.

Nonlinear dynamics, fractals, cardiac physiology and sudden death

NASA Technical Reports Server (NTRS)

Goldberger, Ary L.

1987-01-01

The authors propose a diametrically opposite viewpoint to the generally accepted tendency of equating healthy function with order and disease with chaos. With regard to the question of sudden cardiac death and chaos, it is suggested that certain features of dynamical chaos related to fractal structure and fractal dynamics may be important organizing principles in normal physiology and that certain pathologies, including ventricular fibrillation, represent a class of 'pathological periodicities'. Some laboratory work bearing on the relation of nonlinear analysis to physiological and pathophysiological data is briefly reviewed, with tentative theories and models described in reference to the mechanism of ventricular fibrillation.

Ancient Martian Lakestands and Fluvial Processes in Iani Chaos: Geology of Light-Toned Layered Deposits and their Relationship to Ares Vallis Outflow Channels

NASA Astrophysics Data System (ADS)

Guallini, Luca; Gilmore, Martha; Marinangeli, Lucia; Thomas, Nicolas

2015-04-01

Iani Chaos is a ~30,000 square kilometers region that lies at the head of the Ares Vallis outflow channel system. Mapping of Ares Vallis reveals multiple episodes of erosion, probably linked to several discharge events from the Iani Chaos aquifer. We present the first detailed geomorphological map of the Iani region. Five chaos units have been distinguished with varying degrees of modification (primarily by erosion and fracturing), starting from a common terrain (Noachian highlands). We observe a general progressive decrease of their mean elevation from the Mesas, Mesas & Knobs and Hummocky (Hy) terrains to the Knobs and Knobby morphologies. This trend is consistent with an initial collapse of the original surface with an increase of the fracturing and/or of the erosion. Light-toned Layered Deposits (LLD) have been also mapped and described in Iani Chaos. These terrains are clearly distinguished by a marked light-toned albedo, high thermal inertia and a pervasively fractured morphology. LLD both fill the basins made by the collapsed chaotic terrains and are found to be partially modified by the chaos formation. LLD also overlap chaos mounds or are themselves eroded into mounds after deposition. These stratigraphic relationships demonstrate that LLD deposition occurred episodically in the Iani region and throughout the history of the development of the chaos. Water seems to have had an active role in the geological history of Iani. The composition and morphologies of the LLD are consistent with deposition in an evaporitic environment and with erosion by outflows, requiring stable water on the surface. For the first time, we have also mapped and analyzed potential fluvial features (i.e., channels, streamlined islands, terraces, grooved surfaces) on the surface of the LLD. These landforms describe a fluvial system that can be traced from central Iani and linked northward to Ares Vallis. Using topographic data, we have compared the elevation of the LLD and channel units and find that their altitudes are remarkably similar to the altitude of the floors of the major Ares Vallis channels. This is decisive evidence of 1) a possible fluvial system within Iani linked to the Ares Vallis outflow system, characterized by five episodes of outflow at least (S1 to S5), and 2) of the existence of the LLD within Iani during the occurrence of the outflows (i.e., the LLD are coeval with or postdate the Ares Vallis outflow channels). On the basis of our analysis, we propose the following formation model for Iani Chaos: 1) Initial fracturing and tectonic subsidence of the pristine Noachian materials and subsequent outflow erosion of the bedrock (Ares Vallis S1 channel origin); 2) Evaporitic deposition of older LLD units on top and between chaotic terrains. Layering suggests cyclic wetting and drying; 3) Tectonic subsidence and fluvial erosion of chaos and LLD (Ares Vallis S2 to S3 channels); 4) Deposition of younger LLD units in central and northern Iani; 5) Tectonic subsidence and outflows, erosion of chaos and LLD (Ares Vallis S4 to S5 channel origin and subsequent downdropping of NW and N(e) Iani).

Basic dynamics from a pulse-coupled network of autonomous integrate-and-fire chaotic circuits.

PubMed

Nakano, H; Saito, T

2002-01-01

This paper studies basic dynamics from a novel pulse-coupled network (PCN). The unit element of the PCN is an integrate-and-fire circuit (IFC) that exhibits chaos. We an give an iff condition for the chaos generation. Using two IFC, we construct a master-slave PCN. It exhibits interesting chaos synchronous phenomena and their breakdown phenomena. We give basic classification of the phenomena and their existence regions can be elucidated in the parameter space. We then construct a ring-type PCN and elucidate that the PCN exhibits interesting grouping phenomena based on the chaos synchronization patterns. Using a simple test circuit, some of typical phenomena can be verified in the laboratory.

Evolution of intrinsic disorder in eukaryotic proteins.

PubMed

Ahrens, Joseph B; Nunez-Castilla, Janelle; Siltberg-Liberles, Jessica

2017-09-01

Conformational flexibility conferred though regions of intrinsic structural disorder allows proteins to behave as dynamic molecules. While it is well-known that intrinsically disordered regions can undergo disorder-to-order transitions in real-time as part of their function, we also are beginning to learn more about the dynamics of disorder-to-order transitions along evolutionary time-scales. Intrinsically disordered regions endow proteins with functional promiscuity, which is further enhanced by the ability of some of these regions to undergo real-time disorder-to-order transitions. Disorder content affects gene retention after whole genome duplication, but it is not necessarily conserved. Altered patterns of disorder resulting from evolutionary disorder-to-order transitions indicate that disorder evolves to modify function through refining stability, regulation, and interactions. Here, we review the evolution of intrinsically disordered regions in eukaryotic proteins. We discuss the interplay between secondary structure and disorder on evolutionary time-scales, the importance of disorder for eukaryotic proteome expansion and functional divergence, and the evolutionary dynamics of disorder.

Limitations of polynomial chaos expansions in the Bayesian solution of inverse problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lu, Fei; Department of Mathematics, University of California, Berkeley; Morzfeld, Matthias, E-mail: mmo@math.lbl.gov

2015-02-01

Polynomial chaos expansions are used to reduce the computational cost in the Bayesian solutions of inverse problems by creating a surrogate posterior that can be evaluated inexpensively. We show, by analysis and example, that when the data contain significant information beyond what is assumed in the prior, the surrogate posterior can be very different from the posterior, and the resulting estimates become inaccurate. One can improve the accuracy by adaptively increasing the order of the polynomial chaos, but the cost may increase too fast for this to be cost effective compared to Monte Carlo sampling without a surrogate posterior.

Gullies of Gorgonus Chaos

NASA Technical Reports Server (NTRS)

2002-01-01

(Released 11 June 2002) The Science This fractured surface belongs to a portion of a region called Gorgonum Chaos located in the southern hemisphere of Mars. Gorgonum Chaos is named after the Gorgons in ancient Greek mythology. The Gorgons were monstrous sisters with snakes for hair, tusks like boars and lolling tongues who lived in caves. As it turns out this is indeed a fitting name for this region of Mars because it contains a high density of gullies that 'snake' their way down the walls of the troughs located in this region of chaos. Upon closer examination one finds that these gullies and alluvial deposits, initially discovered by Mars Global Surveyor, are visible on the trough walls (best seen near the bottom of the image). These gullies appear to emanate from a specific layer in the walls. The gullies have been proposed to have formed by the subsurface release of water. The Story This fractured, almost spooky-looking surface belongs to a region called Gorgonum Chaos in the southern hemisphere of Mars. Chaos is a term used for regions of Mars with distinctive areas of broken terrain like the one seen above. This area of Martian chaos is named after the Gorgons in ancient Greek mythology. The Gorgons were monstrous sisters with snakes for hair, tusks like boars, and lolling tongues, who lived in caves. The Gorgons, including famous sister Medusa, could turn a person to stone, and their writhing, snakelike locks cause revulsion to this day. Given the afflicted nature of this contorted terrain, with all of its twisted, branching channels and hard, stony-looking hills in the top half of the image, this is indeed a fitting name for this region of Mars. The name also has great appeal, because the area contains a high density of gullies that 'snake' their way down the walls of the troughs located in this region of Martian chaos. Gullies are trenches cut into the land as accelerated streams of water (or another liquid) erode the surface. To see these, click on the above image to get a high-resolution view, and then focus on the trenches at the bottom. Running down the walls of the trough are the thin, dark lines of the gullies. Beneath the grooved, gully channels are faint, softer-looking fans of material. These are called alluvial deposits. Alluvial simply means all of the sand, gravel, and dirt that is carried and deposited by a liquid. On Earth, that liquid is typically water. As the liquid carves the gully, the eroded material from the channels get carried along and deposited below in fan-like shapes. These gully features were initially discovered by Odyssey's sister orbiter, Mars Global Surveyor, and caused quite a bit of emotional chaos in the scientific community when they were announced. Why? If you look closely, you can see that the gullies seem to form from a specific layer in the wall. That is, they all seem to begin at roughly the same point on the wall. That suggests that maybe, just maybe, there's a subsurface source of water at that layer that sometimes leaks out and runs down the walls to form both the gullies and the skirt-like fans of deposits beneath them. Other scientists, however, loudly assert that another liquid besides water could have carved the gullies. The debate sometimes gets so intense, you'd think that the opposing sides would want to turn each other's ideas to stone! But not for long. While the debate rages on, the neat thing is that everyone's really united. The goal is to find out, and the way to find out is to keep proposing different hypotheses and testing them out. That's the excitement of science, where everyone's solid research counts, and divergent views are appreciated for keeping science sound.

Study the complexity and control of the recycling-supply chain of China's color TVs market based on the government subsidy

NASA Astrophysics Data System (ADS)

Xie, Lei; Ma, Junhai

2016-09-01

In these days, as the recycling of household appliances becomes increasingly popular, the recycling network tends to be perfect in television industry. This paper focuses on the game among two recyclers and a processor in a Duopoly market of color TV recycling. We find that if the adjustment coefficients of the decision variables are changed abruptly, the system will fall into chaotic state. In order to avoid hazard of falling into a chaotic state, we adopt the method of delay control, providing the manufacturers with effective measures about chaos control. This paper analyzes the system's reactions to government decision, finding that when the parameters become beneficial for manufacturers, consumers and the environment, the system will fall into chaos and system's regional stability will reduce. Resulting from our analysis, this paper gives advice on the improvement of the environment and enhance in social welfare. Tested through the data we collected, this study is practical in both its theory and its applicability.

DTU candidate field models for IGRF-12 and the CHAOS-5 geomagnetic field model

NASA Astrophysics Data System (ADS)

Finlay, Christopher C.; Olsen, Nils; Tøffner-Clausen, Lars

2015-07-01

We present DTU's candidate field models for IGRF-12 and the parent field model from which they were derived, CHAOS-5. Ten months of magnetic field observations from ESA's Swarm mission, together with up-to-date ground observatory monthly means, were used to supplement the data sources previously used to construct CHAOS-4. The internal field part of CHAOS-5, from which our IGRF-12 candidate models were extracted, is time-dependent up to spherical harmonic degree 20 and involves sixth-order splines with a 0.5 year knot spacing. In CHAOS-5, compared with CHAOS-4, we update only the low-degree internal field model (degrees 1 to 24) and the associated external field model. The high-degree internal field (degrees 25 to 90) is taken from the same model CHAOS-4h, based on low-altitude CHAMP data, which was used in CHAOS-4. We find that CHAOS-5 is able to consistently fit magnetic field data from six independent low Earth orbit satellites: Ørsted, CHAMP, SAC-C and the three Swarm satellites (A, B and C). It also adequately describes the secular variation measured at ground observatories. CHAOS-5 thus contributes to an initial validation of the quality of the Swarm magnetic data, in particular demonstrating that Huber weighted rms model residuals to Swarm vector field data are lower than those to Ørsted and CHAMP vector data (when either one or two star cameras were operating). CHAOS-5 shows three pulses of secular acceleration at the core surface over the past decade; the 2006 and 2009 pulses have previously been documented, but the 2013 pulse has only recently been identified. The spatial signature of the 2013 pulse at the core surface, under the Atlantic sector where it is strongest, is well correlated with the 2006 pulse, but anti-correlated with the 2009 pulse.

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 crisis and bistability of self-pulsing dynamics in a laser diode with phase-conjugate feedback

DOE Office of Scientific and Technical Information (OSTI.GOV)

Virte, Martin; Karsaklian Dal Bosco, Andreas; Wolfersberger, Delphine

2011-10-15

A laser diode subject to a phase-conjugate optical feedback can exhibit rich nonlinear dynamics and chaos. We report here on two bifurcation mechanisms that appear when increasing the amount of light being fed back to the laser. First, we report on a full suppression of chaos from a crisis induced by a saddle-node bifurcation on self-pulsing, so-called external-cavity-mode solutions (ECMs). Second, the feedback-dependent torus and saddle-node bifurcations on ECMs may be responsible for large regions of bistability between ECMs of different and high (beyond gigahertz) frequencies.

Signature of chaos in the 4 f -core-excited states for highly-charged tungsten ions

NASA Astrophysics Data System (ADS)

Safronova, Ulyana; Safronova, Alla

2014-05-01

We evaluate radiative and autoionizing transition rates in highly charged W ions in search for the signature of chaos. In particularly, previously published results for Ag-like W27+, Tm-like W5+, and Yb-like W4+ ions as well as newly obtained for I-like W21+, Xe-like W20+, Cs-like W19+, and La-like W17+ ions (with ground configuration [Kr] 4d10 4fk with k = 7, 8, 9, and 11, respectively) are considered that were calculated using the multiconfiguration relativistic Hebrew University Lawrence Livermore Atomic Code (HULLAC code) and the Hartree-Fock-Relativistic method (COWAN code). The main emphasis was on verification of Gaussian statistics of rates as a function of transition energy. There was no evidence of such statistics for above mentioned previously published results as well as for the transitions between the excited and autoionizing states for newly calculated results. However, we did find the Gaussian profile for the transitions between excited states such as the [Kr] 4d10 4fk - [Kr] 4d10 4f k - 1 5 d transitions , for newly calculated W ions. This work is supported in part by DOE under NNSA Cooperative Agreement DE-NA0001984.

Secure free-space communication, turbulence mitigation, and other applications using acousto-optic chaos.

PubMed

Chatterjee, Monish R; Mohamed, Ali; Almehmadi, Fares S

2018-04-01

Use of acousto-optic (A-O) chaos via the feedback loop in a Bragg cell for signal encryption began as a conceptual demonstration around 2008. Radio frequency (RF) chaos from a hybrid A-O feedback device may be used for secure communications of analog and digital signals. In this paper, modulation of RF chaos via first-order feedback is discussed with results corroborated by nonlinear dynamics, bifurcation maps, and Lyapunov analyses. Applications based on encryption with profiled optical beams, and extended to medical and embedded steganographic data, and video signals are discussed. It is shown that the resulting encryption is significantly robust with key tolerances potentially less than 0.1%. Results are also presented for the use of chaotic encryption for image restoration during propagation through atmospheric turbulence.

Method of phase space beam dilution utilizing bounded chaos generated by rf phase modulation

DOE PAGES

Pham, Alfonse N.; Lee, S. Y.; Ng, K. Y.

2015-12-10

This paper explores the physics of chaos in a localized phase-space region produced by rf phase modulation applied to a double rf system. The study can be exploited to produce rapid particle bunch broadening exhibiting longitudinal particle distribution uniformity. Hamiltonian models and particle-tracking simulations are introduced to understand the mechanism and applicability of controlled particle diffusion. When phase modulation is applied to the double rf system, regions of localized chaos are produced through the disruption and overlapping of parametric resonant islands and configured to be bounded by well-behaved invariant tori to prevent particle loss. The condition of chaoticity and themore » degree of particle dilution can be controlled by the rf parameters. As a result, the method has applications in alleviating adverse space-charge effects in high-intensity beams, particle bunch distribution uniformization, and industrial radiation-effects experiments.« less

Chaos and Localization in Dieterich-Ruina Friction

NASA Astrophysics Data System (ADS)

Erickson, B. A.; Birnir, B.; Lavallee, D.

2009-12-01

We consider two models derived from a 1-D Burridge-Knopoff chain of spring connected blocks subject to the Dieterich-Ruina (D-R) friction law. We analyze both the discrete ordinary differential equations, as well as the continuum model. Preliminary investigation into the ODEs shows evidence of the Dieterich-Ruina law exhibiting chaos, dependent on the size of the system. Periodic behavior occurs when considering chains of 3 or 5 blocks, while a chain of 10 blocks with the same parameter values results in chaotic motion. The continuum model (PDE) undergoes a transition to chaos when a specific parameter is increased and the chaotic regime is reached for smaller critical values than in the case of a single block (see Erickson et. al. 2008). This parameter, epsilon is the ratio of the stress parameters (B-A) and A in the D-R friction law. The parameter A is a measure of the direct velocity dependence (sometimes called the "direct effect") while (A-B) is a measure of the steady-state velocity dependence. When compared to the slip weakening friction law, the parameter (B-A) plays a role of a stress drop while A corresponds to the strength excess. In the case of a single block, transitions to chaos occur when epsilon = 11, a value too high for applications in seismology. For the continuum model however, the chaotic regime is reached for epsilon = 1. That the transition to chaos ensues for smaller parameter values than in the case of a single block may also be an indication that a careful rescaling of the friction law is necessary, similar to the conclusions made by Schmittbuhl et. al. (1996) who studied a "hierarchical array of blocks" and found that velocity weakening friction was scale dependent. We also observe solutions to both the discrete and the continuous model where the slip remains localized in space, suggesting the presence of solitonic behavior. Initial data in the form of a gaussian pulse tends to remain localized under certain parameter values and we explore the space of values for which this occurs. These solitonic or localized solutions can be understood as proxy for the propagation of the rupture across the fault during an earthquake. Under the Dieterich-Ruina law we may have discovered only a small subset of solutions to both the discrete and the continuous model, but there is no question that even in one spatial dimension, a rich phenomenology of dynamics exists.

Chaos in quantum channels

DOE PAGES

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

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

USGS Publications Warehouse

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

2005-01-01

The undulating, warped, and densely fractured surfaces of highland regions east of Valles Marineris (located north of the eastern Aureum Chaos, east of the Hydraotes Chaos, and south of the Hydaspis Chaos) resulted from extensional surface warping related to ground subsidence, caused when pressurized water confined in subterranean caverns was released to the surface. Water emanations formed crater lakes and resulted in channeling episodes involved in the excavation of Ares, Tiu, and Simud Valles of the eastern part of the circum-Chryse outflow channel system. Progressive surface subsidence and associated reduction of the subsurface cavernous volume, and/or episodes of magmatic-driven activity, led to increases of the hydrostatic pressure, resulting in reactivation of both catastrophic and non-catastrophic outflow activity. Ancient cratered highland and basin materials that underwent large-scale subsidence grade into densely fractured terrains. Collapse of rock materials in these regions resulted in the formation of chaotic terrains, which occur in and near the headwaters of the eastern circum-Chryse outflow channels. The deepest chaotic terrain in the Hydaspis Chaos region resulted from the collapse of pre-existing outflow channel floors. The release of volatiles and related collapse may have included water emanations not necessarily linked to catastrophic outflow. Basal warming related to dike intrusions, thermokarst activity involving wet sediments and/or dissected ice-enriched country rock, permafrost exposed to the atmosphere by extensional tectonism and channel incision, and/or the injection of water into porous floor material, may have enhanced outflow channel floor instability and subsequent collapse. In addition to the possible genetic linkage to outflow channel development dating back to at least the Late Noachian, clear disruption of impact craters with pristine ejecta blankets and rims, as well as preservation of fine tectonic fabrics, suggest that plateau subsidence and chaos formation may have continued well into the Amazonian Period. The geologic and paleohydrologic histories presented here have important implications, as new mechanisms for outflow channel formation and other fluvial activity are described, and new reactivation mechanisms are proposed for the origin of chaotic terrain as contributors to flooding. Detailed geomorphic analysis indicates that subterranean caverns may have been exposed during chaos formation, and thus chaotic terrains mark prime locations for future geologic, hydrologic, and possible astrobiologic exploration. ?? 2004 Elsevier Inc. All rights reserved.

Emergent dynamics of spatio-temporal chaos in a heterogeneous excitable medium.

PubMed

Bittihn, Philip; Berg, Sebastian; Parlitz, Ulrich; Luther, Stefan

2017-09-01

Self-organized activation patterns in excitable media such as spiral waves and spatio-temporal chaos underlie dangerous cardiac arrhythmias. While the interaction of single spiral waves with different types of heterogeneity has been studied extensively, the effect of heterogeneity on fully developed spatio-temporal chaos remains poorly understood. We investigate how the complexity and stability properties of spatio-temporal chaos in the Bär-Eiswirth model of excitable media depend on the heterogeneity of the underlying medium. We employ different measures characterizing the chaoticity of the system and find that the spatial arrangement of multiple discrete lower excitability regions has a strong impact on the complexity of the dynamics. Varying the number, shape, and spatial arrangement of the heterogeneities, we observe strong emergent effects ranging from increases in chaoticity to the complete cessation of chaos, contrasting the expectation from the homogeneous behavior. The implications of our findings for the development and treatment of arrhythmias in the heterogeneous cardiac muscle are discussed.

Emergent dynamics of spatio-temporal chaos in a heterogeneous excitable medium

NASA Astrophysics Data System (ADS)

Bittihn, Philip; Berg, Sebastian; Parlitz, Ulrich; Luther, Stefan

2017-09-01

Self-organized activation patterns in excitable media such as spiral waves and spatio-temporal chaos underlie dangerous cardiac arrhythmias. While the interaction of single spiral waves with different types of heterogeneity has been studied extensively, the effect of heterogeneity on fully developed spatio-temporal chaos remains poorly understood. We investigate how the complexity and stability properties of spatio-temporal chaos in the Bär-Eiswirth model of excitable media depend on the heterogeneity of the underlying medium. We employ different measures characterizing the chaoticity of the system and find that the spatial arrangement of multiple discrete lower excitability regions has a strong impact on the complexity of the dynamics. Varying the number, shape, and spatial arrangement of the heterogeneities, we observe strong emergent effects ranging from increases in chaoticity to the complete cessation of chaos, contrasting the expectation from the homogeneous behavior. The implications of our findings for the development and treatment of arrhythmias in the heterogeneous cardiac muscle are discussed.

The reasons for the application of chaos theory to the analysis of catastrophes.

NASA Astrophysics Data System (ADS)

Valery, Kudin

2014-05-01

The study of catastrophes is necessary for understanding the nature of the interaction between the individual and the universal in the process of the development of complex systems. Chaos theory, allowing describing adaptation and bifurcation mechanisms for the development of systems, defines the catastrophes as a transition of the system into a different state (change of structure). The previous state of the system is destroyed because of fluctuations, which do not play a role in the development of the system until it reaches the instability region that is inherent to any system. The catastrophe is considered in this theory as a stage in the evolution of the system, and thus emphasizes the importance of catastrophes for the development of any system. We rarely manage events comprehensively, as events are always subject to changes like gas molecules changing the trajectory of motion each moment under the influence of countless blows. The concept of catastrophes is much broader and is generally applicable to any final result of collision of opposing aspirations. Philosophical definition of catastrophes comes down to the destruction of the unity, accompanied by violent collision between different parts, the growing disruption, failure to prevent crossing the dangerous threshold... As a final vertex of action, disaster is not, however, directly its end: the action may continue after the catastrophe, but in the direction that is determined by the character of opposing aspirations. Major catastrophes, which have already destroyed and continue to ravage the world today, come from a superficial use of the laws of the development of complex systems and, in particular, of individual techniques of the chaos theory.

Nonlinear Dynamics, Chaotic and Complex Systems

NASA Astrophysics Data System (ADS)

Infeld, E.; Zelazny, R.; Galkowski, A.

2011-04-01

Part I. Dynamic Systems Bifurcation Theory and Chaos: 1. Chaos in random dynamical systems V. M. Gunldach; 2. Controlling chaos using embedded unstable periodic orbits: the problem of optimal periodic orbits B. R. Hunt and E. Ott; 3. Chaotic tracer dynamics in open hydrodynamical flows G. Karolyi, A. Pentek, T. Tel and Z. Toroczkai; 4. Homoclinic chaos L. P. Shilnikov; Part II. Spatially Extended Systems: 5. Hydrodynamics of relativistic probability flows I. Bialynicki-Birula; 6. Waves in ionic reaction-diffusion-migration systems P. Hasal, V. Nevoral, I. Schreiber, H. Sevcikova, D. Snita, and M. Marek; 7. Anomalous scaling in turbulence: a field theoretical approach V. Lvov and I. Procaccia; 8. Abelian sandpile cellular automata M. Markosova; 9. Transport in an incompletely chaotic magnetic field F. Spineanu; Part III. Dynamical Chaos Quantum Physics and Foundations Of Statistical Mechanics: 10. Non-equilibrium statistical mechanics and ergodic theory L. A. Bunimovich; 11. Pseudochaos in statistical physics B. Chirikov; 12. Foundations of non-equilibrium statistical mechanics J. P. Dougherty; 13. Thermomechanical particle simulations W. G. Hoover, H. A. Posch, C. H. Dellago, O. Kum, C. G. Hoover, A. J. De Groot and B. L. Holian; 14. Quantum dynamics on a Markov background and irreversibility B. Pavlov; 15. Time chaos and the laws of nature I. Prigogine and D. J. Driebe; 16. Evolutionary Q and cognitive systems: dynamic entropies and predictability of evolutionary processes W. Ebeling; 17. Spatiotemporal chaos information processing in neural networks H. Szu; 18. Phase transitions and learning in neural networks C. Van den Broeck; 19. Synthesis of chaos A. Vanecek and S. Celikovsky; 20. Computational complexity of continuous problems H. Wozniakowski; Part IV. Complex Systems As An Interface Between Natural Sciences and Environmental Social and Economic Sciences: 21. Stochastic differential geometry in finance studies V. G. Makhankov; Part V. Conference Banquet Speech: Where will the future go? M. J. Feigenbaum.

Order in the House!: Associations among Household Chaos, the Home Literacy Environment, Maternal Reading Ability, and Children's Early Reading

ERIC Educational Resources Information Center

Johnson, Anna D.; Martin, Anne; Brooks-Gunn, Jeanne; Petrill, Stephen A.

2008-01-01

The current study examines whether associations exist between household chaos and children's early reading skills, after controlling for a comprehensive battery of home literacy environment characteristics. Our sample included 455 kindergarten and first-grade children who are enrolled in the Western Reserve Reading Project. We go on to test…

How to couple identical ring oscillators to get quasiperiodicity, extended chaos, multistability, and the loss of symmetry

NASA Astrophysics Data System (ADS)

Hellen, Edward H.; Volkov, Evgeny

2018-09-01

We study the dynamical regimes demonstrated by a pair of identical 3-element ring oscillators (reduced version of synthetic 3-gene genetic Repressilator) coupled using the design of the 'quorum sensing (QS)' process natural for interbacterial communications. In this work QS is implemented as an additional network incorporating elements of the ring as both the source and the activation target of the fast diffusion QS signal. This version of indirect nonlinear coupling, in cooperation with the reasonable extension of the parameters which control properties of the isolated oscillators, exhibits the formation of a very rich array of attractors. Using a parameter-space defined by the individual oscillator amplitude and the coupling strength, we found the extended area of parameter-space where the identical oscillators demonstrate quasiperiodicity, which evolves to chaos via the period doubling of either resonant limit cycles or complex antiphase symmetric limit cycles with five winding numbers. The symmetric chaos extends over large parameter areas up to its loss of stability, followed by a system transition to an unexpected mode: an asymmetric limit cycle with a winding number of 1:2. In turn, after long evolution across the parameter-space, this cycle demonstrates a period doubling cascade which restores the symmetry of dynamics by formation of symmetric chaos, which nevertheless preserves the memory of the asymmetric limit cycles in the form of stochastic alternating "polarization" of the time series. All stable attractors coexist with some others, forming remarkable and complex multistability including the coexistence of torus and limit cycles, chaos and regular attractors, symmetric and asymmetric regimes. We traced the paths and bifurcations leading to all areas of chaos, and presented a detailed map of all transformations of the dynamics.

Complex transitions between spike, burst or chaos synchronization states in coupled neurons with coexisting bursting patterns

NASA Astrophysics Data System (ADS)

Gu, Hua-Guang; Chen, Sheng-Gen; Li, Yu-Ye

2015-05-01

We investigated the synchronization dynamics of a coupled neuronal system composed of two identical Chay model neurons. The Chay model showed coexisting period-1 and period-2 bursting patterns as a parameter and initial values are varied. We simulated multiple periodic and chaotic bursting patterns with non-(NS), burst phase (BS), spike phase (SS), complete (CS), and lag synchronization states. When the coexisting behavior is near period-2 bursting, the transitions of synchronization states of the coupled system follows very complex transitions that begins with transitions between BS and SS, moves to transitions between CS and SS, and to CS. Most initial values lead to the CS state of period-2 bursting while only a few lead to the CS state of period-1 bursting. When the coexisting behavior is near period-1 bursting, the transitions begin with NS, move to transitions between SS and BS, to transitions between SS and CS, and then to CS. Most initial values lead to the CS state of period-1 bursting but a few lead to the CS state of period-2 bursting. The BS was identified as chaos synchronization. The patterns for NS and transitions between BS and SS are insensitive to initial values. The patterns for transitions between CS and SS and the CS state are sensitive to them. The number of spikes per burst of non-CS bursting increases with increasing coupling strength. These results not only reveal the initial value- and parameter-dependent synchronization transitions of coupled systems with coexisting behaviors, but also facilitate interpretation of various bursting patterns and synchronization transitions generated in the nervous system with weak coupling strength. Project supported by the National Natural Science Foundation of China (Grant Nos. 11372224 and 11402039) and the Fundamental Research Funds for Central Universities designated to Tongji University (Grant No. 1330219127).

A discrete-time chaos synchronization system for electronic locking devices

NASA Astrophysics Data System (ADS)

Minero-Ramales, G.; López-Mancilla, D.; Castañeda, Carlos E.; Huerta Cuellar, G.; Chiu Z., R.; Hugo García López, J.; Jaimes Reátegui, R.; Villafaña Rauda, E.; Posadas-Castillo, C.

2016-11-01

This paper presents a novel electronic locking key based on discrete-time chaos synchronization. Two Chen chaos generators are synchronized using the Model-Matching Approach, from non-linear control theory, in order to perform the encryption/decryption of the signal to be transmitted. A model/transmitter system is designed, generating a key of chaotic pulses in discrete-time. A plant/receiver system uses the above mentioned key to unlock the mechanism. Two alternative schemes to transmit the private chaotic key are proposed. The first one utilizes two transmission channels. One channel is used to encrypt the chaotic key and the other is used to achieve output synchronization. The second alternative uses only one transmission channel for obtaining synchronization and encryption of the chaotic key. In both cases, the private chaotic key is encrypted again with chaos to solve secure communication-related problems. The results obtained via simulations contribute to enhance the electronic locking devices.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Luo, Shaohua; School of Automation, Chongqing University, Chongqing 400044; Sun, Quanping

This paper addresses chaos control of the micro-electro- mechanical resonator by using adaptive dynamic surface technology with extended state observer. To reveal the mechanism of the micro- electro-mechanical resonator, the phase diagrams and corresponding time histories are given to research the nonlinear dynamics and chaotic behavior, and Homoclinic and heteroclinic chaos which relate closely with the appearance of chaos are presented based on the potential function. To eliminate the effect of chaos, an adaptive dynamic surface control scheme with extended state observer is designed to convert random motion into regular motion without precise system model parameters and measured variables. Puttingmore » tracking differentiator into chaos controller solves the ‘explosion of complexity’ of backstepping and poor precision of the first-order filters. Meanwhile, to obtain high performance, a neural network with adaptive law is employed to approximate unknown nonlinear function in the process of controller design. The boundedness of all the signals of the closed-loop system is proved in theoretical analysis. Finally, numerical simulations are executed and extensive results illustrate effectiveness and robustness of the proposed scheme.« less

Household chaos moderates the link between maternal attribution bias and parenting: Parenting: Science and Practice.

PubMed

Wang, Z; Deater-Deckard, K; Bell, M A

2013-10-01

Parents who attribute child misbehavior to children's intentions and dismiss situational factors tend to show more hostility and less warmth in their parenting behavior, and are at greater risk for maltreatment. We extended this literature by investigating the role of household chaos as a moderator of the link between maternal attribution biases and parenting behaviors. The current sample included 160 mothers of 3- to7-year-old children. Mothers provided reports on their attribution biases and household chaos levels. Maternal negativity and positivity were measured using self-reports and observers' ratings. The links between attribution bias and parenting behavior were stronger in more chaotic environments, with the moderating effect of chaos being particularly strong for internal attribution bias. The findings point to the importance of social cognitive biases in the etiology of maternal behavior in family contexts that lack order and predictability.

Household chaos moderates the link between maternal attribution bias and parenting

PubMed Central

Wang, Z.; Deater-Deckard, K.; Bell, M.A.

2013-01-01

Objective Parents who attribute child misbehavior to children's intentions and dismiss situational factors tend to show more hostility and less warmth in their parenting behavior, and are at greater risk for maltreatment. We extended this literature by investigating the role of household chaos as a moderator of the link between maternal attribution biases and parenting behaviors. Design The current sample included 160 mothers of 3- to7-year-old children. Mothers provided reports on their attribution biases and household chaos levels. Maternal negativity and positivity were measured using self-reports and observers’ ratings. Results The links between attribution bias and parenting behavior were stronger in more chaotic environments, with the moderating effect of chaos being particularly strong for internal attribution bias. Conclusions The findings point to the importance of social cognitive biases in the etiology of maternal behavior in family contexts that lack order and predictability. PMID:24358017

Quantum mushroom billiards

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barnett, Alex H.; Betcke, Timo; School of Mathematics, University of Manchester, Manchester, M13 9PL

2007-12-15

We report the first large-scale statistical study of very high-lying eigenmodes (quantum states) of the mushroom billiard proposed by L. A. Bunimovich [Chaos 11, 802 (2001)]. The phase space of this mixed system is unusual in that it has a single regular region and a single chaotic region, and no KAM hierarchy. We verify Percival's conjecture to high accuracy (1.7%). We propose a model for dynamical tunneling and show that it predicts well the chaotic components of predominantly regular modes. Our model explains our observed density of such superpositions dying as E{sup -1/3} (E is the eigenvalue). We compare eigenvaluemore » spacing distributions against Random Matrix Theory expectations, using 16 000 odd modes (an order of magnitude more than any existing study). We outline new variants of mesh-free boundary collocation methods which enable us to achieve high accuracy and high mode numbers ({approx}10{sup 5}) orders of magnitude faster than with competing methods.« less

Generalized model for k -core percolation and interdependent networks

NASA Astrophysics Data System (ADS)

Panduranga, Nagendra K.; Gao, Jianxi; Yuan, Xin; Stanley, H. Eugene; Havlin, Shlomo

2017-09-01

Cascading failures in complex systems have been studied extensively using two different models: k -core percolation and interdependent networks. We combine the two models into a general model, solve it analytically, and validate our theoretical results through extensive simulations. We also study the complete phase diagram of the percolation transition as we tune the average local k -core threshold and the coupling between networks. We find that the phase diagram of the combined processes is very rich and includes novel features that do not appear in the models studying each of the processes separately. For example, the phase diagram consists of first- and second-order transition regions separated by two tricritical lines that merge and enclose a two-stage transition region. In the two-stage transition, the size of the giant component undergoes a first-order jump at a certain occupation probability followed by a continuous second-order transition at a lower occupation probability. Furthermore, at certain fixed interdependencies, the percolation transition changes from first-order → second-order → two-stage → first-order as the k -core threshold is increased. The analytic equations describing the phase boundaries of the two-stage transition region are set up, and the critical exponents for each type of transition are derived analytically.

Chaos Theory and James Joyce's "ulysses": Leopold Bloom as a Human COMPLEX@SYSTEM^

NASA Astrophysics Data System (ADS)

Mackey, Peter Francis

1995-01-01

These four ideas apply as much to our lives as to the life of Leopold Bloom: (1) A trivial decision can wholly change a life. (2) A chance encounter can dramatically alter life's course. (3) A contingent nexus exists between consciousness and environment. (4) A structure of meaning helps us interpret life's chaos. These ideas also relate to a contemporary science called by some "chaos theory." The connection between Ulysses and chaos theory enhances our understanding of Bloom's day; it also suggests that this novel may be about the real process of life itself. The first chapter explains how Joyce's own essays and comments to friends compel attention to the links between Ulysses and chaos theory. His scientific contemporaries anticipated chaos theory, and their ideas seem to have rubbed off on him. We see this in his sense of trivial things and chance, his modernistic organizational impulses, and the contingent nature of Bloom's experience. The second chapter studies what chaos theory and Joyce's ideas tell us about "Ithaca," the episode which particularly implicates our processes of interpreting this text as well as life itself as we face their chaos. The third chapter examines Bloom's close feel for the aboriginal world, a contingency that clarifies his vulnerability to trivial changes. The fourth chapter studies how Bloom's stream of consciousness unfolds--from his chance encounters with trivial things. Beneath this stream's seeming chaos, Bloom's distinct personality endures, similar to how Joyce's schemas give Ulysses an imbedded, underlying order. The fifth chapter examines how trivial perturbations, such as Lyons' misunderstanding about "Throwaway," produce small crises for Bloom, exacerbating his seeming impotence before his lonely "fate.". The final chapter analyzes Bloom's views that fate and chance dictate his life. His views provide an opportunity to explore the implications chaos theory has for our understanding of free will and determinism. Ultimately, despite ungovernable fate and chance, Bloom asserts his will with Stephen and Molly, proving that he will live on, attempting to create his own destiny, wresting hope from the "chaos" of his experience.

Chaotic Mountain Blocks in Pluto’s Sputnik Planitia

NASA Astrophysics Data System (ADS)

Singer, Kelsi N.; Knight, Katherine I.; Stern, S. Alan; Olkin, Catherine; Grundy, William M.; McKinnon, William B.; Moore, Jeffrey M.; Schenk, Paul M.; Spencer, John R.; Weaver, Harold A.; Young, Leslie; Ennico, Kimberly; New Horizons Geology, Geophysics and Imaging Science Theme Team, The New Horizons Surface Composition Science Theme Team

2017-10-01

One of the first high-resolution Pluto images returned by New Horizons displayed a collection of tall, jagged peaks rising out of the large nitrogen ice sheet informally known as Sputnik Planitia (SP). This mountain range was later revealed to be one of several along the western edge of SP. The mountains are several hundred broken-up blocks of Pluto’s primarily water ice lithosphere and some retain surface terrains similar to the nearby intact crust surrounding SP. Water ice with some fractures or porosity is likely >5% less dense than solid N2 ice at Pluto’s temperatures. Thus it is possible the blocks are, or were, floating icebergs or at least partially suspended to the point that some blocks appear to be tilted as if they have faltered (Moore et al., 2016, Science, 351, 1284-1293).We analyze four mountain ranges on the western edge of SP and compare to chaotic terrains on Europa and Mars. The blocks on Pluto have angular planforms but we characterize their size using block surface area converted to an equivalent circular diameter. Topography was used to define block extents. The blocks range in size from 3-30 km in diameter, with a mode of ~8-10 km. Blocks range from 0.2-3.8 km in height, and block height generally increases with block diameter. One or more dark layers can be identified in a few scarp faces, and are at a similar depth to each other and to layers seen in fault and crater walls elsewhere on Pluto. A large N-S trending fault system runs tangential to SP and may be the source of crustal disruption on the western side.On Europa and Mars block sizes vary greatly between different chaos regions, but Conamara Chaos has an average block size of ~5 km in diameter, smaller than that typically seen on Pluto. Also the blocks often transition into fractured terrain still connected to the surround lithosphere at the periphery of the chaos regions. The source regions for the blocks are more obvious on Europa and Mars. Additionally the block heights on Europa and Mars generally do not increase with block size. Thus, the main mechanism of crustal breakup is likely different between these bodies.

The value of instructional communication in crisis situations: restoring order to chaos.

PubMed

Sellnow, Timothy L; Sellnow, Deanna D; Lane, Derek R; Littlefield, Robert S

2012-04-01

This article explores the nature of instructional communication in responding to crisis situations. Through the lens of chaos theory, the relevance of instructional messages in restoring order is established. This perspective is further advanced through an explanation of how various learning styles impact the receptivity of various instructional messages during the acute phase of crises. We then summarize an exploratory study focusing on the relationship between learning styles and the demands of instructional messages in crisis situations. We conclude the article with a series of conclusions and implications. © 2011 Society for Risk Analysis.

Externalizing problems, attention regulation, and household chaos: a longitudinal behavioral genetic study.

PubMed

Wang, Zhe; Deater-Deckard, Kirby; Petrill, Stephen A; Thompson, Lee A

2012-08-01

Previous research documented a robust link between difficulties in self-regulation and development of externalizing problems (i.e., aggression and delinquency). In this study, we examined the longitudinal additive and interactive genetic and environmental covariation underlying this well-established link using a twin design. The sample included 131 pairs of monozygotic twins and 173 pairs of same-sex dizygotic twins who participated in three waves of annual assessment. Mothers and fathers provided reports of externalizing problems. Teacher report and observer rating were used to assess twin's attention regulation. The etiology underlying the link between externalizing problems and attention regulation shifted from a common genetic mechanism to a common environmental mechanism in the transition across middle childhood. Household chaos moderated the genetic variance of and covariance between externalizing problems and attention regulation. The genetic influence on individual differences in both externalizing problems and attention regulation was stronger in more chaotic households. However, higher levels of household chaos attenuated the genetic link between externalizing problems and attention regulation.

Externalizing problems, attention regulation, and household chaos: A longitudinal behavioral genetic study

PubMed Central

Wang, Zhe; Deater-Deckard, Kirby; Petrill, Stephen A.; Thompson, Lee A.

2015-01-01

Previous research has documented a robust link between difficulties in self-regulation and development of externalizing problems (i.e., aggression and delinquency). In the current study, we examined the longitudinal additive and interactive genetic and environmental covariation underlying this well-established link using a twin design. The sample included 131 pairs of monozygotic twins and 173 pairs of same-sex dizygotic twins who participated in three waves of annual assessment. Mothers and fathers provided reports of externalizing problems. Teacher report and observer rating were used to assess twin’s attention regulation. The etiology underlying the link between externalizing problems and attention regulation shifted from a common genetic mechanism to a common environmental mechanism in the transition across middle childhood. Household chaos moderated the genetic variance of and covariance between externalizing problems and attention regulation. The genetic influence on individual differences in both externalizing problems and attention regulation was stronger in more chaotic household. However, higher levels of household chaos attenuated the genetic link between externalizing problems and attention regulation. PMID:22781853

A numerical study of bifurcations in a barotropic shear flow

NASA Technical Reports Server (NTRS)

Huerre, P.; Keefe, L. R.; Meunier, G.; Redekopp, L. G.; Spalart, P. R.; Rogers, M. M.

1988-01-01

In the last few years, more and more evidence has emerged suggesting that transition to turbulence may be viewed as a succession of bifurcations to deterministic chaos. Most experimental and numerical observations have been restricted to Rayleigh-Benard convection and Taylor-Couette flow between concentric cylinders. An attempt is made to accurately describe the bifurcation sequence leading to chaos in a 2-D temporal free shear layer on the beta-plane. The beta-plane is a locally Cartesian reduction of the equations describing the dynamicss of a shallow layer of fluid on a rotating spherical planet. It is a valid model for large scale flows of interest in meteorology and oceanography.

Menstruation, perimenopause, and chaos theory.

PubMed

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.

The Mysteries and Curiosities of Mars: A Tour of Unusual and Unexplained Terrains

NASA Astrophysics Data System (ADS)

Kerber, L.

2017-12-01

The large amount of data available from orbiting satellites around Mars has provided a wealth of information about the Martian surface and geological history. The published literature tends to focus on regions of Mars for which there are ready explanations; however, many regions of Mars remain mysterious. In this contribution, we present some of the strangest and least explained terrains on Mars: The Taffy Terrain: This complex terrain, consisting of swirling layers with variably sized bands, is present mostly at the bottom of Hellas Basin, but versions of it can also be found on the floor of Melas Chasma and in the Medusae Fossae Formation near Apollinaris Sulci. While little has been written about the taffy terrain, hypotheses include "glacial features" and salt domes. The taffy terrain bears some resemblance to submarine salt domes in the Gulf of Mexico, glacial deposits with mixed ash and ice in Iceland, or chalk formations in Egypt's White Desert. The Fishscale Terrain: At the northern edge of Lucus Planum, the friable Medusae Fossae Formation transitions into a chaos-like terrain with hundreds of mesas forming a pattern like the scales of a fish. While chaos terrains are mysterious in general, this morphologically fresh, near-equatorial chaos is especially unusual. Polygonal Ridges in Gordii Dorsum: Also a part of the Medusae Fossae Formation, the ridges in Gordii Dorsum represent a negative image of the fishscale terrain—a intricate lattice of slender black ridges. These are thought to form via the embayment of the fishscale terrain with lava and the subsequent erosion of the original mesas. Horseshoe Features: These geomorphological features look like inverted barchan dunes, but they are actually pits eroded into the surface of the Medusae Fossae Formation. Channels surrounding Elysium Mons: These channel systems are among the most complex on Mars, but they appear on a young Amazonian lava surface. The channels cut through topography, anastomose, and create streamlined islands. Strange flows around cones: Some rootless cones in Cerberus Palus have unusual flows coming out of them. Possible hypotheses include lava or mudflows. Sinus Meridiani: This region is host to arcuate ridge lattices, circular mesas with concentric patterns, and straight, subparallel ridges, similar to other ridges found near the South Pole.

Chaos control of Hastings-Powell model by combining chaotic motions

NASA Astrophysics Data System (ADS)

Danca, Marius-F.; Chattopadhyay, Joydev

2016-04-01

In this paper, we propose a Parameter Switching (PS) algorithm as a new chaos control method for the Hastings-Powell (HP) system. The PS algorithm is a convergent scheme that switches the control parameter within a set of values while the controlled system is numerically integrated. The attractor obtained with the PS algorithm matches the attractor obtained by integrating the system with the parameter replaced by the averaged value of the switched parameter values. The switching rule can be applied periodically or randomly over a set of given values. In this way, every stable cycle of the HP system can be approximated if its underlying parameter value equalizes the average value of the switching values. Moreover, the PS algorithm can be viewed as a generalization of Parrondo's game, which is applied for the first time to the HP system, by showing that losing strategy can win: "losing + losing = winning." If "loosing" is replaced with "chaos" and, "winning" with "order" (as the opposite to "chaos"), then by switching the parameter value in the HP system within two values, which generate chaotic motions, the PS algorithm can approximate a stable cycle so that symbolically one can write "chaos + chaos = regular." Also, by considering a different parameter control, new complex dynamics of the HP model are revealed.

Two Strain Dengue Model with Temporary Cross Immunity and Seasonality

NASA Astrophysics Data System (ADS)

Aguiar, Maíra; Ballesteros, Sebastien; Stollenwerk, Nico

2010-09-01

Models on dengue fever epidemiology have previously shown critical fluctuations with power law distributions and also deterministic chaos in some parameter regions due to the multi-strain structure of the disease pathogen. In our first model including well known biological features, we found a rich dynamical structure including limit cycles, symmetry breaking bifurcations, torus bifurcations, coexisting attractors including isola solutions and deterministic chaos (as indicated by positive Lyapunov exponents) in a much larger parameter region, which is also biologically more plausible than the previous results of other researches. Based on these findings we will investigate the model structures further including seasonality.

Two Strain Dengue Model with Temporary Cross Immunity and Seasonality

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aguiar, Maira; Ballesteros, Sebastien; Stollenwerk, Nico

Models on dengue fever epidemiology have previously shown critical fluctuations with power law distributions and also deterministic chaos in some parameter regions due to the multi-strain structure of the disease pathogen. In our first model including well known biological features, we found a rich dynamical structure including limit cycles, symmetry breaking bifurcations, torus bifurcations, coexisting attractors including isola solutions and deterministic chaos (as indicated by positive Lyapunov exponents) in a much larger parameter region, which is also biologically more plausible than the previous results of other researches. Based on these findings we will investigate the model structures further including seasonality.

Numerical simulation of the transition to chaos in a dissipative Duffing oscillator with two-frequency excitation

NASA Astrophysics Data System (ADS)

Zavrazhina, T. V.

2007-10-01

A mathematical modeling technique is proposed for oscillation chaotization in an essentially nonlinear dissipative Duffing oscillator with two-frequency excitation on an invariant torus in ℝ2. The technique is based on the joint application of the parameter continuation method, Floquet stability criteria, bifurcation theory, and the Everhart high-accuracy numerical integration method. This approach is used for the numerical construction of subharmonic solutions in the case when the oscillator passes to chaos through a sequence of period-multiplying bifurcations. The value of a universal constant obtained earlier by the author while investigating oscillation chaotization in dissipative oscillators with single-frequency periodic excitation is confirmed.

Effect of smoothing on robust chaos.

PubMed

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

2010-08-01

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

On stability of fixed points and chaos in fractional systems.

PubMed

Edelman, Mark

2018-02-01

In this paper, we propose a method to calculate asymptotically period two sinks and define the range of stability of fixed points for a variety of discrete fractional systems of the order 0<α<2. The method is tested on various forms of fractional generalizations of the standard and logistic maps. Based on our analysis, we make a conjecture that chaos is impossible in the corresponding continuous fractional systems.

Chaos Suppression in Fractional order Permanent Magnet Synchronous Generator in Wind Turbine Systems

NASA Astrophysics Data System (ADS)

Rajagopal, Karthikeyan; Karthikeyan, Anitha; Duraisamy, Prakash

2017-06-01

In this paper we investigate the control of three-dimensional non-autonomous fractional-order uncertain model of a permanent magnet synchronous generator (PMSG) via a adaptive control technique. We derive a dimensionless fractional order model of the PMSM from the integer order presented in the literatures. Various dynamic properties of the fractional order model like eigen values, Lyapunov exponents, bifurcation and bicoherence are investigated. The system chaotic behavior for various orders of fractional calculus are presented. An adaptive controller is derived to suppress the chaotic oscillations of the fractional order model. As the direct Lyapunov stability analysis of the robust controller is difficult for a fractional order first derivative, we have derived a new lemma to analyze the stability of the system. Numerical simulations of the proposed chaos suppression methodology are given to prove the analytical results derived through which we show that for the derived adaptive controller and the parameter update law, the origin of the system for any bounded initial conditions is asymptotically stable.

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

NASA Technical Reports Server (NTRS)

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

2015-01-01

Aram Chaos, Mars is a crater 280 kilometers in diameter with elevations circa. minus 2 to minus 3 kilometers below datum that provides a compelling landing site for future human explorers as it features multiple scientific regions of interest (ROI) paired with a rich extensible Resource ROI that features poly-hydrated sulfates [1]. The geologic history of Aram Chaos suggests several past episodes of groundwater recharge and infilling by liquid water, ice, and other materials [1-3]. The creation of the fractured region with no known terrestrial equivalent may have been caused by melting of deep ice reservoirs that triggered the collapse of terrain followed by catastrophic water outflows over the region. Aram Chaos is of particular scientific interest because it is hypothesized that the chaotic terrain may be the source of water that contributed to the creation of nearby valleys such as Ares Vallis flowing toward Chryse Planitia. The liquid water was likely sourced as groundwater and therefore represents water derived from a protected subsurface environment making it a compelling astrobiological site [2]. The past history of water is also represented by high concentrations of hematite, Fe-oxyhydroxides, mono-hydrated and poly-hydrated sulfates [1, 2]. Poly-hydrated sulfates are likely to contain abundant water that evolves at temperatures below 500 degrees Centigrade thus conferring Aram Chaos a potentially high value for early in-situ resource utilization (ISRU) [4]. The geologic history also calls for future prospecting of deep ice deposits and possibly liquid water via deep drilling. The most recent stratigraphic units in the central part of Aram Chaos are not fractured, and are part of a dome-shaped formation that features bright, poorly-consolidated material that contains both hydrated sulfates and ferric oxides according to OMEGA (Observatoire pour la Minéralogie, l'Eau, les Glaces et l'Activité) data [5]. These surface material characteristics are preliminary indications of their potential use in civil engineering activities that involve regolith moving and hauling, while further study is needed to assess traverse-ability challenges. The widespread distribution of sulfates is also of interest as a resource for the use of sulfur as a binding compound in regolith-based concrete for constructions. The terrain depressions caused by the rock fracturing events may challenge surface mobility but also suggest the possibility of using such natural features for additional shielding from space radiation and as emplacement of nuclear surface power reactors for the same reason. The high concentration of hematite (up to 16 percent) in some of the smoother recent terrains of the central part of Aram Chaos [2] is a favorable attribute for metal extraction ISRU to create iron-based feedstock for in-situ fabrication of replacement parts or their repairs. Preliminary data on Aram Chaos indicate that it offers a combination of many critical criteria for human missions to the surface of Mars: equatorial region at low Mars Orbiter Laser Altimeter (MOLA), evidence of hydrated minerals over large areas and at high concentrations tied to historic evidence of liquid water over long periods.

K-T Transition into Chaos.

ERIC Educational Resources Information Center

McLean, Dewey M.

1988-01-01

Discusses the destabilizing influences that affect feedback systems in the earth and trigger disorganization. Presents information that integrates mantle degassing with feed-back systems, and the Sun-Earth-Space energy flow system which is the primary source of energy that drives the Earth's biosphere. (RT)

Transition from propagating localized states to spatiotemporal chaos in phase dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brand, H.R.; Deissler, R.J.; Brand, H.R.

1998-10-01

We study the nonlinear phase equation for propagating patterns. We investigate the transition from a propagating localized pattern to a space-filling spatiotemporally disordered pattern and discuss in detail to what extent there are propagating localized states that breathe in time periodically, quasiperiodically, and chaotically. Differences and similarities to the phenomena occurring for the quintic complex Ginzburg-Landau equation are elucidated. We also discuss for which experimentally accessible systems one could observe the phenomena described. {copyright} {ital 1998} {ital The American Physical Society}

Reynolds number effects on mixing due to topological chaos.

PubMed

Smith, Spencer A; Warrier, Sangeeta

2016-03-01

Topological chaos has emerged as a powerful tool to investigate fluid mixing. While this theory can guarantee a lower bound on the stretching rate of certain material lines, it does not indicate what fraction of the fluid actually participates in this minimally mandated mixing. Indeed, the area in which effective mixing takes place depends on physical parameters such as the Reynolds number. To help clarify this dependency, we numerically simulate the effects of a batch stirring device on a 2D incompressible Newtonian fluid in the laminar regime. In particular, we calculate the finite time Lyapunov exponent (FTLE) field for three different stirring protocols, one topologically complex (pseudo-Anosov) and two simple (finite-order), over a range of viscosities. After extracting appropriate measures indicative of both the amount of mixing and the area of effective mixing from the FTLE field, we see a clearly defined Reynolds number range in which the relative efficacy of the pseudo-Anosov protocol over the finite-order protocols justifies the application of topological chaos. More unexpectedly, we see that while the measures of effective mixing area increase with increasing Reynolds number for the finite-order protocols, they actually exhibit non-monotonic behavior for the pseudo-Anosov protocol.

Sensitivity to perturbations and quantum phase transitions.

PubMed

Wisniacki, D A; Roncaglia, A J

2013-05-01

The local density of states or its Fourier transform, usually called fidelity amplitude, are important measures of quantum irreversibility due to imperfect evolution. In this Rapid Communication we study both quantities in a paradigmatic many body system, the Dicke Hamiltonian, where a single-mode bosonic field interacts with an ensemble of N two-level atoms. This model exhibits a quantum phase transition in the thermodynamic limit, while for finite instances the system undergoes a transition from quasi-integrability to quantum chaotic. We show that the width of the local density of states clearly points out the imprints of the transition from integrability to chaos but no trace remains of the quantum phase transition. The connection with the decay of the fidelity amplitude is also established.

Mode locking and quasiperiodicity in a discrete-time Chialvo neuron model

NASA Astrophysics Data System (ADS)

Wang, Fengjuan; Cao, Hongjun

2018-03-01

The two-dimensional parameter spaces of a discrete-time Chialvo neuron model are investigated. Our studies demonstrate that for all our choice of two parameters (i) the fixed point is destabilized via Neimark-Sacker bifurcation; (ii) there exist mode locking structures like Arnold tongues and shrimps, with periods organized in a Farey tree sequence, embedded in quasiperiodic/chaotic region. We determine analytically the location of the parameter sets where Neimark-Sacker bifurcation occurs, and the location on this curve where Arnold tongues of arbitrary period are born. Properties of the transition that follows the so-called two-torus from quasiperiodicity to chaos are presented clearly and proved strictly by using numerical simulations such as bifurcation diagrams, the largest Lyapunov exponent diagram on MATLAB and C++.

Sliding Mode Control of Fractional-Order Delayed Memristive Chaotic System with Uncertainty and Disturbance

NASA Astrophysics Data System (ADS)

Ding, Da-Wei; Liu, Fang-Fang; Chen, Hui; Wang, Nian; Liang, Dong

2017-12-01

In this paper, a simplest fractional-order delayed memristive chaotic system is proposed in order to control the chaos behaviors via sliding mode control strategy. Firstly, we design a sliding mode control strategy for the fractional-order system with time delay to make the states of the system asymptotically stable. Then, we obtain theoretical analysis results of the control method using Lyapunov stability theorem which guarantees the asymptotic stability of the non-commensurate order and commensurate order system with and without uncertainty and an external disturbance. Finally, numerical simulations are given to verify that the proposed sliding mode control method can eliminate chaos and stabilize the fractional-order delayed memristive system in a finite time. Supported by the National Nature Science Foundation of China under Grant No. 61201227, Funding of China Scholarship Council, the Natural Science Foundation of Anhui Province under Grant No. 1208085M F93, 211 Innovation Team of Anhui University under Grant Nos. KJTD007A and KJTD001B

Transition of chaotic motion to a limit cycle by intervention of economic policy: an empirical analysis in agriculture.

PubMed

Sakai, Kenshi; Managi, Shunsuke; Vitanov, Nikolay K; Demura, Katsuhiko

2007-04-01

This paper investigates the transition of dynamics observed in an actual real agricultural economic dataset. Lyapunov spectrum analysis is conducted on the data to distinguish deterministic chaos and the limit cycle. Chaotic and periodic oscillation were identified before and after the second oil crisis, respectively. The statitonarity of the time series is investigated using recurrence plots. This shows that government intervention might reduce market instability by removing a chaotic market's long-term unpredictability.

Flow field topology of transient mixing driven by buoyancy

NASA Technical Reports Server (NTRS)

Duval, Walter M B.

2004-01-01

Transient mixing driven by buoyancy occurs through the birth of a symmetric Rayleigh-Taylor morphology (RTM) structure for large length scales. Beyond its critical bifurcation the RTM structure exhibits self-similarity and occurs on smaller and smaller length scales. The dynamics of the RTM structure, its nonlinear growth and internal collision, show that its genesis occurs from an explosive bifurcation which leads to the overlap of resonance regions in phase space. This event shows the coexistence of regular and chaotic regions in phase space which is corroborated with the existence of horseshoe maps. A measure of local chaos given by the topological entropy indicates that as the system evolves there is growth of uncertainty. Breakdown of the dissipative RTM structure occurs during the transition from explosive to catastrophic bifurcation; this event gives rise to annihilation of the separatrices which drives overlap of resonance regions. The global bifurcation of explosive and catastrophic events in phase space for the large length scale of the RTM structure serves as a template for which mixing occurs on smaller and smaller length scales. Copyright 2004 American Institute of Physics.

Chaos in nuclei: Theory and experiment

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Chaos control in solar fed DC-DC boost converter by optimal parameters using nelder-mead algorithm powered enhanced BFOA

NASA Astrophysics Data System (ADS)

Sudhakar, N.; Rajasekar, N.; Akhil, Saya; Jyotheeswara Reddy, K.

2017-11-01

The boost converter is the most desirable DC-DC power converter for renewable energy applications for its favorable continuous input current characteristics. In other hand, these DC-DC converters known as practical nonlinear systems are prone to several types of nonlinear phenomena including bifurcation, quasiperiodicity, intermittency and chaos. These undesirable effects has to be controlled for maintaining normal periodic operation of the converter and to ensure the stability. This paper presents an effective solution to control the chaos in solar fed DC-DC boost converter since the converter experiences wide range of input power variation which leads to chaotic phenomena. Controlling of chaos is significantly achieved using optimal circuit parameters obtained through Nelder-Mead Enhanced Bacterial Foraging Optimization Algorithm. The optimization renders the suitable parameters in minimum computational time. The results are compared with the traditional methods. The obtained results of the proposed system ensures the operation of the converter within the controllable region.

Chaotic Oscillations of Second Order Linear Hyperbolic Equations with Nonlinear Boundary Conditions: A Factorizable but Noncommutative Case

NASA Astrophysics Data System (ADS)

Li, Liangliang; Huang, Yu; Chen, Goong; Huang, Tingwen

If a second order linear hyperbolic partial differential equation in one-space dimension can be factorized as a product of two first order operators and if the two first order operators commute, with one boundary condition being the van der Pol type and the other being linear, one can establish the occurrence of chaos when the parameters enter a certain regime [Chen et al., 2014]. However, if the commutativity of the two first order operators fails to hold, then the treatment in [Chen et al., 2014] no longer works and significant new challenges arise in determining nonlinear boundary conditions that engenders chaos. In this paper, we show that by incorporating a linear memory effect, a nonlinear van der Pol boundary condition can cause chaotic oscillations when the parameter enters a certain regime. Numerical simulations illustrating chaotic oscillations are also presented.

Flavors of Chaos in the Asteroid Belt

NASA Astrophysics Data System (ADS)

Tsiganis, Kleomenis

2016-10-01

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

Convergence of moment expansions for expectation values with embedded random matrix ensembles and quantum chaos

NASA Astrophysics Data System (ADS)

Kota, V. K. B.

2003-07-01

Smoothed forms for expectation values < K> E of positive definite operators K follow from the K-density moments either directly or in many other ways each giving a series expansion (involving polynomials in E). In large spectroscopic spaces one has to partition the many particle spaces into subspaces. Partitioning leads to new expansions for expectation values. It is shown that all the expansions converge to compact forms depending on the nature of the operator K and the operation of embedded random matrix ensembles and quantum chaos in many particle spaces. Explicit results are given for occupancies < ni> E, spin-cutoff factors < JZ2> E and strength sums < O†O> E, where O is a one-body transition operator.

Chaotic Strings in AdS /CFT

NASA Astrophysics Data System (ADS)

de Boer, Jan; Llabrés, Eva; Pedraza, Juan F.; Vegh, David

2018-05-01

Holographic theories with classical gravity duals are maximally chaotic; i.e., they saturate the universal bound on the rate of growth of chaos [J. Maldacena, S. H. Shenker, and D. Stanford, J. High Energy Phys. 08 (2016) 106, 10.1007/JHEP08(2016)106]. It is interesting to ask whether this property is true only for leading large N correlators or if it can show up elsewhere. In this Letter, we consider the simplest setup to tackle this question: a Brownian particle coupled to a thermal ensemble. We find that the four-point out-of-time-order correlator that diagnoses chaos initially grows at an exponential rate that saturates the chaos bound, i.e., with a Lyapunov exponent λL=2 π /β . However, the scrambling time is parametrically smaller than for plasma excitations, t*˜β log √{λ } instead of t*˜β log N2. Our result shows that, at least in certain cases, maximal chaos can be attained in the probe sector without the explicit need of gravitational degrees of freedom.

Efficient topological chaos embedded in the blinking vortex system.

PubMed

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.

Spatial Distribution and Secular Variation of Geomagnetic Filed in China Described by the CHAOS-6 Model and its Error Analysis

NASA Astrophysics Data System (ADS)

Wang, Z.; Gu, Z.; Chen, B.; Yuan, J.; Wang, C.

2016-12-01

The CHAOS-6 geomagnetic field model, presented in 2016 by the Denmark's national space institute (DTU Space), is a model of the near-Earth magnetic field. According the CHAOS-6 model, seven component data of geomagnetic filed at 30 observatories in China in 2015 and at 3 observatories in China spanning the time interval 2008.0-2016.5 were calculated. Also seven component data of geomagnetic filed from the geomagnetic data of practical observations in China was obtained. Based on the model calculated data and the practical data, we have compared and analyzed the spatial distribution and the secular variation of the geomagnetic field in China. There is obvious difference between the two type data. The CHAOS-6 model cannot describe the spatial distribution and the secular variation of the geomagnetic field in China with comparative precision because of the regional and local magnetic anomalies in China.

Shake, Rupture And Flow: Hydraulic Constraints On The Formation Of Europa’s Chaos

NASA Astrophysics Data System (ADS)

Schmidt, Britney E.; Gooch, B. T.; Blankenship, D. D.; Soderlund, K. M.

2012-10-01

Europa’s chaos terrains may have formed above shallow water lenses formed by melting of the upper ice shell with ascending thermo-compositional plumes. A key factor in the creation of chaos terrain may be dramatic disruption and collapse of the ice lid above the forming melt lens along with potentially violent mixing upon its rupture; this is analogous to the collapse of terrestrial ice shelves in which massive ice bodies disintegrate in a few days. At Thera Macula, there is evidence for modification by water immediately external to the scarp that bounds the collapsed region. Since water runs either subaerially down hill or from high pressure to low when below or within ice, the swollen appearance of bands entering Thera Macula, which are uphill in terms of hydraulic and topographic gradients, raises the possibility that this steep scarp represents the place where the lens initially broke. As the ice lid ruptures, the overpressure within the lens may create sufficient pressure within the fracture to drive water through it, allowing water to escape into and modify surrounding terrain. Similar effects are seen when aquifers or subglacial water sources are tapped: water flows up the pipe until the pressure in the water body is relieved and the hydraulic “pressure head” in the pipe is lowered. We have modeled the hydraulic potential associated with a rupturing lens in order to investigate the range of parameters for overpressure, fracture width, and lid thickness that could produce such modification as is observed at Thera Macula. These place important constraints on the pressure within the lens and the energetics of a collapse event. These estimates may explain how ice masses within chaos are initially disrupted and provide a means for quantifying the vigor of surface-subsurface mixing that could be critical to Europa’s habitability.

Chaos-assisted tunneling in the presence of Anderson localization.

PubMed

Doggen, Elmer V H; Georgeot, Bertrand; Lemarié, Gabriel

2017-10-01

Tunneling between two classically disconnected regular regions can be strongly affected by the presence of a chaotic sea in between. This phenomenon, known as chaos-assisted tunneling, gives rise to large fluctuations of the tunneling rate. Here we study chaos-assisted tunneling in the presence of Anderson localization effects in the chaotic sea. Our results show that the standard tunneling rate distribution is strongly modified by localization, going from the Cauchy distribution in the ergodic regime to a log-normal distribution in the strongly localized case, for both a deterministic and a disordered model. We develop a single-parameter scaling description which accurately describes the numerical data. Several possible experimental implementations using cold atoms, photonic lattices, or microwave billiards are discussed.

Study of Quantum Chaos in the Framework of Triaxial Rotator Models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Proskurins, J.; Bavrins, K.; Andrejevs, A.

2009-01-28

Dynamical quantum chaos criteria--a perturbed wave function entropy W({psi}{sub i}) and a fragmentation width {kappa}({phi}{sub k}) of basis states were studied in two cases of nuclear rigid triaxial rotator models. The first model is characterized by deformation angle {gamma} only, while the second model depends on both quadrupole deformation parameters ({beta},{gamma}). The degree of chaoticity has been determined in the studies of the dependence of criteria W({psi}{sub i}) and {kappa}({phi}{sub k}) from nuclear spin values up to I{<=}101 for model parameters {gamma} and ({beta},{gamma}) correspondingly. The transition from librational to rotational type energy spectra has been considered for both modelsmore » as well.« less

Creation of a magnetic barrier at a noble q close to physical midpoint between two resonant surfaces in the ASDEX UG tokamak

NASA Astrophysics Data System (ADS)

Vazquez, Justin; Ali, Halima; Punjabi, Alkesh

2009-11-01

Ciraolo, Vittot and Chandre method of building invariant manifolds inside chaos in Hamiltonian systems [Ali H. and Punjabi A, Plasma Phys. Control. Fusion, 49, 1565--1582 (2007)] is used in the ASDEX UG tokamak. In this method, a second order perturbation is added to the perturbed Hamiltonian [op cit]. It creates an invariant torus inside the chaos, and reduces the plasma transport. The perturbation that is added to the equilibrium Hamiltonian is at least an order of magnitude smaller than the perturbation that causes chaos. This additional term has a finite, limited number of Fourier modes. Resonant magnetic perturbations (m,n) = (3,2)+(4,3) are added to the field line Hamiltonian for the ASDEX UG. An area-preserving map for the field line trajectories in the ASDEX UG is used. The common amplitude δ of these modes that gives complete chaos between the resonant surfaces ψ43 and ψ32 is determined. A magnetic barrier is built at a surface with noble q that is very nearly equals to the q at the physical midpoint between the two resonant surfaces. The maximum amplitude of magnetic perturbation for which this barrier can be sustained is determined. This work is supported by US Department of Energy grants DE-FG02-07ER54937, DE-FG02-01ER54624 and DE-FG02-04ER54793.

Chaos without nonlinear dynamics.

PubMed

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

2006-07-14

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

Self-trapping and tunneling of Bose-Einstein condensates in a cavity-mediated triple-well system

NASA Astrophysics Data System (ADS)

Wang, Bin; Zhang, Hui; Chen, Yan; Tan, Lei

2017-03-01

We have investigated tunneling characteristics of Bose-Einstein condensates (BECs) in a triple-well potential coupled to a high finesse optical cavity within a mean field approach. Due to the intrinsic atom-cavity field nonlinearity, several interesting phenomena arise which are the focuses of this work. In the dynamical process, an extensive numerical simulation of localization of the BECs for atoms initially trapped in one-, two-, and three-wells are performed for the symmetric and asymmetric cases in detail. It is shown that the the transition from the oscillation to the localization can be modified by the cavity-mediated potential, which will enlarge the regions of oscillation. With the increasing of the atomic interaction, the oscillation is blocked and the localization emerges. The condensates atoms can be trapped either in one-, two-, or in three wells eventually where they are initially uploaded for certain parameters. In particular, we find that the transition from the oscillation to the localization is accompanied with some irregular regime where tunneling dynamics is dominated by chaos for this cavity-mediated system.

Entanglement as a signature of quantum chaos.

PubMed

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

2004-01-01

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

Unusual biophysics of intrinsically disordered proteins.

PubMed

Uversky, Vladimir N

2013-05-01

Research of a past decade and a half leaves no doubt that complete understanding of protein functionality requires close consideration of the fact that many functional proteins do not have well-folded structures. These intrinsically disordered proteins (IDPs) and proteins with intrinsically disordered protein regions (IDPRs) are highly abundant in nature and play a number of crucial roles in a living cell. Their functions, which are typically associated with a wide range of intermolecular interactions where IDPs possess remarkable binding promiscuity, complement functional repertoire of ordered proteins. All this requires a close attention to the peculiarities of biophysics of these proteins. In this review, some key biophysical features of IDPs are covered. In addition to the peculiar sequence characteristics of IDPs these biophysical features include sequential, structural, and spatiotemporal heterogeneity of IDPs; their rough and relatively flat energy landscapes; their ability to undergo both induced folding and induced unfolding; the ability to interact specifically with structurally unrelated partners; the ability to gain different structures at binding to different partners; and the ability to keep essential amount of disorder even in the bound form. IDPs are also characterized by the "turned-out" response to the changes in their environment, where they gain some structure under conditions resulting in denaturation or even unfolding of ordered proteins. It is proposed that the heterogeneous spatiotemporal structure of IDPs/IDPRs can be described as a set of foldons, inducible foldons, semi-foldons, non-foldons, and unfoldons. They may lose their function when folded, and activation of some IDPs is associated with the awaking of the dormant disorder. It is possible that IDPs represent the "edge of chaos" systems which operate in a region between order and complete randomness or chaos, where the complexity is maximal. This article is part of a Special Issue entitled: The emerging dynamic view of proteins: Protein plasticity in allostery, evolution and self-assembly. Copyright © 2012 Elsevier B.V. All rights reserved.

Creation of second order magnetic barrier inside chaos created by NTMs in the ASDEX UG

NASA Astrophysics Data System (ADS)

Ali, Halima; Punjabi, Alkesh

2012-10-01

Understanding and stabilization of neoclassical tearing modes (NTM) in tokamaks is an important problem. For low temperature plasmas, tearing modes are believed to be mainly driven by current density gradient. For collisionless plasmas, even when plasma is stable to classical tearing modes, helical reduction in bootstrap current in O-point of an island can destabilize NTMs when an initial island is seeded by other global MHD instabilities or when microturbulence triggers the transition from a linear to nonlinear instability. The onset of NTMs leads to the most serious beta limit in ASDEX UG tokamak [O. Gubner et al 2005 NF 39 1321]. The important NTMs in the ASDDEX UG are (m,n)=(3,2)+(4,3)+(1,1). Realistic parameterization of these NTMs and the safety factor in ASDEX UG are given in [O. Dumbrajs et al 2005 POP 12 1107004]. We use a symplectic map in magnetic coordinates for the ASDEX UG to integrate field lines in presence of the NTMs. We add a second order control term [H. Ali and A. Punjabi 2007 PPCF 49 1565] to this ASDEX UG field line Hamiltonian to create an invariant magnetic surface inside the chaos generated by the NTMs. The relative strength, robustness, and resilience of this barrier are studied to ascertain the most desirable noble barrier in the ASDEX UG with NTMs. We present preliminary results of this work, and discuss its implications with regard to magnetic transport barriers for increasing strength of magnetic perturbations. This work is supported by the grants DE-FG02-01ER54624 and DE-FG02-04ER54793.

Hopf bifurcation and chaos in a third-order phase-locked loop

NASA Astrophysics Data System (ADS)

Piqueira, José Roberto C.

2017-01-01

Phase-locked loops (PLLs) are devices able to recover time signals in several engineering applications. The literature regarding their dynamical behavior is vast, specifically considering that the process of synchronization between the input signal, coming from a remote source, and the PLL local oscillation is robust. For high-frequency applications it is usual to increase the PLL order by increasing the order of the internal filter, for guarantying good transient responses; however local parameter variations imply structural instability, thus provoking a Hopf bifurcation and a route to chaos for the phase error. Here, one usual architecture for a third-order PLL is studied and a range of permitted parameters is derived, providing a rule of thumb for designers. Out of this range, a Hopf bifurcation appears and, by increasing parameters, the periodic solution originated by the Hopf bifurcation degenerates into a chaotic attractor, therefore, preventing synchronization.

Quasiperiodicity and Frequency Locking in Electronic Conduction in Germanium.

NASA Astrophysics Data System (ADS)

Gwinn, Elisabeth Gray

1987-09-01

This thesis presents an experimental study of a driven spatio-temporal instability in high-field transport in cooled, p-type Ge. The instability is produced at liquid He temperatures by d.c. voltage bias above the threshold for breakdown by impurity impact ionization, and is associated experimentally with voltage-controlled negative differential conductivity. The instability is coupled to an external oscillator by applying a sinusoidal voltage bias across the Ge sample. The driven instability exhibits frequency locking, quasiperiodicity, and chaos as the frequency and amplitude of the sinusoidal bias are varied. An iterative map of the circle provides a simple model for such a coupled, dissipative nonlinear oscillator system. The transition from quasiperiodicity to chaos in this model system occurs in a universal way; for example, the circle map has a universal, self-similar power spectrum at the onset of chaos with the golden mean winding number. When normalized appropriately, the power spectrum at the onset of chaos in the driven instability in Ge displays the same structure, with good agreement between the amplitudes of the experimental and theoretical spectral peaks. The relevance of universal theory to experiment can also be tested with a spectrum of scaling indices f( alpha), which is used to compare the probability distribution for the circle map at the onset of chaos with the golden mean winding number to the distribution of probability on a Poincare section of the experimental attractor. The procedure used to find f(alpha ) for the driven transport instability overcomes the sensitivity of f(alpha) to noise and to deviation from the critical amplitude. The f( alpha) curve for the driven instability in Ge is found to be in good agreement with the universal circle map result.

Early Adjustment, Gender Differences, and Classroom Organizational Climate in First Grade

ERIC Educational Resources Information Center

Ponitz, Claire Cameron; Rimm-Kaufman, Sara E.; Brock, Laura L.

2009-01-01

We examined gender differences in the first-grade transition, exploring child and classroom contributions to self-control and achievement in a rural sample. Teachers (n = 36) reported on children's (n = 172) initial adjustment difficulty and end-of-year self-control. Observed classroom organization and teacher-reported classroom chaos measured…

Turbulence in the Ott-Antonsen equation for arrays of coupled phase oscillators

NASA Astrophysics Data System (ADS)

Wolfrum, M.; Gurevich, S. V.; Omel'chenko, O. E.

2016-02-01

In this paper we study the transition to synchrony in an one-dimensional array of oscillators with non-local coupling. For its description in the continuum limit of a large number of phase oscillators, we use a corresponding Ott-Antonsen equation, which is an integro-differential equation for the evolution of the macroscopic profiles of the local mean field. Recently, it was reported that in the spatially extended case at the synchronisation threshold there appear partially coherent plane waves with different wave numbers, which are organised in the well-known Eckhaus scenario. In this paper, we show that for Kuramoto-Sakaguchi phase oscillators the phase lag parameter in the interaction function can induce a Benjamin-Feir-type instability of the partially coherent plane waves. The emerging collective macroscopic chaos appears as an intermediate stage between complete incoherence and stable partially coherent plane waves. We give an analytic treatment of the Benjamin-Feir instability and its onset in a codimension-two bifurcation in the Ott-Antonsen equation as well as a numerical study of the transition from phase turbulence to amplitude turbulence inside the Benjamin-Feir unstable region.

Arsinoes Chaos Landforms

NASA Technical Reports Server (NTRS)

2004-01-01

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

Terahertz radiation induced chaotic electron transport in semiconductor superlattices with a tilted magnetic field.

PubMed

Wang, C; Wang, F; Cao, J C

2014-09-01

Chaotic electron transport in semiconductor superlattice induced by terahertz electric field that is superimposed on a dc electric field along the superlattice axis are studied using the semiclassical motion equations including the effect of dissipation. A magnetic field that is tilted relative to the superlattice axis is also applied to the system. Numerical simulation shows that electrons in superlattice miniband exhibit complicate nonlinear oscillating modes with the influence of terahertz radiation. Transitions between frequency-locking and chaos via pattern forming bifurcations are observed with the varying of terahertz amplitude. It is found that the chaotic regions gradually contract as the dissipation increases. We attribute the appearance of complicate nonlinear oscillation in superlattice to the interaction between terahertz radiation and internal cooperative oscillating mode relative to Bloch oscillation and cyclotron oscillation.

Examination of Regional Transit Service under Contracting : A Case Study in the Greater New Orleans Region : [Executive Summary

DOT National Transportation Integrated Search

2011-03-01

In late 2008, New Orleans Regional Transit Authority (RTA) began to execute a delegated management contract with a multinational private firm, in order to not only increase efficiency and effectiveness in operation and maintenance of public tra...

Reynolds number effects on mixing due to topological chaos

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smith, Spencer A.; Warrier, Sangeeta

2016-03-15

Topological chaos has emerged as a powerful tool to investigate fluid mixing. While this theory can guarantee a lower bound on the stretching rate of certain material lines, it does not indicate what fraction of the fluid actually participates in this minimally mandated mixing. Indeed, the area in which effective mixing takes place depends on physical parameters such as the Reynolds number. To help clarify this dependency, we numerically simulate the effects of a batch stirring device on a 2D incompressible Newtonian fluid in the laminar regime. In particular, we calculate the finite time Lyapunov exponent (FTLE) field for threemore » different stirring protocols, one topologically complex (pseudo-Anosov) and two simple (finite-order), over a range of viscosities. After extracting appropriate measures indicative of both the amount of mixing and the area of effective mixing from the FTLE field, we see a clearly defined Reynolds number range in which the relative efficacy of the pseudo-Anosov protocol over the finite-order protocols justifies the application of topological chaos. More unexpectedly, we see that while the measures of effective mixing area increase with increasing Reynolds number for the finite-order protocols, they actually exhibit non-monotonic behavior for the pseudo-Anosov protocol.« less

Intimations of water on Mars.

PubMed

2000-08-01

This photo essay contains images of Mars that propose evidence of the possible present or past existence of liquid water on Mars. Images were taken by the Mars Global Surveyor Mars Orbiter Camera. Images presented include: Polar Wall Pit region, consisting of gully landforms possibly caused by seepage and runoff of liquid water; Noachis Terra region, an area of gullies eroded into the wall of a meteor impact crater, where channels and related debris are seen, possibly formed by seepage, runoff, and debris flow; two images of Gorgonum Chaos region, one a series of troughs and layers of gullies and the other of gullies in a specific layer forming an alcove similar to an aquifer; Sirenum Fossae/Gorgonum Chaos mosaic of two images from this region of the southern hemisphere of Mars, showing 20 different channels coming down from a trough and their associated debris fans. Images and their enhancements are from NASA/JPL/Malin Space Science System.

Recent geomagnetic secular variation from Swarm and ground observatories as estimated in the CHAOS-6 geomagnetic field model

NASA Astrophysics Data System (ADS)

Finlay, Christopher C.; Olsen, Nils; Kotsiaros, Stavros; Gillet, Nicolas; Tøffner-Clausen, Lars

2016-07-01

We use more than 2 years of magnetic data from the Swarm mission, and monthly means from 160 ground observatories as available in March 2016, to update the CHAOS time-dependent geomagnetic field model. The new model, CHAOS-6, provides information on time variations of the core-generated part of the Earth's magnetic field between 1999.0 and 2016.5. We present details of the secular variation (SV) and secular acceleration (SA) from CHAOS-6 at Earth's surface and downward continued to the core surface. At Earth's surface, we find evidence for positive acceleration of the field intensity in 2015 over a broad area around longitude 90°E that is also seen at ground observatories such as Novosibirsk. At the core surface, we are able to map the SV up to at least degree 16. The radial field SA at the core surface in 2015 is found to be largest at low latitudes under the India-South-East Asia region, under the region of northern South America, and at high northern latitudes under Alaska and Siberia. Surprisingly, there is also evidence for significant SA in the central Pacific region, for example near Hawaii where radial field SA is observed on either side of a jerk in 2014. On the other hand, little SV or SA has occurred over the past 17 years in the southern polar region. Inverting for a quasi-geostrophic core flow that accounts for this SV, we obtain a prominent planetary-scale, anti-cyclonic, gyre centred on the Atlantic hemisphere. We also find oscillations of non-axisymmetric, azimuthal, jets at low latitudes, for example close to 40°W, that may be responsible for localized SA oscillations. In addition to scalar data from Ørsted, CHAMP, SAC-C and Swarm, and vector data from Ørsted, CHAMP and Swarm, CHAOS-6 benefits from the inclusion of along-track differences of scalar and vector field data from both CHAMP and the three Swarm satellites, as well as east-west differences between the lower pair of Swarm satellites, Alpha and Charlie. Moreover, ground observatory SV estimates are fit to a Huber-weighted rms level of 3.1 nT/year for the eastward components and 3.8 and 3.7 nT/year for the vertical and southward components. We also present an update of the CHAOS high-degree lithospheric field, making use of along-track differences of CHAMP scalar and vector field data to produce a new static field model that agrees well with the MF7 field model out to degree 110.

Stability and bifurcation analysis of a generalized scalar delay differential equation.

PubMed

Bhalekar, Sachin

2016-08-01

This paper deals with the stability and bifurcation analysis of a general form of equation D(α)x(t)=g(x(t),x(t-τ)) involving the derivative of order α ∈ (0, 1] and a constant delay τ ≥ 0. The stability of equilibrium points is presented in terms of the stability regions and critical surfaces. We provide a necessary condition to exist chaos in the system also. A wide range of delay differential equations involving a constant delay can be analyzed using the results proposed in this paper. The illustrative examples are provided to explain the theory.

Hydaspis Chaos in Nighttime Infrared

NASA Technical Reports Server (NTRS)

2002-01-01

This nighttime infrared image, taken by the thermal emission imaging system, captures a massively disrupted region on Mars called Hydaspis Chaos, which is located near the equator at two degrees north, 29 degrees west. The total vertical difference from the lowest to highest points in this region is about five kilometers (three miles.)

The steep slopes leading down into the canyon of Hydaspsis Chaos are strewn with rocks, while the plateaus and mesas above are covered in dust. This pattern indicates that processes are at work to prevent the dust from completely covering the surface of these slopes, even over the very long period since these canyons were formed.

The slopes and floor of these canyons show remarkable variability in the distribution of rocks and fine-grained material. Chaotic terrain may have been formed when subsurface ground water or ice was removed, and the overlying ground collapsed. The release of this water or ice (or both)formed the outflow channel Tiu Valles, which flowed across the Mars Pathfinder landing site.

This image captures a region of chaotic terrain about 106 kilometers (65 miles) long and 32 kilometers (20 miles) wide. The channel that feeds into the chaos at the bottom of the image is about 7 kilometers (4.3 miles)wide and 280 meters (930 feet) deep. The image was acquired on February 19, 2002. North is to the right of the image.

NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The thermal emission imaging system was provided by Arizona State University, Tempe. Lockheed Martin Astronautics, Denver, is the prime contractor for the project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.

Chaos of radiative heat-loss-induced flame front instability.

PubMed

Kinugawa, Hikaru; Ueda, Kazuhiro; Gotoda, Hiroshi

2016-03-01

We are intensively studying the chaos via the period-doubling bifurcation cascade in radiative heat-loss-induced flame front instability by analytical methods based on dynamical systems theory and complex networks. Significant changes in flame front dynamics in the chaotic region, which cannot be seen in the bifurcation diagrams, were successfully extracted from recurrence quantification analysis and nonlinear forecasting and from the network entropy. The temporal dynamics of the fuel concentration in the well-developed chaotic region is much more complicated than that of the flame front temperature. It exhibits self-affinity as a result of the scale-free structure in the constructed visibility graph.

Robust finite-time chaos synchronization of uncertain permanent magnet synchronous motors.

PubMed

Chen, Qiang; Ren, Xuemei; Na, Jing

2015-09-01

In this paper, a robust finite-time chaos synchronization scheme is proposed for two uncertain third-order permanent magnet synchronous motors (PMSMs). The whole synchronization error system is divided into two cascaded subsystems: a first-order subsystem and a second-order subsystem. For the first subsystem, we design a finite-time controller based on the finite-time Lyapunov stability theory. Then, according to the backstepping idea and the adding a power integrator technique, a second finite-time controller is constructed recursively for the second subsystem. No exogenous forces are required in the controllers design but only the direct-axis (d-axis) and the quadrature-axis (q-axis) stator voltages are used as manipulated variables. Comparative simulations are provided to show the effectiveness and superior performance of the proposed method. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Equilibrium 𝛽-limits in classical stellarators

NASA Astrophysics Data System (ADS)

Loizu, J.; Hudson, S. R.; Nührenberg, C.; Geiger, J.; Helander, P.

2017-12-01

A numerical investigation is carried out to understand the equilibrium -limit in a classical stellarator. The stepped-pressure equilibrium code (Hudson et al., Phys. Plasmas, vol. 19 (11), 2012) is used in order to assess whether or not magnetic islands and stochastic field-lines can emerge at high . Two modes of operation are considered: a zero-net-current stellarator and a fixed-iota stellarator. Despite the fact that relaxation is allowed (Taylor, Rev. Mod. Phys., vol. 58 (3), 1986, pp. 741-763), the former is shown to maintain good flux surfaces up to the equilibrium -limit predicted by ideal-magnetohydrodynamics (MHD), above which a separatrix forms. The latter, which has no ideal equilibrium -limit, is shown to develop regions of magnetic islands and chaos at sufficiently high , thereby providing a `non-ideal -limit'. Perhaps surprisingly, however, the value of at which the Shafranov shift of the axis reaches a fraction of the minor radius follows in all cases the scaling laws predicted by ideal-MHD. We compare our results to the High-Beta-Stellarator theory of Freidberg (Ideal MHD, 2014, Cambridge University Press) and derive a new prediction for the non-ideal equilibrium -limit above which chaos emerges.

Landslide in Aureum Chaos

NASA Technical Reports Server (NTRS)

2004-01-01

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

Order or chaos in Boolean gene networks depends on the mean fraction of canalizing functions

NASA Astrophysics Data System (ADS)

Karlsson, Fredrik; Hörnquist, Michael

2007-10-01

We explore the connection between order/chaos in Boolean networks and the naturally occurring fraction of canalizing functions in such systems. This fraction turns out to give a very clear indication of whether the system possesses ordered or chaotic dynamics, as measured by Derrida plots, and also the degree of order when we compare different networks with the same number of vertices and edges. By studying also a wide distribution of indegrees in a network, we show that the mean probability of canalizing functions is a more reliable indicator of the type of dynamics for a finite network than the classical result on stability relating the bias to the mean indegree. Finally, we compare by direct simulations two biologically derived networks with networks of similar sizes but with power-law and Poisson distributions of indegrees, respectively. The biologically motivated networks are not more ordered than the latter, and in one case the biological network is even chaotic while the others are not.

Chaos on the conveyor belt.

PubMed

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

2013-04-01

The dynamics of a spring-block train placed on a moving conveyor belt is investigated both by simple experiments and computer simulations. The first block is connected by a spring to an external static point and, due to the dragging effect of the belt, the blocks undergo complex stick-slip dynamics. A qualitative agreement with the experimental results can be achieved only by taking into account the spatial inhomogeneity of the friction force on the belt's surface, modeled as noise. As a function of the velocity of the conveyor belt and the noise strength, the system exhibits complex, self-organized critical, sometimes chaotic, dynamics and phase transition-like behavior. Noise-induced chaos and intermittency is also observed. Simulations suggest that the maximum complexity of the dynamical states is achieved for a relatively small number of blocks (around five).

Nonlinear analysis of EEG in major depression with fractal dimensions.

PubMed

Akar, Saime A; Kara, Sadik; Agambayev, Sumeyra; Bilgic, Vedat

2015-01-01

Major depressive disorder (MDD) is a psychiatric mood disorder characterized by cognitive and functional impairments in attention, concentration, learning and memory. In order to investigate and understand its underlying neural activities and pathophysiology, EEG methodologies can be used. In this study, we estimated the nonlinearity features of EEG in MDD patients to assess the dynamical properties underlying the frontal and parietal brain activity. EEG data were obtained from 16 patients and 15 matched healthy controls. A wavelet-chaos methodology was used for data analysis. First, EEGs of subjects were decomposed into 5 EEG sub-bands by discrete wavelet transform. Then, both the Katz's and Higuchi's fractal dimensions (KFD and HFD) were calculated as complexity measures for full-band and sub-bands EEGs. Last, two-way analyses of variances were used to test EEG complexity differences on each fractality measures. As a result, a significantly increased complexity was found in both parietal and frontal regions of MDD patients. This significantly increased complexity was observed not only in full-band activity but also in beta and gamma sub-bands of EEG. The findings of the present study indicate the possibility of using the wavelet-chaos methodology to discriminate the EEGs of MDD patients from healthy controls.

On the Origin of Chaos in the Asteroid Belt

NASA Technical Reports Server (NTRS)

Murray, N.; Holman, M.; Potter, M.

1998-01-01

We consider the effect of gravitational perturbations from Jupiter on the dynamics of asteroids, when Jupiter is itself perturbed by Saturn. The presence of Saturn introduces a number of additional frequencies into Jupiters orbit. These frequencies in turn produce chaos in narrow regions on either side of the chaotic zones associated with the mean motion resonances between the asteroids and Jupiter. The resonant arguments of these three-body resonances contain the longitudes of Jupiter and the asteroid together with either the secular frequency 9-6, or the longitude of Saturn. Resonances involving the longitude of Saturn are analogs of the Laplace resonance in the Jovian satellite system. We show that many three-body resonances involving the longitude of Saturn are chaotic. We give simple expressions for the width of the chaotic region and the associated Lyapunov time. In some cases the chaos can produce a diffusive growth in the 4 eccentricity of the asteroid that leads to ejection of the asteroid on times shorter than the age of the solar system. We give simple estimates for the diffusion time. Finally, we present the results of numerical integrations testing the theory.

Genomes: At the edge of chaos with maximum information capacity

NASA Astrophysics Data System (ADS)

Kong, Sing-Guan; Chen, Hong-Da; Torda, Andrew; Lee, H. C.

2016-12-01

We propose an order index, ϕ, which quantifies the notion of “life at the edge of chaos” when applied to genome sequences. It maps genomes to a number from 0 (random and of infinite length) to 1 (fully ordered) and applies regardless of sequence length and base composition. The 786 complete genomic sequences in GenBank were found to have ϕ values in a very narrow range, 0.037 ± 0.027. We show this implies that genomes are halfway towards being completely random, namely, at the edge of chaos. We argue that this narrow range represents the neighborhood of a fixed-point in the space of sequences, and genomes are driven there by the dynamics of a robust, predominantly neutral evolution process.

Second-order variational equations for N-body simulations

NASA Astrophysics Data System (ADS)

Rein, Hanno; Tamayo, Daniel

2016-07-01

First-order variational equations are widely used in N-body simulations to study how nearby trajectories diverge from one another. These allow for efficient and reliable determinations of chaos indicators such as the Maximal Lyapunov characteristic Exponent (MLE) and the Mean Exponential Growth factor of Nearby Orbits (MEGNO). In this paper we lay out the theoretical framework to extend the idea of variational equations to higher order. We explicitly derive the differential equations that govern the evolution of second-order variations in the N-body problem. Going to second order opens the door to new applications, including optimization algorithms that require the first and second derivatives of the solution, like the classical Newton's method. Typically, these methods have faster convergence rates than derivative-free methods. Derivatives are also required for Riemann manifold Langevin and Hamiltonian Monte Carlo methods which provide significantly shorter correlation times than standard methods. Such improved optimization methods can be applied to anything from radial-velocity/transit-timing-variation fitting to spacecraft trajectory optimization to asteroid deflection. We provide an implementation of first- and second-order variational equations for the publicly available REBOUND integrator package. Our implementation allows the simultaneous integration of any number of first- and second-order variational equations with the high-accuracy IAS15 integrator. We also provide routines to generate consistent and accurate initial conditions without the need for finite differencing.

Devil's staircase and the absence of chaos in the dc- and ac-driven overdamped Frenkel-Kontorova model

NASA Astrophysics Data System (ADS)

Sokolović, I.; Mali, P.; Odavić, J.; Radošević, S.; Medvedeva, S. Yu.; Botha, A. E.; Shukrinov, Yu. M.; Tekić, J.

2017-08-01

The devil's staircase structure arising from the complete mode locking of an entirely nonchaotic system, the overdamped dc+ac driven Frenkel-Kontorova model with deformable substrate potential, was observed. Even though no chaos was found, a hierarchical ordering of the Shapiro steps was made possible through the use of a previously introduced continued fraction formula. The absence of chaos, deduced here from Lyapunov exponent analyses, can be attributed to the overdamped character and the Middleton no-passing rule. A comparative analysis of a one-dimensional stack of Josephson junctions confirmed the disappearance of chaos with increasing dissipation. Other common dynamic features were also identified through this comparison. A detailed analysis of the amplitude dependence of the Shapiro steps revealed that only for the case of a purely sinusoidal substrate potential did the relative sizes of the steps follow a Farey sequence. For nonsinusoidal (deformed) potentials, the symmetry of the Stern-Brocot tree, depicting all members of particular Farey sequence, was seen to be increasingly broken, with certain steps being more prominent and their relative sizes not following the Farey rule.

Quantum Tunneling and Chaos in Classical Scale Walkers

NASA Astrophysics Data System (ADS)

Su, Jenny; Dijksman, Joshua; Ward, Jeremy; Behringer, Robert

2014-03-01

We study the behavior of `walkers' small droplets bouncing on a fluid layer vibrated at amplitudes just below the onset of Faraday instability. It was shown recently that despite their macroscopic size, the droplet dynamics are stochastic in nature and reminiscent of the dual particle-wave dynamics in the realm of quantum mechanics (Couder PRL 2006). We use these walkers to study how chaos, which is macroscopically unpredictable, will manifest in a quantum setting. Pecora showed in 2011 that tunneling for particles that have a chaotic ground state is different from tunneling for particles with a regular ground state (PRE 2011). In the experiment we gather data that illustrates the particle trajectory and tunneling behavior as particles transition across the barrier in the double well system with both integrable and chaotic shapes.

The Polomeno Family Intervention Framework for Perinatal Education: Preparing Couples for the Transition to Parenthood

PubMed Central

Polomeno, Viola

2000-01-01

Couples face many challenges as they transform themselves from dyad to triad. For some couples, these challenges are life-enriching experiences, while for others, chaos ensues, potentially leading to separation and divorce. The transition to first-time parenthood, even for well-functioning couples, is fraught with potential disorganization. At the same time, it provides opportunities for simultaneous self-growth and conjugal enrichment. What role can perinatal educators play in preparing couples to deal with the changes associated with this transition? To answer this vital question, the author presents her conceptualization of perinatal education as a primary family intervention framework during the perinatal period. PMID:17273190

Impact of predator dormancy on prey-predator dynamics

NASA Astrophysics Data System (ADS)

Freire, Joana G.; Gallas, Marcia R.; Gallas, Jason A. C.

2018-05-01

The impact of predator dormancy on the population dynamics of phytoplankton-zooplankton in freshwater ecosystems is investigated using a simple model including dormancy, a strategy to avoid extinction. In addition to recently reported chaos-mediated mixed-mode oscillations, as the carrying capacity grows, we find surprisingly wide phases of nonchaos-mediated mixed-mode oscillations to be present well before the onset of chaos in the system. Nonchaos-mediated cascades display spike-adding sequences, while chaos-mediated cascades show spike-doubling. A host of braided periodic phases with exotic shapes is found embedded in a region of control parameters dominated by chaotic oscillations. We describe the organization of these complicated phases and show how they are interconnected and how their complexity unfolds as control parameters change. The novel nonchaos-mediated phases are found to be large and stable, even for low carrying capacity.

Dynamical manifestations of quantum chaos: correlation hole and bulge

NASA Astrophysics Data System (ADS)

Torres-Herrera, E. J.; Santos, Lea F.

2017-10-01

A main feature of a chaotic quantum system is a rigid spectrum where the levels do not cross. We discuss how the presence of level repulsion in lattice many-body quantum systems can be detected from the analysis of their time evolution instead of their energy spectra. This approach is advantageous to experiments that deal with dynamics, but have limited or no direct access to spectroscopy. Dynamical manifestations of avoided crossings occur at long times. They correspond to a drop, referred to as correlation hole, below the asymptotic value of the survival probability and to a bulge above the saturation point of the von Neumann entanglement entropy and the Shannon information entropy. By contrast, the evolution of these quantities at shorter times reflects the level of delocalization of the initial state, but not necessarily a rigid spectrum. The correlation hole is a general indicator of the integrable-chaos transition in disordered and clean models and as such can be used to detect the transition to the many-body localized phase in disordered interacting systems. This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.

Investigating chaotic wake dynamics past a flapping airfoil and the role of vortex interactions behind the chaotic transition

NASA Astrophysics Data System (ADS)

Bose, Chandan; Sarkar, Sunetra

2018-04-01

The present study investigates the complex vortex interactions in two-dimensional flow-field behind a symmetric NACA0012 airfoil undergoing a prescribed periodic pitching-plunging motion in low Reynolds number regime. The flow-field transitions from periodic to chaotic through a quasi-periodic route as the plunge amplitude is gradually increased. This study unravels the role of the complex interactions that take place among the main vortex structures in making the unsteady flow-field transition from periodicity to chaos. The leading-edge separation plays a key role in providing the very first trigger for aperiodicity. Subsequent mechanisms like shredding, merging, splitting, and collision of vortices in the near-field that propagate and sustain the disturbance have also been followed and presented. These fundamental mechanisms are seen to give rise to spontaneous and irregular formation of new vortex couples at arbitrary locations, which are the primary agencies for sustaining chaos in the flow-field. The interactions have been studied for each dynamical state to understand the course of transition in the flow-field. The qualitative changes observed in the flow-field are manifestation of changes in the underlying dynamical system. The overall dynamics are established in the present study by means of robust quantitative measures derived from classical and non-classical tools from the dynamical system theory. As the present analysis involves a high fidelity multi-unknown system, non-classical dynamical tools such as recurrence-based time series methods are seen to be very efficient. Moreover, their application is novel in the context of pitch-plunge flapping flight.

Torus Breakdown and Homoclinic Chaos in a Glow Discharge Tube

NASA Astrophysics Data System (ADS)

Ginoux, Jean-Marc; Meucci, Riccardo; Euzzor, Stefano

2017-12-01

Starting from historical researches, we used, like Van der Pol and Le Corbeiller, a cubic function for modeling the current-voltage characteristic of a direct current low-pressure plasma discharge tube, i.e. a neon tube. This led us to propose a new four-dimensional autonomous dynamical system allowing to describe the experimentally observed phenomenon. Then, mathematical analysis and detailed numerical investigations of such a fourth-order torus circuit enabled to highlight bifurcation routes from torus breakdown to homoclinic chaos following the Newhouse-Ruelle-Takens scenario.

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

PubMed

Ecke, Robert E

2015-09-01

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

Noise, chaos, and (ɛ, τ)-entropy per unit time

NASA Astrophysics Data System (ADS)

Gaspard, Pierre; Wang, Xiao-Jing

1993-12-01

The degree of dynamical randomness of different time processes is characterized in terms of the (ε, τ)-entropy per unit time. The (ε, τ)-entropy is the amount of information generated per unit time, at different scales τ of time and ε of the observables. This quantity generalizes the Kolmogorov-Sinai entropy per unit time from deterministic chaotic processes, to stochastic processes such as fluctuations in mesoscopic physico-chemical phenomena or strong turbulence in macroscopic spacetime dynamics. The random processes that are characterized include chaotic systems, Bernoulli and Markov chains, Poisson and birth-and-death processes, Ornstein-Uhlenbeck and Yaglom noises, fractional Brownian motions, different regimes of hydrodynamical turbulence, and the Lorentz-Boltzmann process of nonequilibrium statistical mechanics. We also extend the (ε, τ)-entropy to spacetime processes like cellular automata, Conway's game of life, lattice gas automata, coupled maps, spacetime chaos in partial differential equations, as well as the ideal, the Lorentz, and the hard sphere gases. Through these examples it is demonstrated that the (ε, τ)-entropy provides a unified quantitative measure of dynamical randomness to both chaos and noises, and a method to detect transitions between dynamical states of different degrees of randomness as a parameter of the system is varied.

Properties of a Martian local dust storm in Atlantis Chaos from OMEGA/MEX data

NASA Astrophysics Data System (ADS)

Oliva, F.; Geminale, A.; D'Aversa, E.; Altieri, F.; Bellucci, G.; Carrozzo, F. G.; Sindoni, G.; Grassi, D.

2018-01-01

In this study we present the analysis of the dust properties of a local storm imaged in the Atlantis Chaos region on Mars by the OMEGA imaging spectrometer on March 2nd, 2005. We use the radiative transfer model MITRA to study the dust properties at solar wavelengths between 0.5 μm and 2.5 μm and infer the connection between the local storm dynamics and the topography. We retrieve maps of effective grain radius (reff), optical depth at 9.3 μm (τ9.3) and top altitude (ta) of the dust layer. Our results show that large particles (reff = 1.6 μm) are gathered in the centre of the storm (lat = 33.5° S; lon = 183.5° W), where the optical depth is maximum (τ9.3 > 7.0) and the top altitude exceeds 18 km. Outside the storm, we obtain τ9.3<0.2, in agreement with the estimates derived from global climate models (GCM). We speculate that a low thermal inertia region at the western border of Atlantis Chaos is a possible source of the dust storm. Moreover, we find evidence that topography plays a role in confining the local storm in Atlantis Chaos. The vertical wind component from the GCM does not provide any hint for the triggering of dust lifting. On the other hand, the combination of the horizontal and vertical wind profiles suggests that the dust, once lifted, is pushed eastward and then downward and gets confined within the north-east ridge of Atlantis Chaos. From our results, the thickness of the dust layer collapsed on the surface ranges from about 1 μm at the storm boundaries up to more than 100 μm at its centre. We verify that a layer of dust thicker than 1 μm, deposited on the surface, can prevent the detection of mafic absorption features. However, such features are still present in OMEGA data of Atlantis Chaos registered after the storm. Hence, we deduce that, once the storm is over, the dust deposited on an area larger than the one where it has been observed.

A novel image encryption algorithm based on chaos maps with Markov properties

NASA Astrophysics Data System (ADS)

Liu, Quan; Li, Pei-yue; Zhang, Ming-chao; Sui, Yong-xin; Yang, Huai-jiang

2015-02-01

In order to construct high complexity, secure and low cost image encryption algorithm, a class of chaos with Markov properties was researched and such algorithm was also proposed. The kind of chaos has higher complexity than the Logistic map and Tent map, which keeps the uniformity and low autocorrelation. An improved couple map lattice based on the chaos with Markov properties is also employed to cover the phase space of the chaos and enlarge the key space, which has better performance than the original one. A novel image encryption algorithm is constructed on the new couple map lattice, which is used as a key stream generator. A true random number is used to disturb the key which can dynamically change the permutation matrix and the key stream. From the experiments, it is known that the key stream can pass SP800-22 test. The novel image encryption can resist CPA and CCA attack and differential attack. The algorithm is sensitive to the initial key and can change the distribution the pixel values of the image. The correlation of the adjacent pixels can also be eliminated. When compared with the algorithm based on Logistic map, it has higher complexity and better uniformity, which is nearer to the true random number. It is also efficient to realize which showed its value in common use.

Ashkin-Teller criticality and weak first-order behavior of the phase transition to a fourfold degenerate state in two-dimensional frustrated Ising antiferromagnets

NASA Astrophysics Data System (ADS)

Liu, R. M.; Zhuo, W. Z.; Chen, J.; Qin, M. H.; Zeng, M.; Lu, X. B.; Gao, X. S.; Liu, J.-M.

2017-07-01

We study the thermal phase transition of the fourfold degenerate phases (the plaquette and single-stripe states) in the two-dimensional frustrated Ising model on the Shastry-Sutherland lattice using Monte Carlo simulations. The critical Ashkin-Teller-like behavior is identified both in the plaquette phase region and the single-stripe phase region. The four-state Potts critical end points differentiating the continuous transitions from the first-order ones are estimated based on finite-size-scaling analyses. Furthermore, a similar behavior of the transition to the fourfold single-stripe phase is also observed in the anisotropic triangular Ising model. Thus, this work clearly demonstrates that the transitions to the fourfold degenerate states of two-dimensional Ising antiferromagnets exhibit similar transition behavior.

Some bifurcation routes to chaos of thermocapillary convection in two-dimensional liquid layers of finite extent

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, K., E-mail: likai@imech.ac.cn; University of Chinese Academy of Sciences, Beijing 100190; Xun, B.

2016-05-15

As a part of the preliminary studies for the future space experiment (Zona-K) in the Russian module of the International Space Station, some bifurcation routes to chaos of thermocapillary convection in two-dimensional liquid layers filled with 10 cSt silicone oil have been numerically studied in this paper. As the laterally applied temperature difference is raised, variations in the spatial structure and temporal evolution of the thermocapillary convection and a complex sequence of transitions are observed. The results show that the finite extent of the liquid layer significantly influences the tempo-spatial evolution of the thermocapillary convection. Moreover, the bifurcation route ofmore » the thermocapillary convection changes very sensitively by the aspect ratio of the liquid layer. With the increasing Reynolds number (applied temperature difference), the steady thermocapillary convection experiences two consecutive transitions from periodic oscillatory state to quasi-periodic oscillatory state with frequency-locking before emergence of chaotic convection in a liquid layer of aspect ratio 14.25, and the thermocapillary convection undergoes period-doubling cascades leading to chaotic convection in a liquid layer of aspect ratio 13.0.« less

Latin American petroleum sector at crossroads

DOE Office of Scientific and Technical Information (OSTI.GOV)

Williams, B.

1992-07-06

This paper reports that Latin America's petroleum industry stands at a precarious crossroads of change. Fundamental changes of democratization, privatization, and economic reform that have marked South America's petroleum sectors since the late 1980s are seeping into other Latin American regions. An unprecedented return of capital that had fled the region in the 1980s - Latin America's lost decade - is under way in full force. That demonstrates the improved credibility of the region's economic reform programs, reports the Inter-American Development Bank (IDB). Even as those reform efforts marked progress in South America in 1991, however, that progress has beenmore » threatened in 1992 by political scandal, government crisis, and environmental controversy. Just as the fitful transition to capitalism in the former U.S.S.R. has threatened to collapse the former Soviet republics into chaos because of its economic fallout, so has economic reform in such nations as Brazil, Peru, and Venezuela stumbled. On the other hand, privatization continues apace in Argentina and Mexico. Those Latin American nations and others caught in the rising tide of privatization pulled by an increasingly market oriented global economy continue to avow their commitment to economic reform.« less

PREFACE: The 15th International Couette-Taylor Worskhop

NASA Astrophysics Data System (ADS)

Mutabazi, Innocent; Crumeyrolle, Olivier

2008-07-01

The 15th International Couette-Taylor Worskhop (ICTW15) was held in Le Havre, France from 9-12 July 2007. This regular international conference started in 1979 in Leeds, UK when the research interest in simple models of fluid flows was revitalized by systematic investigation of Rayleigh-Bénard convection and the Couette-Taylor flow. These two flow systems are good prototypes for the study of the transition to chaos and turbulence in closed flows. The workshop themes have been expanded from the original Couette-Taylor flow to include other centrifugal instabilities (Dean, Görtler, Taylor-Dean), spherical Couette flows, thermal convection instabilities, MHD, nonlinear dynamics and chaos, transition to turbulence, development of numerical and experimental techniques. The impressive longevity of the ICTW is due to the close interaction and fertile exchanges between international research groups from different disciplines: Physics and Astrophysics, Applied Mathematics, Mechanical Engineering, Chemical Engineering. The present workshop was attended by 100 participants, the program included over 83 contributions with 4 plenary lectures, 68 oral communications and 17 posters. The topics include, besides the classical Couette-Taylor flows, the centrifugal flows with longitudinal vortices, the shear flows, the thermal convection in curved geometries, the spherical Couette-Taylor flow, the geophysical flows, the magneto-hydrodynamic effects including the dynamo effect, the complex flows (viscoelasticity, immiscible fluids, bubbles and migration). Selected papers have been processed through the peer review system and are published in this issue of the Journal of Physics: Conference Series. The Workshop has been sponsored by Le Havre University, the Region Council of Haute-Normandie, Le Havre City Council, CNRS (ST2I, GdR-DYCOEC), and the European Space Agency through GEOFLOW program. The French Ministry of Defense (DGA), the Ministry of Foreign Affairs, the Ministry of Research and the University Association of Mechanics have provided some support. Innocent Mutabazi and Olivier Crumeyrolle Proceedings editors Le Havre, France 15 July 2008

Chaos tool implementation for non-singer and singer voice comparison (preliminary study)

NASA Astrophysics Data System (ADS)

Dajer, Me; Pereira, Jc; Maciel, Cd

2007-11-01

Voice waveform is linked to the stretch, shorten, widen or constrict vocal tract. The articulation effects of the singer's vocal tract modify the voice acoustical characteristics and differ from the non-singer voices. In the last decades, Chaos Theory has shown the possibility to explore the dynamic nature of voice signals from a different point of view. The purpose of this paper is to apply the chaos technique of phase space reconstruction to analyze non- singers and singer voices in order to explore the signal nonlinear dynamic, and correlate them with traditional acoustic parameters. Eight voice samples of sustained vowel /i/ from non-singers and eight from singers were analyzed with "ANL" software. The samples were also acoustically analyzed with "Analise de Voz 5.0" in order to extract acoustic perturbation measures jitter and shimmer, and the coefficient of excess - (EX). The results showed different visual patterns for the two groups correlated with different jitter, shimmer, and coefficient of excess values. We conclude that these results clearly indicate the potential of phase space reconstruction technique for analysis and comparison of non-singers and singer voices. They also show a promising tool for training voices application.

The First USGS Global Geologic Map of Europa

NASA Astrophysics Data System (ADS)

Leonard, E. J.; Patthoff, D. A.; Senske, D.; Collins, G. C.

2017-12-01

Understanding the global scale geology of Europa is paramount to gaining insight into the potential habitability of this icy world. To this end, work is ongoing to complete a global geological map at the scale of 1:15 million that incorporates data at all resolutions collected by the Voyager and Galileo missions. The results of this work will aid the Europa Clipper mission, now in formulation, by providing a framework for collaborative and synergistic science investigations. To understand global geologic and tectonic relations, a total of 10 geologic units have been defined. These include: Low Albedo Ridge Material (lam)—low albedo material that irregularly surrounds large (>20 km) ridge structures; Ridged plains (pr)—distributed over all latitudes and characterized by subparallel to cross-cutting ridges and troughs visible at high resolution (<100 m/px); Band material (b)—linear to curvilinear zones with a distinct, abrupt albedo change from the surrounding region; Crater material (c), Continuous Crater Ejecta (ce) and Discontinuous Crater Ejecta (dce)—features associated with impact craters including the site of the impact, crater material, and the fall-out debris respectively; Low Albedo Chaos (chl), Mottled Albedo Chaos (chm) and High Albedo Chaos (chh)—disrupted terrain with a relatively uniform low albedo, patchy/variegated albedo, and uniform high albedo appearance respectively; Knobby Chaos (chk) - disrupted terrain with rough and blocky texture occurring in the high latitudes. In addition to the geologic units, our mapping also includes structural features—Ridges, Cycloids, Undifferentiated Linea, Crater Rims, Depression Margins, Dome Margins and Troughs. We also introduce a point feature (at the global scale), Microchaos, to denote small (<10 km) patches of discontinuous chaos material. The completed map will constrain the distribution of different Europa terrains and provide a general stratigraphic framework to assess the geologic history of Europa from the regional to the global scale. Here, we present the map submitted to the USGS for review.

A Global Geologic Map of Europa

NASA Astrophysics Data System (ADS)

Janelle Leonard, Erin; Patthoff, Donald Alex; Senske, David A.; Collins, Geoffrey

2017-10-01

Understanding the global scale geology of Europa is paramount to gaining insight into the potential habitability of this icy world. To this end, work is ongoing to complete a global geological map at the scale of 1:15 million that incorporates data at all resolutions collected by the Voyager and Galileo missions. The results of this work will aid the Europa Clipper mission, now in formulation, by providing a framework for collaborative and synergistic science investigations.To understand global geologic and tectonic relations, a total of 10 geologic units have been defined. These include: Low Albedo Ridge Material (lam)—low albedo material that irregularly surrounds large (>20 km) ridge structures; Ridged plains (pr)—distributed over all latitudes and characterized by subparallel to cross-cutting ridges and troughs visible at high resolution (<100 m/px); Band material (b)—linear to curvilinear zones with a distinct, abrupt albedo change from the surrounding region; Crater material (c), Continuous Crater Ejecta (ce) and Discontinuous Crater Ejecta (dce)—features associated with impact craters including the site of the impact, crater material, and the fall-out debris respectively; Low Albedo Chaos (chl), Mottled Albedo Chaos (chm) and High Albedo Chaos (chh)—disrupted terrain with a relatively uniform low albedo, patchy/variegated albedo, and uniform high albedo appearance respectively; Knobby Chaos (chk) - disrupted terrain with rough and blocky texture occurring in the high latitudes.In addition to the geologic units, our mapping also includes structural features—Ridges, Cycloids, Undifferentiated Linea, Crater Rims, Depression Margins, Dome Margins and Troughs. We also introduce a point feature (at the global scale), Microchaos, to denote small (<10 km) patches of discontinuous chaos material. The completed map will constrain the distribution of different Europa terrains and provide a general stratigraphic framework to assess the geologic history of Europa from the regional to the global scale.

Synchronous behaviour of two interacting oscillatory systems undergoing quasiperiodic route to chaos.

PubMed

Mondal, S; Pawar, S A; Sujith, R I

2017-10-01

Thermoacoustic instability, caused by a positive feedback between the unsteady heat release and the acoustic field in a combustor, is a major challenge faced in most practical combustors such as those used in rockets and gas turbines. We employ the synchronization theory for understanding the coupling between the unsteady heat release and the acoustic field of a thermoacoustic system. Interactions between coupled subsystems exhibiting different collective dynamics such as periodic, quasiperiodic, and chaotic oscillations are addressed. Even though synchronization studies have focused on different dynamical states separately, synchronous behaviour of two coupled systems exhibiting a quasiperiodic route to chaos has not been studied. In this study, we report the first experimental observation of different synchronous behaviours between two subsystems of a thermoacoustic system exhibiting such a transition as reported in Kabiraj et al. [Chaos 22, 023129 (2012)]. A rich variety of synchronous behaviours such as phase locking, intermittent phase locking, and phase drifting are observed as the dynamics of such subsystem change. The observed synchronization behaviour is further characterized using phase locking value, correlation coefficient, and relative mean frequency. These measures clearly reveal the boundaries between different states of synchronization.

Singularity spectrum of intermittent seismic tremor at Kilauea Volcano, Hawaii

USGS Publications Warehouse

Shaw, H.R.; Chouet, B.

1989-01-01

Fractal singularity analysis (FSA) is used to study a 22-yr record of deep seismic tremor (30-60 km depth) for regions below Kilauea Volcano on the assumption that magma transport and fracture can be treated as a system of coupled nonlinear oscillators. Tremor episodes range from 1 to 100 min (cumulative duration = 1.60 ?? 104 min; yearly average - 727 min yr-1; mean gradient = 24.2 min yr-1km-1). Partitioning of probabilities, Pi, in the phase space of normalized durations, xi, are expressed in terms of a function f(??), where ?? is a variable exponent of a length scale, l. Plots of f(??) vs. ?? are called multifractal singularity spectra. The spectrum for deep tremor durations is bounded by ?? values of about 0.4 and 1.9 at f = O; fmax ???1.0 for ?? ??? 1. Results for tremor are similar to those found for systems transitional between complete mode locking and chaos. -Authors

Poverty, household chaos, and interparental aggression predict children’s ability to recognize and modulate negative emotions

PubMed Central

Raver, C. Cybele; Blair, Clancy; Garrett-Peters, Patricia

2015-01-01

The following prospective longitudinal study considers the ways that protracted exposure to verbal and physical aggression between parents may take a substantial toll on emotional adjustment for 1,025 children followed from 6 to 58 months of age. Exposure to chronic poverty from infancy to early childhood as well as multiple measures of household chaos were also included as predictors of children’s ability to recognize and modulate negative emotions in order to disentangle the role of interparental conflict from the socioeconomic forces that sometimes accompany it. Analyses revealed that exposure to greater levels of interparental conflict, more chaos in the household, and a higher number of years in poverty can be empirically distinguished as key contributors to 58-month-olds’ ability to recognize and modulate negative emotion. Implications for models of experiential canalization of emotional processes within the context of adversity are discussed. PMID:25215541

Poverty, household chaos, and interparental aggression predict children's ability to recognize and modulate negative emotions.

PubMed

Raver, C Cybele; Blair, Clancy; Garrett-Peters, Patricia

2015-08-01

The following prospective longitudinal study considers the ways that protracted exposure to verbal and physical aggression between parents may take a substantial toll on emotional adjustment for 1,025 children followed from 6 to 58 months of age. Exposure to chronic poverty from infancy to early childhood as well as multiple measures of household chaos were also included as predictors of children's ability to recognize and modulate negative emotions in order to disentangle the role of interparental conflict from the socioeconomic forces that sometimes accompany it. Analyses revealed that exposure to greater levels of interparental conflict, more chaos in the household, and a higher number of years in poverty can be empirically distinguished as key contributors to 58-month-olds' ability to recognize and modulate negative emotion. Implications for models of experiential canalization of emotional processes within the context of adversity are discussed.

Spatiotemporal chaos in the dynamics of buoyantly and diffusively unstable chemical fronts

NASA Astrophysics Data System (ADS)

Baroni, M. P. M. A.; Guéron, E.; De Wit, A.

2012-03-01

Nonlinear dynamics resulting from the interplay between diffusive and buoyancy-driven Rayleigh-Taylor (RT) instabilities of autocatalytic traveling fronts are analyzed numerically for various values of the relevant parameters. These are the Rayleigh numbers of the reactant A and autocatalytic product B solutions as well as the ratio D =DB/DA between the diffusion coefficients of the two key chemical species. The interplay between the coarsening dynamics characteristic of the RT instability and the constant short wavelength modulation of the diffusive instability can lead in some regimes to complex dynamics dominated by irregular succession of birth and death of fingers. By using spectral entropy measurements, we characterize the transition between order and spatial disorder in this system. The analysis of the power spectrum and autocorrelation function, moreover, identifies similarities between the various spatial patterns. The contribution of the diffusive instability to the complex dynamics is discussed.

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.

Uncertainty Quantification in Simulations of Epidemics Using Polynomial Chaos

PubMed Central

Santonja, F.; Chen-Charpentier, B.

2012-01-01

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

Global behavior of a vibro-impact system with asymmetric clearances

NASA Astrophysics Data System (ADS)

Li, Guofang; Ding, Wangcai

2018-06-01

A simple dynamic model of a vibro-impact system subjected to harmonic excitation with two asymmetric clearances is considered. The Semi-Analytical Method for getting periodic solutions of the vibro-impact system is proposed. Diversity and evolution of the fundamental periodic impact motions are analyzed. The formation mechanism of the complete chatting-impact periodic motion with sticking motion by the influence of gazing bifurcation is analyzed. The transitional law of periodic motions in the periodical inclusions area is presented. The coexistence of periodic motions and the extreme sensitivity of the initial value within the high frequency region are studied. The global distribution of the periodic and chaos motions of the system is obtained by the state-parameter space co-simulation method which very few have considered before. The distribution of the attractor and the corresponding attracting domain corresponding to different periodic motions are also studied.

The Six Fundamental Characteristics of Chaos and Their Clinical Relevance to Psychiatry: a New Hypothesis for the Origin of Psychosis

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: Process-Oriented PSYchiatry or "POPSY", for short. Four aspects of the relationship between chaos theory and POPSY are discussed: (1) The first of these, namely, Identification of Chaos / Picture of Illness involves a definition of Chaos / Psychosis and a discussion of the 6 logical characteristics of each. This leads to the concept of dynamical disease (definition, characteristics and examples) and to the idea of "psychological disturbance as dynamical illness". On the one hand, it is argued that the developmental course of psychosis is chaotic. On the other hand, we propose the hypothesis that the mental state of psychosis may be a linear information processing pathology. (2) The second aspect under discussion is the Assessment of Chaos / Diagnosis of Illness. In order to better understand how POPSY research treats this aspect, we take a look at the 3 different classes of (non-quantum) motion as models of 3 different possible courses of illness and outline present-day methods available for the quantitative assessment of chaotic (fractal) motion. (3) The third aspect, namely. Prediction of Chaos / Prognosis of Illness considers how each of these 3 classes of motion implies a different way of looking into the future: linear-causal, statistical and nonlinear-fractal, respectively (4) The fourth aspect of the relationship between chaos theory and POPSY, Control of Chaos / Treatment of Illness, is shown to have certain implications to complementary medicine. This paper completes with a short summary, conclusion and a closing remark.

Dynamical behavior of lean swirling premixed flame generated by change in gravitational orientation

NASA Astrophysics Data System (ADS)

Gotoda, Hiroshi; Miyano, Takaya; Shepherd, Ian

2010-11-01

The dynamic behavior of flame front instability in lean swirling premixed flame generated by the effect of gravitational orientation has been experimentally investigated in this work. When the gravitational direction is changed relative to the flame front, i.e., in inverted gravity, an unstably fluctuating flame (unstable flame) is formed in a limited domain of equivalence ratio and swirl number (Gotoda. H et al., Physical Review E, vol. 81, 026211, 2010). The time history of flame front fluctuations show that in the buoyancy-dominated region, chaotic irregular fluctuation with low frequencies is superimposed on the dominant periodic oscillation of the unstable flame. This periodic oscillation is produced by unstable large-scale vortex motion in combustion products generated by a change in the buoyancy/swirl interaction due to the inversion of gravitational orientation. As a result, the dynamic behavior of the unstable flame becomes low-dimensional deterministic chaos. Its dynamics maintains low-dimensional deterministic chaos even in the momentum-dominated region, in which vortex breakdown in the combustion products clearly occurs. These results were clearly demonstrated by the use of nonlinear time series analysis based on chaos theory, which has not been widely applied to the investigation of combustion phenomena.

Spin-flop quasi-first order phase transition and putative tricritical point in Gd3Co

NASA Astrophysics Data System (ADS)

Samatham, S. Shanmukharao; Barua, Soumendu; Suresh, K. G.

2017-12-01

Magnetic nature of Gd3Co is investigated using detailed measurements of temperature and field dependent magnetization. The antiferromagnetic phase is field-instable due to prevailing ferromagnetic exchange correlations above Néel temperature TN ∼ 130K . Below TN , with gradually increasing magnetic fields, the compound undergoes a quasi-first order phase transition from AFM to spin-flop over region and eventually acquires ferromagnetic phase in higher fields. Further the point at which the quasi-first order transition ends and second order transition sets in is the tricritical point, TTCP ∼ 125.6K , HTCP ∼ 4.4kOe .

Phase Transitions in Model Active Systems

NASA Astrophysics Data System (ADS)

Redner, Gabriel S.

The amazing collective behaviors of active systems such as bird flocks, schools of fish, and colonies of microorganisms have long amazed scientists and laypeople alike. Understanding the physics of such systems is challenging due to their far-from-equilibrium dynamics, as well as the extreme diversity in their ingredients, relevant time- and length-scales, and emergent phenomenology. To make progress, one can categorize active systems by the symmetries of their constituent particles, as well as how activity is expressed. In this work, we examine two categories of active systems, and explore their phase behavior in detail. First, we study systems of self-propelled spherical particles moving in two dimensions. Despite the absence of an aligning interaction, this system displays complex emergent dynamics, including phase separation into a dense active solid and dilute gas. Using simulations and analytic modeling, we quantify the phase diagram and separation kinetics. We show that this nonequilibrium phase transition is analogous to an equilibrium vapor-liquid system, with binodal and spinodal curves and a critical point. We also characterize the dense active solid phase, a unique material which exhibits the structural signatures of a crystalline solid near the crystal-hexatic transition point, as well as anomalous dynamics including superdiffusive motion on intermediate timescales. We also explore the role of interparticle attraction in this system. We demonstrate that attraction drastically changes the phase diagram, which contains two distinct phase-separated regions and is reentrant as a function of propulsion speed. We interpret this complex situation with a simple kinetic model, which builds from the observed microdynamics of individual particles to a full description of the macroscopic phase behavior. We also study active nematics, liquid crystals driven out of equilibrium by energy-dissipating active stresses. The equilibrium nematic state is unstable in these materials, leading to beautiful and surprising behaviors including the spontaneous generation of topological defect pairs which stream through the system and later annihilate, yielding a complex, seemingly chaotic dynamical steady-state. Here, we describe the emergence of order from this chaos in the form of previously unknown broken-symmetry phases in which the topological defects themselves undergo orientational ordering. We have identified these defect-ordered phases in two realizations of an active nematic: first, a suspension of extensile bundles of microtubules and molecular motor proteins, and second, a computational model of extending hard rods. We will describe the defect-stabilized phases that manifest in these systems, our current understanding of their origins, and discuss whether such phases may be a general feature of extensile active nematics.

Paternal Multiple Partner Fertility and Environmental Chaos Among Unmarried Nonresident Fathers

PubMed Central

Petren, Raymond E.

2017-01-01

This study examined the association between paternal multiple partner fertility (MPF; having children with two or more partners) and indicators of environmental chaos (partnership instability, residential instability, work stability, material hardship, and perceived social support) among unmarried, non-resident fathers. Survey data from the Fragile Families and Child Wellbeing Study (N = 873) were used to compare unmarried non-resident fathers who experienced MPF to those who had children with one partner. Results show that paternal MPF is associated with most indicators of environmental chaos (greater partnership instability, residential instability, work instability, material hardship), but not social support. Results suggest that fathers who experience MPF face challenges beyond those of other non-resident fathers. Policies and interventions should address aspects of instability and hardship that are unique to paternal MPF in order to encourage fathers’ positive contributions to children and families. Directions for future research are discussed. PMID:29755155

Crop identification for the delineation of irrigated regions under scarce data conditions: a new approach based on chaos theory

NASA Astrophysics Data System (ADS)

Mangiarotti, S.; Muddu, S.; Sharma, A. K.; Corgne, S.; Ruiz, L.; Hubert-Moy, L.

2015-12-01

Groundwater is one of the main water reservoirs used for irrigation in regions of scarce water resources. For this reason, crop irrigation is expected to have a direct influence on this reservoir. To understand the time evolution of the groundwater table and its storage changes, it is important to delineate irrigated crops, whose evaporative demand is relatively higher. Such delineation may be performed based on classical classification approaches using optical remote sensing. However, it remains a difficult problem in regions where plots do not exceed a few hectares and exhibit a very heterogeneous pattern with multiple crops. This difficulty is emphasized in South India where two or three months of cloudy conditions during the monsoon period can hide crop growth during the year. An alternative approach is introduced here that takes advantage of such scarce signal. Ten different crops are considered in the present study. A bank of crop models is first established based on the global modeling technique [1]. These models are then tested using original time series (from which models were obtained) in order to evaluate the information that can be deduced from these models in an inverse approach. The approach is then tested on an independent data set and is finally applied to a large ensemble of 10,000 time series of plot data extracted from the Berambadi catchment (AMBHAS site) part of the Kabini River basin CZO, South India. Results show that despite the important two-month gap in satellite observations in the visible band, interpolated vegetation index remains an interesting indicator for identification of crops in South India. [1] S. Mangiarotti, R. Coudret, L. Drapeau, & L. Jarlan, Polynomial search and global modeling: Two algorithms for modeling chaos, Phys. Rev. E, 86(4), 046205 (2012).

Features in Aureum Chaos

NASA Technical Reports Server (NTRS)

2004-01-01

12 November 2004 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows light-toned, sedimentary rock outcrops in the Aureum Chaos region of Mars. On the brightest and steepest slope in this scene, dry talus shed from the outcrop has formed a series of dark fans along its base. These outcrops are located near 3.4oS, 27.5oW. The image covers an area approximately 3 km (1.9 mi) across and sunlight illuminates the scene from the upper left.

Enter the Dragon: China Regains Its Place in the World and a U.S. Strategy for Cooperation and Confidence Building

DTIC Science & Technology

2010-10-27

chaos phobia (a deep fear of political chaos and instability); and (6) the fact that the community is paramount over the individual. 22 Scobell...A key fact to remember about China as she faces these myriad challenges is that she does so virtually alone, being a member of no large alliances...These steps should be taken in the context of a continued strong and flexible U.S. military presence in the region and awareness of the reality that the

Competitions hatch butterfly attractors in foreign exchange markets

NASA Astrophysics Data System (ADS)

Jin, Yu Ying

2005-03-01

Chaos in foreign exchange markets is a common issue of concern in the study of economic dynamics. In this work, we mainly investigate the competition effect on chaos in foreign exchange markets. As one of the main economic structures in the globalization process, competition between two target exchange rates with the same base currency forms a simple competitive exchange rate relation, where each exchange rate follows the chaotic model of De Grauwe (Exchange Rate Theory-Chaotic Models of Foreign Exchange Markets, Blackwell, Oxford, Cambridge, MA, 1993). The main discovery is, while each exchange rate is in its non-chaotic parameter regions, the effect of competition will “hatch” butterfly-like chaotic attractors in the competitive market. The positive Lyapunov exponent in the market explains the reason why chaos occurs.

Closer look at time averages of the logistic map at the edge of chaos

NASA Astrophysics Data System (ADS)

Tirnakli, Ugur; Tsallis, Constantino; Beck, Christian

2009-05-01

The probability distribution of sums of iterates of the logistic map at the edge of chaos has been recently shown [U. Tirnakli , Phys. Rev. E 75, 040106(R) (2007)] to be numerically consistent with a q -Gaussian, the distribution which—under appropriate constraints—maximizes the nonadditive entropy Sq , which is the basis of nonextensive statistical mechanics. This analysis was based on a study of the tails of the distribution. We now check the entire distribution, in particular, its central part. This is important in view of a recent q generalization of the central limit theorem, which states that for certain classes of strongly correlated random variables the rescaled sum approaches a q -Gaussian limit distribution. We numerically investigate for the logistic map with a parameter in a small vicinity of the critical point under which conditions there is convergence to a q -Gaussian both in the central region and in the tail region and find a scaling law involving the Feigenbaum constant δ . Our results are consistent with a large number of already available analytical and numerical evidences that the edge of chaos is well described in terms of the entropy Sq and its associated concepts.

Chaos, creativity, and substance abuse: the nonlinear dynamics of choice.

PubMed

Zausner, Tobi

2011-04-01

Artists create their work in conditions of disequilibrium, states of creative chaos that may appear turbulent but are capable of bringing forth new order. By absorbing information from the environment and discharging it negentropically as new work, artists can be modeled as dissipative systems. A characteristic of chaotic systems is a heightened sensitivity to stimuli, which can generate either positive experiences or negative ones that can lead some artists to substance abuse and misguided searches for a creative chaos. Alcohol and drug use along with inadequately addressed co-occurring emotional disorders interfere with artists' quest for the nonlinearity of creativity. Instead, metaphorically modeled by a limit cycle of addiction and then a spiral to disorder, the joys of a creative chaos become an elusive chimera for them rather than a fulfilling experience. Untreated mental illness and addiction to substances have shortened the lives of artists such as Vincent Van Gogh, Frida Kahlo, Henri de Toulouse-Lautrec, and Jackson Pollock, all of whom committed suicide. In contrast Edvard Munch and John Callahan, who chose to address their emotional problems and substance abuse, continued to live and remain creative. Choosing to access previously avoided moments of pain can activate the nonlinear power of self-transformation.

Analysis of tristable energy harvesting system having fractional order viscoelastic material

DOE Office of Scientific and Technical Information (OSTI.GOV)

Oumbé Tékam, G. T.; Woafo, P.; Kitio Kwuimy, C. A.

2015-01-15

A particular attention is devoted to analyze the dynamics of a strongly nonlinear energy harvester having fractional order viscoelastic flexible material. The strong nonlinearity is obtained from the magnetic interaction between the end free of the flexible material and three equally spaced magnets. Periodic responses are computed using the KrylovBogoliubov averaging method, and the effects of fractional order damping on the output electric energy are analyzed. It is obtained that the harvested energy is enhanced for small order of the fractional derivative. Considering the order and strength of the fractional viscoelastic property as control parameter, the complexity of the systemmore » response is investigated through the Melnikov criteria for horseshoes chaos, which allows us to derive the mathematical expression of the boundary between intra-well motion and bifurcations appearance domain. We observe that the order and strength of the fractional viscoelastic property can be effectively used to control chaos in the system. The results are confirmed by the smooth and fractal shape of the basin of attraction as the order of derivative decreases. The bifurcation diagrams and the corresponding Lyapunov exponents are plotted to get insight into the nonlinear response of the system.« less

First ultraviolet observations of the transition regions of X-ray bright solar-type stars in the Pleiades

NASA Technical Reports Server (NTRS)

Caillault, J.-P.; Vilhu, O.; Linsky, J. L.

1990-01-01

Results are reported from A UV study of the transition regions of two X-ray-bright solar-type stars from the Pleiades, in an attempt to extend the main sequence age baseline for the transition-region activity-age relation over more than two orders of magnitude. However, no emission lines were detected from either star; the upper limits to the fluxes are consistent with previously determined saturation levels, but do not help to further constrain evolutionary models.

Lagrangian coherent structures at the onset of hyperchaos in the two-dimensional Navier-Stokes equations.

PubMed

Miranda, Rodrigo A; Rempel, Erico L; Chian, Abraham C-L; Seehafer, Norbert; Toledo, Benjamin A; Muñoz, Pablo R

2013-09-01

We study a transition to hyperchaos in the two-dimensional incompressible Navier-Stokes equations with periodic boundary conditions and an external forcing term. Bifurcation diagrams are constructed by varying the Reynolds number, and a transition to hyperchaos (HC) is identified. Before the onset of HC, there is coexistence of two chaotic attractors and a hyperchaotic saddle. After the transition to HC, the two chaotic attractors merge with the hyperchaotic saddle, generating random switching between chaos and hyperchaos, which is responsible for intermittent bursts in the time series of energy and enstrophy. The chaotic mixing properties of the flow are characterized by detecting Lagrangian coherent structures. After the transition to HC, the flow displays complex Lagrangian patterns and an increase in the level of Lagrangian chaoticity during the bursty periods that can be predicted statistically by the hyperchaotic saddle prior to HC transition.

Intermittency and solitons in the driven dissipative nonlinear Schroedinger equation

NASA Technical Reports Server (NTRS)

Moon, H. T.; Goldman, M. V.

1984-01-01

The cubic nonlinear Schroedinger equation, in the presence of driving and Landau damping, is studied numerically. As the pump intensity is increased, the system exhibits a transition from intermittency to a two-torus to chaos. The laminar phase of the intermittency is also a two-torus motion which corresponds in physical space to two identical solitons of amplitude determined by a power-balance equation.

Terminal Transient Phase of Chaotic Transients

NASA Astrophysics Data System (ADS)

Lilienkamp, Thomas; Parlitz, Ulrich

2018-03-01

Transient chaos in spatially extended systems can be characterized by the length of the transient phase, which typically grows quickly with the system size (supertransients). For a large class of these systems, the chaotic phase terminates abruptly, without any obvious precursors in commonly used observables. Here we investigate transient spatiotemporal chaos in two different models of this class. By probing the state space using perturbed trajectories we show the existence of a "terminal transient phase," which occurs prior to the abrupt collapse of chaotic dynamics. During this phase the impact of perturbations is significantly different from the earlier transient and particular patterns of (non)susceptible regions in state space occur close to the chaotic trajectories. We therefore hypothesize that even without perturbations proper precursors for the collapse of chaotic transients exist, which might be highly relevant for coping with spatiotemporal chaos in cardiac arrhythmias or brain functionality, for example.

Modeling Transit Patterns Via Mobile App Logs.

DOT National Transportation Integrated Search

2016-01-01

Transit planners need detailed information of the trips people take using public transit in : order to design more optimal routes, address new construction projects, and address the : constantly changing needs of a city and metro region. Better trans...

Child-care chaos and teachers' responsiveness: The indirect associations through teachers' emotion regulation and coping.

PubMed

Jeon, Lieny; Hur, Eunhye; Buettner, Cynthia K

2016-12-01

Teachers in early child-care settings are key contributors to children's development. However, the role of teachers' emotional abilities (i.e., emotion regulation and coping skills) and the role of teacher-perceived environmental chaos in relation to their responsiveness to children are understudied. The current study explored the direct and indirect associations between teachers' perceptions of child-care chaos and their self-reported contingent reactions towards children's negative emotions and challenging social interactions via teachers' emotional regulation and coping strategies. The sample consisted of 1129 preschool-aged classroom teachers in day care and public pre-K programs across the US. We first found that child-care chaos was directly associated with teachers' non-supportive reactions after controlling for multiple program and teacher characteristics. In addition, teachers in more chaotic child-care settings had less reappraisal and coping skills, which in turn, was associated with lower levels of positive responsiveness to children. Teachers reporting a higher degree of chaos used more suppression strategies, which in turn, was associated with teachers' non-supportive reactions and fewer expressive encouragement reactions to children's emotions. Results of this exploratory study suggest that it is important to prepare teachers to handle chaotic environments with clear guidelines and rules. In order to encourage teachers' supportive responses to children, intervention programs are needed to address teachers' coping and emotion regulation strategies in early childhood education. Copyright © 2016 Society for the Study of School Psychology. Published by Elsevier Ltd. All rights reserved.

Surface energy from order parameter profile: At the QCD phase transition

NASA Technical Reports Server (NTRS)

Frei, Z.; Patkos, A.

1989-01-01

The order parameter profile between coexisting confined and plasma regions at the quantum chromodynamic (QCD) phase transition is constructed. The dimensionless combination of the surface energy (Sigma) and the correlation length (Zeta) is estimated to be Sigma Zeta 3 approximately equals 0.8.

Higher order cumulants in colorless partonic plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cherif, S.; Laboratoire de Physique et de Mathématiques Appliquées; Ahmed, M. A. A.

2016-06-10

Any physical system considered to study the QCD deconfinement phase transition certainly has a finite volume, so the finite size effects are inevitably present. This renders the location of the phase transition and the determination of its order as an extremely difficult task, even in the simplest known cases. In order to identify and locate the colorless QCD deconfinement transition point in finite volume T{sub 0}(V), a new approach based on the finite-size cumulant expansion of the order parameter and the ℒ{sub m,n}-Method is used. We have shown that both cumulants of higher order and their ratios, associated to themore » thermodynamical fluctuations of the order parameter, in QCD deconfinement phase transition behave in a particular enough way revealing pronounced oscillations in the transition region. The sign structure and the oscillatory behavior of these in the vicinity of the deconfinement phase transition point might be a sensitive probe and may allow one to elucidate their relation to the QCD phase transition point. In the context of our model, we have shown that the finite volume transition point is always associated to the appearance of a particular point in whole higher order cumulants under consideration.« less

Shear-induced criticality near a liquid-solid transition of colloidal suspensions

NASA Astrophysics Data System (ADS)

Miyama, Masamichi J.; Sasa, Shin-Ichi

2011-02-01

We investigate colloidal suspensions under shear flow through numerical experiments. By measuring the time-correlation function of a bond-orientational order parameter, we find a divergent time scale near a transition point from a disordered fluid phase to an ordered fluid phase, where the order is characterized by a nonzero value of the bond-orientational order parameter. We also present a phase diagram in the (ρ,γ˙ex) plane, where ρ is the density of the colloidal particles and γ˙ex is the shear rate of the solvent. The transition line in the phase diagram terminates at the equilibrium transition point, while a critical region near the transition line vanishes continuously as γ˙ex→0.

Disease-Associated Mutations Disrupt Functionally Important Regions of Intrinsic Protein Disorder

PubMed Central

Vacic, Vladimir; Markwick, Phineus R. L.; Oldfield, Christopher J.; Zhao, Xiaoyue; Haynes, Chad; Uversky, Vladimir N.; Iakoucheva, Lilia M.

2012-01-01

The effects of disease mutations on protein structure and function have been extensively investigated, and many predictors of the functional impact of single amino acid substitutions are publicly available. The majority of these predictors are based on protein structure and evolutionary conservation, following the assumption that disease mutations predominantly affect folded and conserved protein regions. However, the prevalence of the intrinsically disordered proteins (IDPs) and regions (IDRs) in the human proteome together with their lack of fixed structure and low sequence conservation raise a question about the impact of disease mutations in IDRs. Here, we investigate annotated missense disease mutations and show that 21.7% of them are located within such intrinsically disordered regions. We further demonstrate that 20% of disease mutations in IDRs cause local disorder-to-order transitions, which represents a 1.7–2.7 fold increase compared to annotated polymorphisms and neutral evolutionary substitutions, respectively. Secondary structure predictions show elevated rates of transition from helices and strands into loops and vice versa in the disease mutations dataset. Disease disorder-to-order mutations also influence predicted molecular recognition features (MoRFs) more often than the control mutations. The repertoire of disorder-to-order transition mutations is limited, with five most frequent mutations (R→W, R→C, E→K, R→H, R→Q) collectively accounting for 44% of all deleterious disorder-to-order transitions. As a proof of concept, we performed accelerated molecular dynamics simulations on a deleterious disorder-to-order transition mutation of tumor protein p63 and, in agreement with our predictions, observed an increased α-helical propensity of the region harboring the mutation. Our findings highlight the importance of mutations in IDRs and refine the traditional structure-centric view of disease mutations. The results of this study offer a new perspective on the role of mutations in disease, with implications for improving predictors of the functional impact of missense mutations. PMID:23055912

Structured chaos in a devil's staircase of the Josephson junction.

PubMed

Shukrinov, Yu M; Botha, A E; Medvedeva, S Yu; Kolahchi, M R; Irie, A

2014-09-01

The phase dynamics of Josephson junctions (JJs) under external electromagnetic radiation is studied through numerical simulations. Current-voltage characteristics, Lyapunov exponents, and Poincaré sections are analyzed in detail. It is found that the subharmonic Shapiro steps at certain parameters are separated by structured chaotic windows. By performing a linear regression on the linear part of the data, a fractal dimension of D = 0.868 is obtained, with an uncertainty of ±0.012. The chaotic regions exhibit scaling similarity, and it is shown that the devil's staircase of the system can form a backbone that unifies and explains the highly correlated and structured chaotic behavior. These features suggest a system possessing multiple complete devil's staircases. The onset of chaos for subharmonic steps occurs through the Feigenbaum period doubling scenario. Universality in the sequence of periodic windows is also demonstrated. Finally, the influence of the radiation and JJ parameters on the structured chaos is investigated, and it is concluded that the structured chaos is a stable formation over a wide range of parameter values.

Structured chaos in a devil's staircase of the Josephson junction

NASA Astrophysics Data System (ADS)

Shukrinov, Yu. M.; Botha, A. E.; Medvedeva, S. Yu.; Kolahchi, M. R.; Irie, A.

2014-09-01

The phase dynamics of Josephson junctions (JJs) under external electromagnetic radiation is studied through numerical simulations. Current-voltage characteristics, Lyapunov exponents, and Poincaré sections are analyzed in detail. It is found that the subharmonic Shapiro steps at certain parameters are separated by structured chaotic windows. By performing a linear regression on the linear part of the data, a fractal dimension of D = 0.868 is obtained, with an uncertainty of ±0.012. The chaotic regions exhibit scaling similarity, and it is shown that the devil's staircase of the system can form a backbone that unifies and explains the highly correlated and structured chaotic behavior. These features suggest a system possessing multiple complete devil's staircases. The onset of chaos for subharmonic steps occurs through the Feigenbaum period doubling scenario. Universality in the sequence of periodic windows is also demonstrated. Finally, the influence of the radiation and JJ parameters on the structured chaos is investigated, and it is concluded that the structured chaos is a stable formation over a wide range of parameter values.

Structured chaos in a devil's staircase of the Josephson junction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shukrinov, Yu. M.; Botha, A. E., E-mail: bothaae@unisa.ac.za; Medvedeva, S. Yu.

2014-09-01

The phase dynamics of Josephson junctions (JJs) under external electromagnetic radiation is studied through numerical simulations. Current-voltage characteristics, Lyapunov exponents, and Poincaré sections are analyzed in detail. It is found that the subharmonic Shapiro steps at certain parameters are separated by structured chaotic windows. By performing a linear regression on the linear part of the data, a fractal dimension of D = 0.868 is obtained, with an uncertainty of ±0.012. The chaotic regions exhibit scaling similarity, and it is shown that the devil's staircase of the system can form a backbone that unifies and explains the highly correlated and structured chaotic behavior.more » These features suggest a system possessing multiple complete devil's staircases. The onset of chaos for subharmonic steps occurs through the Feigenbaum period doubling scenario. Universality in the sequence of periodic windows is also demonstrated. Finally, the influence of the radiation and JJ parameters on the structured chaos is investigated, and it is concluded that the structured chaos is a stable formation over a wide range of parameter values.« less

Statistical crossover characterization of the heterotic localized-extended transition.

PubMed

Ugajin, Ryuichi

2003-07-01

We investigated the spectral statistics of a quantum particle in a superlattice consisting of a disordered layer and a clean layer, possibly accompanied by random magnetic fields. Because a disordered layer has localized states and a clean layer has extended states, our quantum system shows a heterotic phase of an Anderson insulator and a normal metal. As the ratio of the volume of these two layers changes, the spectral statistics change from Poissonian to one of the Gaussian ensembles which characterize quantum chaos. A crossover distribution specified by two parameters is introduced to distinguish the transition from an integrable system to a quantum chaotic system during the heterotic phase from an Anderson transition in which the degree of random potentials is homogenous.

Terrestrial Diapirs as Analogs to Europa's Lenticulae and Chaos, and Implications for Europa Exploration

NASA Astrophysics Data System (ADS)

Pappalardo, R. T.

2007-12-01

Ice diapirism has been cited to explain Europa's pits, spots, and domes (commonly collectively referred to as "lenticulae") as well as the satellite's larger chaos terrains. Europa's diapirs have been modeled as thermal- compositional in origin, rising within an ice shell greater than ~20 km thick. The morphologies and characteristics of terrestrial diapirs shed light on possible diapiric processes within Europa. Diapirs commonly rise in fields of similarly sized subcircular features which can intrude into the shallow subsurface or extrude onto the surface. Rim synclines (peripheral depressions) may form in response to withdrawal of diapiric material from a diapir's surroundings, and peripheral and crestal faults are predicted above intrusive diapirs. The heads of neighboring synchronously active diapirs can flatten against one another. Each of these terrestrial characteristics is consistent with the morphologies of some Europan lenticulae. Terrestrial diapiric heads can merge into a broad canopy, potentially analogous to the formation of some Europan chaos terrains. Xenoliths can be carried upward within terrestrial diapirs, suggesting that diapirism within Europa's ice shell can dredge deep material up toward the surface on the timescale of diapir rise. The deepest strata rise into the central axes of terrestrial diapirs, implying that materials from greatest depth in Europa's ice shell may be exposed in the centers of individual extrusive lenticulae and in discrete locations within chaos regions. Lenticulae and chaos are high priority locations to explore for materials that have risen from near Europa's ice-ocean interface to the surface.

A Tribute to J. C. Sprott

NASA Astrophysics Data System (ADS)

Nazarimehr, Fahimeh; Jafari, Sajad; Chen, Guanrong; Kapitaniak, Tomasz; Kuznetsov, Nikolay V.; Leonov, Gennady A.; Li, Chunbiao; Wei, Zhouchao

2017-12-01

In honor of his 75th birthday, we review the prominent works of Professor Julien Clinton Sprott in chaos and nonlinear dynamics. We categorize his works into three important groups. The first and most important group is identifying new dynamical systems with special properties. He has proposed different chaotic maps, flows, complex variable systems, nonautonomous systems, partial differential equations, fractional-order systems, delay differential systems, spatiotemporal systems, artificial neural networks, and chaotic electrical circuits. He has also studied dynamical properties of complex systems such as bifurcations and basins of attraction. He has done work on generating fractal art. He has examined models of real-world systems that exhibit chaos. The second group of his works comprise control and synchronization of chaos. Finally, the third group is extracting dynamical properties of systems using time-series analysis. This paper highlights the impact of Sprott’s work on the promotion of nonlinear dynamics.

Spin squeezing as an indicator of quantum chaos in the Dicke model.

PubMed

Song, Lijun; Yan, Dong; Ma, Jian; Wang, Xiaoguang

2009-04-01

We study spin squeezing, an intrinsic quantum property, in the Dicke model without the rotating-wave approximation. We show that the spin squeezing can reveal the underlying chaotic and regular structures in phase space given by a Poincaré section, namely, it acts as an indicator of quantum chaos. Spin squeezing vanishes after a very short time for an initial coherent state centered in a chaotic region, whereas it persists over a longer time for the coherent state centered in a regular region of the phase space. We also study the distribution of the mean spin directions when quantum dynamics takes place. Finally, we discuss relations among spin squeezing, bosonic quadrature squeezing, and two-qubit entanglement in the dynamical processes.

Transcending an Urban-Rural Divide: Rural Youth's Resistance to Townization and Schooling, a Case Study of a Middle School in Northwest China

ERIC Educational Resources Information Center

Lou, Jingjing

2011-01-01

Based on an ethnographic study in a rural middle school in Northwest China, the author explores how the transition of the rural countryside, specifically townization, has challenged the urban-rural dichotomy being reproduced in and by formal schooling. Rural students express criticism of the chaos, pollution, and corruption they have experienced…

Reduced Wiener Chaos representation of random fields via basis adaptation and projection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsilifis, Panagiotis, E-mail: tsilifis@usc.edu; Department of Civil Engineering, University of Southern California, Los Angeles, CA 90089; Ghanem, Roger G., E-mail: ghanem@usc.edu

2017-07-15

A new characterization of random fields appearing in physical models is presented that is based on their well-known Homogeneous Chaos expansions. We take advantage of the adaptation capabilities of these expansions where the core idea is to rotate the basis of the underlying Gaussian Hilbert space, in order to achieve reduced functional representations that concentrate the induced probability measure in a lower dimensional subspace. For a smooth family of rotations along the domain of interest, the uncorrelated Gaussian inputs are transformed into a Gaussian process, thus introducing a mesoscale that captures intermediate characteristics of the quantity of interest.

Reduced Wiener Chaos representation of random fields via basis adaptation and projection

NASA Astrophysics Data System (ADS)

Tsilifis, Panagiotis; Ghanem, Roger G.

2017-07-01

A new characterization of random fields appearing in physical models is presented that is based on their well-known Homogeneous Chaos expansions. We take advantage of the adaptation capabilities of these expansions where the core idea is to rotate the basis of the underlying Gaussian Hilbert space, in order to achieve reduced functional representations that concentrate the induced probability measure in a lower dimensional subspace. For a smooth family of rotations along the domain of interest, the uncorrelated Gaussian inputs are transformed into a Gaussian process, thus introducing a mesoscale that captures intermediate characteristics of the quantity of interest.

Single electron dynamics in a Hall thruster electromagnetic field profile

NASA Astrophysics Data System (ADS)

Marini, Samuel; Pakter, Renato

2017-05-01

In this work, the single electron dynamics in a simplified three dimensional Hall thruster model is studied. Using Hamiltonian formalism and the concept of limiting curves, one is able to determine confinement conditions for the electron in the acceleration channel. It is shown that as a given parameter of the electromagnetic field is changed, the particle trajectory may transit from regular to chaotic without affecting the confinement, which allows one to make a detailed analysis of the role played by the chaos. The ionization volume is also computed, which measures the probability of an electron to ionize background gas atoms. It is found that there is a great correlation between chaos and increased effective ionization volume. This indicates that a complex dynamical behavior may improve the device efficiency by augmenting the ionization capability of each electron, requiring an overall lower electron current.

ASTEROIDS: Living in the Kingdom of Chaos

NASA Astrophysics Data System (ADS)

Morbidelli, A.

2000-10-01

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

Stability Analysis of Distributed Order Fractional Chen System

PubMed Central

Aminikhah, H.; Refahi Sheikhani, A.; Rezazadeh, H.

2013-01-01

We first investigate sufficient and necessary conditions of stability of nonlinear distributed order fractional system and then we generalize the integer-order Chen system into the distributed order fractional domain. Based on the asymptotic stability theory of nonlinear distributed order fractional systems, the stability of distributed order fractional Chen system is discussed. In addition, we have found that chaos exists in the double fractional order Chen system. Numerical solutions are used to verify the analytical results. PMID:24489508

Characterizing Strength of Chaotic Dynamics and Numerical Simulation Relevant to Modified Taylor-Couette Flow with Hourglass Geometry

NASA Astrophysics Data System (ADS)

Hou, Yu; Kowalski, Adam; Schroder, Kjell; Halmstad, Andrew; Olsen, Thomas; Wiener, Richard

2006-05-01

We characterize the strength of chaos in two different regimes of Modified Taylor-Couette flow with Hourglass Geometry: the formation of Taylor Vortices with laminar flow and with turbulent flow. We measure the strength of chaos by calculating the correlation dimension and the Kaplan-Yorke dimension based upon the Lyapunov Exponents of each system. We determine the reliability of our calculations by considering data from a chaotic electronic circuit. In order to predict the behavior of the Modified Taylor-Couette flow system, we employ simulations based upon an idealized Reaction-Diffusion model with a third order non-linearity in the reaction rate. Variation of reaction rate with length corresponds to variation of the effective Reynolds Number along the Taylor-Couette apparatus. We present preliminary results and compare to experimental data.

A new feedback image encryption scheme based on perturbation with dynamical compound chaotic sequence cipher generator

NASA Astrophysics Data System (ADS)

Tong, Xiaojun; Cui, Minggen; Wang, Zhu

2009-07-01

The design of the new compound two-dimensional chaotic function is presented by exploiting two one-dimensional chaotic functions which switch randomly, and the design is used as a chaotic sequence generator which is proved by Devaney's definition proof of chaos. The properties of compound chaotic functions are also proved rigorously. In order to improve the robustness against difference cryptanalysis and produce avalanche effect, a new feedback image encryption scheme is proposed using the new compound chaos by selecting one of the two one-dimensional chaotic functions randomly and a new image pixels method of permutation and substitution is designed in detail by array row and column random controlling based on the compound chaos. The results from entropy analysis, difference analysis, statistical analysis, sequence randomness analysis, cipher sensitivity analysis depending on key and plaintext have proven that the compound chaotic sequence cipher can resist cryptanalytic, statistical and brute-force attacks, and especially it accelerates encryption speed, and achieves higher level of security. By the dynamical compound chaos and perturbation technology, the paper solves the problem of computer low precision of one-dimensional chaotic function.

Compressive Sensing with Cross-Validation and Stop-Sampling for Sparse Polynomial Chaos Expansions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huan, Xun; Safta, Cosmin; Sargsyan, Khachik

Compressive sensing is a powerful technique for recovering sparse solutions of underdetermined linear systems, which is often encountered in uncertainty quanti cation analysis of expensive and high-dimensional physical models. We perform numerical investigations employing several com- pressive sensing solvers that target the unconstrained LASSO formulation, with a focus on linear systems that arise in the construction of polynomial chaos expansions. With core solvers of l1 ls, SpaRSA, CGIST, FPC AS, and ADMM, we develop techniques to mitigate over tting through an automated selection of regularization constant based on cross-validation, and a heuristic strategy to guide the stop-sampling decision. Practical recommendationsmore » on parameter settings for these tech- niques are provided and discussed. The overall method is applied to a series of numerical examples of increasing complexity, including large eddy simulations of supersonic turbulent jet-in-cross flow involving a 24-dimensional input. Through empirical phase-transition diagrams and convergence plots, we illustrate sparse recovery performance under structures induced by polynomial chaos, accuracy and computational tradeoffs between polynomial bases of different degrees, and practi- cability of conducting compressive sensing for a realistic, high-dimensional physical application. Across test cases studied in this paper, we find ADMM to have demonstrated empirical advantages through consistent lower errors and faster computational times.« less

Noise induced chaos in optically driven colloidal rings.

NASA Astrophysics Data System (ADS)

Roichman, Yael; Zaslavsky, George; Grier, David G.

2007-03-01

Given a constant flux of energy, many driven dissipative systems rapidly organize themselves into configurations that support steady state motion. Examples include swarming of bacterial colonies, convection in shaken sandpiles, and synchronization in flowing traffic. How simple objects interacting in simple ways self-organize generally is not understood, mainly because so few of the available experimental systems afford the necessary access to their microscopic degrees of freedom. This talk introduces a new class of model driven dissipative systems typified by three colloidal spheres circulating around a ring-like optical trap known as an optical vortex. By controlling the interplay between hydrodynamic interactions and fixed disorder we are able to drive a transition from a previously predicted periodic steady state to fully developed chaos. In addition, by tracking both microscopic trajectories and macroscopic collective fluctuations the relation between the onset of microscopic weak chaos and the evolution of space-time self-similarity in macroscopic transport properties is revealed. In a broader scope, several optical vortices can be coupled to create a large dissipative system where each building block has internal degrees of freedom. In such systems the little understood dynamics of processes like frustration and jamming, fluctuation-dissipation relations and the propagation of collective motion can be tracked microscopically.

Traveling waves and chaos in thermosolutal convection

NASA Technical Reports Server (NTRS)

Deane, A. E.; Toomre, J.; Knobloch, E.

1987-01-01

Numerical experiments on two-dimensional thermosolutal convection reveal oscillations in the form of traveling, standing, modulated, and chaotic waves. Transitions between these wave forms and steady convection are investigated and compared with theory. Such rich nonlinear behavior is possible in fluid layers of wide horizontal extent, and provides an explanation for waves observed in recent laboratory experiments with binary fluid mixtures.

Counterintuitive Constraints on Chaos Formation Set by Heat Flux through Europa's Ocean

NASA Astrophysics Data System (ADS)

Goodman, J. C.

2013-12-01

Models for the formation of disruptive chaos features on the icy surface of Europa fall into two broad categories: either chaos is formed when basal heating causes localized melting and thinning of the ice shell, or basal heating drives diapiric convection within the ice shell. We argue that in both of these cases, heating of the ice shell from below does not lead to chaos formation at the location of heating. If chaos is formed when a localized oceanic heat source, such as a hydrothermal plume, "melts through" the ice crust, we must consider what happens to the melted liquid. If Europa's ocean is salty, the melt will form a buoyant pool inside the melted cavity, leading to a stable interface between cold fresh meltwater and warm salty seawater. This stable interface acts like an ablative heat shield, protecting the ice from further damage. Some heat can be transferred across the stable layer by double diffusion, but this transfer is very inefficient. We calculate that local ocean heating cannot be balanced by local flux through the stable layer: instead, the warm ocean water must spread laterally until it is delivering heat to the ice base on a regional or global scale (a heating zone hundreds or thousands of km across, for conservative parameters.) If chaos is formed by diapiric solid-state convection within the ice shell, many investigators have assumed that diapirism and chaos should be most prevalent where the basal heat flux is strongest. We argue that this is not the case. In Rayleigh-Benard convection, increasing the heat flux will make convection more vigorous --- if and only if the convecting layer thickness does not change. We argue that increased basal heat flux will thin the ice shell, reducing its Rayleigh number and making convection less likely, not more. This insight allows us to reverse the logic of recent discussions of the relationship between ocean circulation and chaos (for instance, Soderlund et al, 2013 LPSC). We argue that global oceanic heat transport is governed by geostrophic quasi-two-dimensional convection, which delivers less heat to the tropics and more to the poles. By the argument above, this implies that the ice layer should be thicker in the tropics, and thus more prone to diapiric convection: thus, chaos should be more common there. Recent mapping efforts by other investigators have shown that this does appear to be the case.

Degenerate operators and the 1/c expansion: Lorentzian resummations, high order computations, and super-Virasoro blocks

DOE PAGES

Chen, Hongbin; Fitzpatrick, A. Liam; Kaplan, Jared; ...

2017-03-30

Here, one can obtain exact information about Virasoro conformal blocks by analytically continuing the correlators of degenerate operators. We argued in recent work that this technique can be used to explicitly resolve information loss problems in AdS 3/CFT 2. In this paper we use the technique to perform calculations in the small 1/c ∝ GN expansion: (1) we prove the all-orders resummation of logarithmic factors ∝1/clog z in the Lorentzian regime, demonstrating that 1/c corrections directly shift Lyapunov exponents associated with chaos, as claimed in prior work, (2) we perform another all-orders resummation in the limit of large c withmore » fixed cz, interpolating between the early onset of chaos and late time behavior, (3) we explicitly compute the Virasoro vacuum block to order 1/c 2 and 1/c 3 with external dimensions fixed, corresponding to 2 and 3 loop calculations in AdS 3, and (4) we derive the heavy-light vacuum blocks in theories with N = 1, 2 superconformal symmetry.« less

Degenerate operators and the 1/c expansion: Lorentzian resummations, high order computations, and super-Virasoro blocks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Hongbin; Fitzpatrick, A. Liam; Kaplan, Jared

Here, one can obtain exact information about Virasoro conformal blocks by analytically continuing the correlators of degenerate operators. We argued in recent work that this technique can be used to explicitly resolve information loss problems in AdS 3/CFT 2. In this paper we use the technique to perform calculations in the small 1/c ∝ GN expansion: (1) we prove the all-orders resummation of logarithmic factors ∝1/clog z in the Lorentzian regime, demonstrating that 1/c corrections directly shift Lyapunov exponents associated with chaos, as claimed in prior work, (2) we perform another all-orders resummation in the limit of large c withmore » fixed cz, interpolating between the early onset of chaos and late time behavior, (3) we explicitly compute the Virasoro vacuum block to order 1/c 2 and 1/c 3 with external dimensions fixed, corresponding to 2 and 3 loop calculations in AdS 3, and (4) we derive the heavy-light vacuum blocks in theories with N = 1, 2 superconformal symmetry.« less

Creating order from chaos: part I: triage, initial care, and tactical considerations in mass casualty and disaster response.

PubMed

Baker, Michael S

2007-03-01

How do we train for the entire spectrum of potential emergency and crisis scenarios? Will we suddenly face large numbers of combat casualties, an earthquake, a plane crash, an industrial explosion, or a terrorist bombing? The daily routine can suddenly be complicated by large numbers of patients, exceeding the ability to treat in a routine fashion. Disaster events can result in patients with penetrating wounds, burns, blast injuries, chemical contamination, or all of these at once. Some events may disrupt infrastructure or result in loss of essential equipment or key personnel. The chaos of a catastrophic event impedes decision-making and effective treatment of patients. Disasters require a paradigm shift from the application of unlimited resources for the greatest good of each individual patient to the allocation of care, with limited resources, for the greatest good for the greatest number of patients. Training and preparation are essential to remain effective during crises and major catastrophic events. Disaster triage and crisis management represent a tactical art that incorporates clinical skills, didactic information, communication ability, leadership, and decision-making. Planning, rehearsing, and exercising various scenarios encourage the flexibility, adaptability, and innovation required in disaster settings. These skills can bring order to the chaos of overwhelming disaster events.

Fine Grained Chaos in AdS2 Gravity

NASA Astrophysics Data System (ADS)

Haehl, Felix M.; Rozali, Moshe

2018-03-01

Quantum chaos can be characterized by an exponential growth of the thermal out-of-time-order four-point function up to a scrambling time u^*. We discuss generalizations of this statement for certain higher-point correlation functions. For concreteness, we study the Schwarzian theory of a one-dimensional time reparametrization mode, which describes two-dimensional anti-de Sitter space (AdS2 ) gravity and the low-energy dynamics of the Sachdev-Ye-Kitaev model. We identify a particular set of 2 k -point functions, characterized as being both "maximally braided" and "k -out of time order," which exhibit exponential growth until progressively longer time scales u^*(k)˜(k -1 )u^*. We suggest an interpretation as scrambling of increasingly fine grained measures of quantum information, which correspondingly take progressively longer time to reach their thermal values.

Fine Grained Chaos in AdS_{2} Gravity.

PubMed

Haehl, Felix M; Rozali, Moshe

2018-03-23

Quantum chaos can be characterized by an exponential growth of the thermal out-of-time-order four-point function up to a scrambling time u[over ^]_{*}. We discuss generalizations of this statement for certain higher-point correlation functions. For concreteness, we study the Schwarzian theory of a one-dimensional time reparametrization mode, which describes two-dimensional anti-de Sitter space (AdS_{2}) gravity and the low-energy dynamics of the Sachdev-Ye-Kitaev model. We identify a particular set of 2k-point functions, characterized as being both "maximally braided" and "k-out of time order," which exhibit exponential growth until progressively longer time scales u[over ^]_{*}^{(k)}∼(k-1)u[over ^]_{*}. We suggest an interpretation as scrambling of increasingly fine grained measures of quantum information, which correspondingly take progressively longer time to reach their thermal values.

Onset of transition from laminar to chaos in MHD mixed convection of a lid-driven trapezoidal cavity filled with Cu-water nanofluid

DOE Office of Scientific and Technical Information (OSTI.GOV)

Azam, Mohammad, E-mail: azam09mebuet@gmail.com; Hasanuzzaman, Md., E-mail: hasanuzzaman138@gmail.com; Saha, Sumon, E-mail: sumonsaha@me.buet.ac.bd

2016-07-12

The present study investigates the thermal mixing scenarios of steady magneto-hydrodynamic (MHD) mixed convection in a two-dimensional lid-driven trapezoidal cavity filled with Cu-water nanofluid. The top wall of the cavity slides with a uniform velocity from left to right direction, while the other walls are fixed. The bottom wall is kept with a constant higher temperature than the top one. The governing mass, momentum and energy equations are expressed in non-dimensional forms and Galerkin finite element method has been employed to solve these equations. Special attention is paid on investigating the onset of transition from laminar to chaos at puremore » mixed convection case. Hence, the computations are carried out for a wide range of Reynolds numbers (Re = 0.1 − 400) and Grashof numbers (Gr = 10{sup −2} − 1.6 × 10{sup 5}) at unity Richardson number and fixed Hartmann number (Ha = 10). The variation of average Nusselt number of the bottom heated wall indicates the influence of governing parameters (Re and Gr) on heat transfer characteristics. The results are presented and explained through the visualisation of isotherms, streamlines and heatlines.« less

Ocean-driven heating of Europa's icy shell at low latitudes

NASA Astrophysics Data System (ADS)

Soderlund, K. M.; Schmidt, B. E.; Wicht, J.; Blankenship, D. D.

2014-01-01

The ice shell of Jupiter's moon Europa is marked by regions of disrupted ice known as chaos terrains that cover up to 40% of the satellite's surface, most commonly occurring within 40° of the equator. Concurrence with salt deposits implies a coupling between the geologically active ice shell and the underlying liquid water ocean at lower latitudes. Europa's ocean dynamics have been assumed to adopt a two-dimensional pattern, which channels the moon's internal heat to higher latitudes. Here we present a numerical model of thermal convection in a thin, rotating spherical shell where small-scale convection instead adopts a three-dimensional structure and is more vigorous at lower latitudes. Global-scale currents are organized into three zonal jets and two equatorial Hadley-like circulation cells. We find that these convective motions transmit Europa's internal heat towards the surface most effectively in equatorial regions, where they can directly influence the thermo-compositional state and structure of the ice shell. We suggest that such heterogeneous heating promotes the formation of chaos features through increased melting of the ice shell and subsequent deposition of marine ice at low latitudes. We conclude that Europa's ocean dynamics can modulate the exchange of heat and materials between the surface and interior and explain the observed distribution of chaos terrains.

Attractors of relaxation discrete-time systems with chaotic dynamics on a fast time scale.

PubMed

Maslennikov, Oleg V; Nekorkin, Vladimir I

2016-07-01

In this work, a new type of relaxation systems is considered. Their prominent feature is that they comprise two distinct epochs, one is slow regular motion and another is fast chaotic motion. Unlike traditionally studied slow-fast systems that have smooth manifolds of slow motions in the phase space and fast trajectories between them, in this new type one observes, apart the same geometric objects, areas of transient chaos. Alternating periods of slow regular motions and fast chaotic ones as well as transitions between them result in a specific chaotic attractor with chaos on a fast time scale. We formulate basic properties of such attractors in the framework of discrete-time systems and consider several examples. Finally, we provide an important application of such systems, the neuronal electrical activity in the form of chaotic spike-burst oscillations.

Chaos Modeling: An Introduction and Research Application.

ERIC Educational Resources Information Center

Newman, Isadore; And Others

1993-01-01

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

78 FR 43972 - Amendments to the Export Administration Regulations: Implementation of Limited Syria Waiver for...

Federal Register 2010, 2011, 2012, 2013, 2014

2013-07-23

... Section 5(b) of the SAA, Executive Order 13338 of May 11, 2004 and the International Emergency Economic... political transition, restore stability, and counter destabilizing influences in the region, and are... support a political transition, restore stability, and counter destabilizing influences in the region, and...

Relaxation Dynamics of Spatiotemporal Chaos in the Nematic Liquid Crystal

NASA Astrophysics Data System (ADS)

Nugroho, Fahrudin; Ueki, Tatsuhiro; Hidaka, Yoshiki; Kai, Shoichi

2011-11-01

We are working on the electroconvection of nematic liquid crystals, in which a kind of spatiotemporal chaos called as a soft-mode turbulence (SMT) is observed. The SMT is caused by the nonlinear interaction between the convective modes and the Nambu--Goldstone (NG) modes. By applying an external magnetic field H, the NG mode is suppressed and an ordered pattern can be observed. By removing the suppression effect the ordered state relax to its original SMT pattern. We revealed two types of instability govern the relaxation process: the zigzag instability and the free rotation of wavevector q(r). This work is partially supported by Grant-in-Aid for Scientific Research (Nos. 20111003, 21340110, and 21540391) from the Ministry of Education, Culture, Sport, Science, and Technology of Japan and the Japan Society for the Promotion of Science (JSPS).

Links between Soil Fungal Diversity and Plant and Soil Properties on the Loess Plateau

PubMed Central

Yang, Yang; Dou, Yanxing; Huang, Yimei; An, Shaoshan

2017-01-01

Previous studies have revealed inconsistent correlations between fungal diversity and plant/soil properties from local to global scales. Here, we investigated the internal relationships between soil fungal diversity and plant/soil properties on the Loess Plateau following vegetation restoration, using Illumina sequencing of the internal transcribed spacer 2 (ITS2) region for fungal identification. We found significant effects of land use types (Af, Artificial forest; Ns, Natural shrub; Ag, Artificial grassland; Ng, Natural grassland; Sc, slope cropland) on soil fungal communities composition, and the dominant phyla were Ascomycota, Basidiomycota, and Zygomycota, which transitioned from Basidiomycota-dominant to Ascomycota-dominant community due to vegetation restoration. The Chao1 richness, Shannon’s diversity and ACE indices were significantly influenced by land use types with the order of Ns > Af > Ng > Ag > Sc, and the total number of OTUs varied widely. In contrast, Good’s coverage and Simpson’s diversity indicated no significant difference among land use types (p > 0.05). Correlation analysis showed that plant and soil properties were closely related to fungal diversity regardless of land use types. In addition, soil organic carbon (SOC) and Hplant (plant richness, Shannon-Wiener index) were strong driving factors that explained fungal diversity. As revealed by the structural equation model (SEM) and generalized additive models (GAMs), fungal diversity was directly and indirectly affected by soil and plant properties, respectively, providing evidence for strong links between soil fungal diversity and plant and soil properties on the Loess Plateau. PMID:29163460

Links between Soil Fungal Diversity and Plant and Soil Properties on the Loess Plateau.

PubMed

Yang, Yang; Dou, Yanxing; Huang, Yimei; An, Shaoshan

2017-01-01

Previous studies have revealed inconsistent correlations between fungal diversity and plant/soil properties from local to global scales. Here, we investigated the internal relationships between soil fungal diversity and plant/soil properties on the Loess Plateau following vegetation restoration, using Illumina sequencing of the internal transcribed spacer 2 (ITS2) region for fungal identification. We found significant effects of land use types (Af, Artificial forest; Ns, Natural shrub; Ag, Artificial grassland; Ng, Natural grassland; Sc, slope cropland) on soil fungal communities composition, and the dominant phyla were Ascomycota, Basidiomycota , and Zygomycota , which transitioned from Basidiomycota -dominant to Ascomycota -dominant community due to vegetation restoration. The Chao1 richness, Shannon's diversity and ACE indices were significantly influenced by land use types with the order of Ns > Af > Ng > Ag > Sc, and the total number of OTUs varied widely. In contrast, Good's coverage and Simpson's diversity indicated no significant difference among land use types ( p > 0.05). Correlation analysis showed that plant and soil properties were closely related to fungal diversity regardless of land use types. In addition, soil organic carbon (SOC) and H plant (plant richness, Shannon-Wiener index) were strong driving factors that explained fungal diversity. As revealed by the structural equation model (SEM) and generalized additive models (GAMs), fungal diversity was directly and indirectly affected by soil and plant properties, respectively, providing evidence for strong links between soil fungal diversity and plant and soil properties on the Loess Plateau.

Optimum inhomogeneity of local lattice distortions in La2CuO4+y

PubMed Central

Poccia, Nicola; Ricci, Alessandro; Campi, Gaetano; Fratini, Michela; Puri, Alessandro; Gioacchino, Daniele Di; Marcelli, Augusto; Reynolds, Michael; Burghammer, Manfred; Saini, Naurang Lal; Aeppli, Gabriel; Bianconi, Antonio

2012-01-01

Electronic functionalities in materials from silicon to transition metal oxides are, to a large extent, controlled by defects and their relative arrangement. Outstanding examples are the oxides of copper, where defect order is correlated with their high superconducting transition temperatures. The oxygen defect order can be highly inhomogeneous, even in optimal superconducting samples, which raises the question of the nature of the sample regions where the order does not exist but which nonetheless form the “glue” binding the ordered regions together. Here we use scanning X-ray microdiffraction (with a beam 300 nm in diameter) to show that for La2CuO4+y, the glue regions contain incommensurate modulated local lattice distortions, whose spatial extent is most pronounced for the best superconducting samples. For an underdoped single crystal with mobile oxygen interstitials in the spacer La2O2+y layers intercalated between the CuO2 layers, the incommensurate modulated local lattice distortions form droplets anticorrelated with the ordered oxygen interstitials, and whose spatial extent is most pronounced for the best superconducting samples. In this simplest of high temperature superconductors, there are therefore not one, but two networks of ordered defects which can be tuned to achieve optimal superconductivity. For a given stoichiometry, the highest transition temperature is obtained when both the ordered oxygen and lattice defects form fractal patterns, as opposed to appearing in isolated spots. We speculate that the relationship between material complexity and superconducting transition temperature Tc is actually underpinned by a fundamental relation between Tc and the distribution of ordered defect networks supported by the materials. PMID:22961255

Chaos and Hyperchaos in Coupled Antiphase Driven Toda Oscillators

NASA Astrophysics Data System (ADS)

Stankevich, Nataliya V.; Dvorak, Anton; Astakhov, Vladimir; Jaros, Patrycja; Kapitaniak, Marcin; Perlikowski, Przemysław; Kapitaniak, Tomasz

2018-01-01

The dynamics of two coupled antiphase driven Toda oscillators is studied. We demonstrate three different routes of transition to chaotic dynamics associated with different bifurcations of periodic and quasi-periodic regimes. As a result of these, two types of chaotic dynamics with one and two positive Lyapunov exponents are observed. We argue that the results obtained are robust as they can exist in a wide range of the system parameters.

Mesa in Aureum Chaos

NASA Technical Reports Server (NTRS)

2004-01-01

2 August 2004 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows a circular mesa and layered materials that are partially-exposed from beneath a thick, dark mantle in the Aureum Chaos region of Mars. The features are part of a much larger circular form (bigger than the image shown here) that marks the location of a crater that was filled with light-toned sedimentary rock, buried, and then later re-exposed when the upper crust of Mars broke apart in this region to form buttes and mesas of 'chaotic terrain.' The circular mesa in this image might also be the location of a formerly filled and buried crater. This image is located near 4.0oS, 26.9oW. It covers an area about 3 km (1.9 mi) across; sunlight illuminates the scene from the left/upper left.

Oscillations and chaos in neural networks: an exactly solvable model.

PubMed Central

Wang, L P; Pichler, E E; Ross, J

1990-01-01

We consider a randomly diluted higher-order network with noise, consisting of McCulloch-Pitts neurons that interact by Hebbian-type connections. For this model, exact dynamical equations are derived and solved for both parallel and random sequential updating algorithms. For parallel dynamics, we find a rich spectrum of different behaviors including static retrieving and oscillatory and chaotic phenomena in different parts of the parameter space. The bifurcation parameters include first- and second-order neuronal interaction coefficients and a rescaled noise level, which represents the combined effects of the random synaptic dilution, interference between stored patterns, and additional background noise. We show that a marked difference in terms of the occurrence of oscillations or chaos exists between neural networks with parallel and random sequential dynamics. Images PMID:2251287

Bivariate- distribution for transition matrix elements in Breit-Wigner to Gaussian domains of interacting particle systems.

PubMed

Kota, V K B; Chavda, N D; Sahu, R

2006-04-01

Interacting many-particle systems with a mean-field one-body part plus a chaos generating random two-body interaction having strength lambda exhibit Poisson to Gaussian orthogonal ensemble and Breit-Wigner (BW) to Gaussian transitions in level fluctuations and strength functions with transition points marked by lambda = lambda c and lambda = lambda F, respectively; lambda F > lambda c. For these systems a theory for the matrix elements of one-body transition operators is available, as valid in the Gaussian domain, with lambda > lambda F, in terms of orbital occupation numbers, level densities, and an integral involving a bivariate Gaussian in the initial and final energies. Here we show that, using a bivariate-t distribution, the theory extends below from the Gaussian regime to the BW regime up to lambda = lambda c. This is well tested in numerical calculations for 6 spinless fermions in 12 single-particle states.

The CHAOS-4 geomagnetic field model

NASA Astrophysics Data System (ADS)

Olsen, Nils; Lühr, Hermann; Finlay, Christopher C.; Sabaka, Terence J.; Michaelis, Ingo; Rauberg, Jan; Tøffner-Clausen, Lars

2014-05-01

We present CHAOS-4, a new version in the CHAOS model series, which aims to describe the Earth's magnetic field with high spatial and temporal resolution. Terms up to spherical degree of at least n = 85 for the lithospheric field, and up to n = 16 for the time-varying core field are robustly determined. More than 14 yr of data from the satellites Ørsted, CHAMP and SAC-C, augmented with magnetic observatory monthly mean values have been used for this model. Maximum spherical harmonic degree of the static (lithospheric) field is n = 100. The core field is expressed by spherical harmonic expansion coefficients up to n = 20; its time-evolution is described by order six splines, with 6-month knot spacing, spanning the time interval 1997.0-2013.5. The third time derivative of the squared radial magnetic field component is regularized at the core-mantle boundary. No spatial regularization is applied to the core field, but the high-degree lithospheric field is regularized for n > 85. CHAOS-4 model is derived by merging two submodels: its low-degree part has been derived using similar model parametrization and data sets as used for previous CHAOS models (but of course including more recent data), while its high-degree lithospheric field part is solely determined from low-altitude CHAMP satellite observations taken during the last 2 yr (2008 September-2010 September) of the mission. We obtain a good agreement with other recent lithospheric field models like MF7 for degrees up to n = 85, confirming that lithospheric field structures down to a horizontal wavelength of 500 km are currently robustly determined.

Topological chaos, braiding and bifurcation of almost-cyclic sets.

PubMed

Grover, Piyush; Ross, Shane D; Stremler, Mark A; Kumar, Pankaj

2012-12-01

In certain two-dimensional time-dependent flows, the braiding of periodic orbits provides a way to analyze chaos in the system through application of the Thurston-Nielsen classification theorem (TNCT). We expand upon earlier work that introduced the application of the TNCT to braiding of almost-cyclic sets, which are individual components of almost-invariant sets [Stremler et al., "Topological chaos and periodic braiding of almost-cyclic sets," Phys. Rev. Lett. 106, 114101 (2011)]. In this context, almost-cyclic sets are periodic regions in the flow with high local residence time that act as stirrers or "ghost rods" around which the surrounding fluid appears to be stretched and folded. In the present work, we discuss the bifurcation of the almost-cyclic sets as a system parameter is varied, which results in a sequence of topologically distinct braids. We show that, for Stokes' flow in a lid-driven cavity, these various braids give good lower bounds on the topological entropy over the respective parameter regimes in which they exist. We make the case that a topological analysis based on spatiotemporal braiding of almost-cyclic sets can be used for analyzing chaos in fluid flows. Hence, we further develop a connection between set-oriented statistical methods and topological methods, which promises to be an important analysis tool in the study of complex systems.

Asymmetric spatiotemporal chaos induced by a polypoid mass in the excised larynx

PubMed Central

Zhang, Yu; Jiang, Jack J.

2008-01-01

In this paper, asymmetric spatiotemporal chaos induced by a polypoid mass simulating the laryngeal pathology of a vocal polyp is experimentally observed using high-speed imaging in an excised larynx. Spatiotemporal analysis reveals that the normal vocal folds show spatiotemporal correlation and symmetry. Normal vocal fold vibrations are dominated mainly by the first vibratory eigenmode. However, pathological vocal folds with a polypoid mass show broken symmetry and spatiotemporal irregularity. The spatial correlation is decreased. The pathological vocal folds spread vibratory energy across a large number of eigenmodes and induce asymmetric spatiotemporal chaos. High-order eigenmodes show complicated dynamics. Spatiotemporal analysis provides a valuable biomedical application for investigating the spatiotemporal chaotic dynamics of pathological vocal fold systems with a polypoid mass and may represent a valuable clinical tool for the detection of laryngeal mass lesion using high-speed imaging. PMID:19123612

Geology and Origin of Europa's Mitten Feature (Murias Chaos)

NASA Technical Reports Server (NTRS)

Figueredo, P. H.; Chuang, F. C.; Rathbun, J.; Kirk, R. L.; Greeley, R.

2002-01-01

The "Mitten" (provisionally named Murias Chaos by the International Astronomical Union) is a region of elevated chaos-like terrain in the leading hemisphere of Europa. Its origin had been explained under the currently debated theories of melting through a thin lithosphere or convection within a thick one. Galileo observations reveal several characteristics that suggest that the Mitten is distinct from typical chaos terrain and point to a different formational process. Photoclinometric elevation estimates suggest that the Mitten is slightly elevated with respect to the surrounding terrain; geologic relations indicate that it must have raised significantly from the plains in its past, resembling disrupted domes on Europa's trailing hemisphere. Moreover, the Mitten material appears to have extruded onto the plains and flowed for tens of kilometers. The area subsequently subsided as a result of isostatic adjustment, viscous relaxation, and/or plains loading. Using plate flexure models, we estimated the elastic lithosphere in the area to be several kilometers thick. We propose that the Mitten originated by the ascent and extrusion of a large thermal diapir. Thermal-mechanical modeling shows that a Mitten-sized plume would remain sufficiently warm and buoyant to pierce through the crust and flow unconfined on the surface. Such a diapir probably had an initial radius between 5 and 8 km and an initial depth of 20-40 km, consistent with a thick-lithosphere model. In this scenario the Mitten appears to represent the surface expression of the rare ascent of a large diapir, in contrast to lenticulae and chaos terrain, which may form by isolated and clustered small diapirs, respectively.

Geology and origin of Europa's "Mitten" feature (Murias Chaos)

USGS Publications Warehouse

Figueredo, P.H.; Chuang, F.C.; Rathbun, J.; Kirk, R.L.; Greeley, R.

2002-01-01

The "Mitten" (provisionally named Murias Chaos by the International Astronomical Union) is a region of elevated chaos-like terrain in the leading hemisphere of Europa. Its origin had been explained under the currently debated theories of melting through a thin lithosphere or convection within a thick one. Galileo observations reveal several characteristics that suggest that the Mitten is distinct from typical chaos terrain and point to a different formational process. Photoclinometric elevation estimates suggest that the Mitten is slightly elevated with respect to the surrounding terrain; geologic relations indicate that it must have raised significantly from the plains in its past, resembling disrupted domes on Europa's trailing hemisphere. Moreover, the Mitten material appears to have extruded onto the plains and flowed for tens of kilometers. The area subsequently subsided as a result of isostatic adjustment, viscous relaxation, and/or plains loading. Using plate flexure models, we estimated the elastic lithosphere in the area to be several kilometers thick. We propose that the Mitten originated by the ascent and extrusion of a large thermal diapir. Thermal-mechanical modeling shows that a Mitten-sized plume would remain sufficiently warm and buoyant to pierce through the crust and flow unconfined on the surface. Such a diapir probably had an initial radius between 5 and 8 km and an initial depth of 20-40 km, consistent with a thick-lithosphere model. In this scenario the Mitten appears to represent the surface expression of the rare ascent of a large diapir, in contrast to lenticulae and chaos terrain, which may form by isolated and clustered small diapirs, respectively.

Tectonics of icy satellites driven by melting and crystallization of water bodies inside their ice shells

NASA Astrophysics Data System (ADS)

Johnston, Stephanie Ann

Enceladus and Europa are icy satellites that currently support bodies of liquid water in the outer solar system Additionally, they show signs of being geologically active. Developing numerical models informed by observations of these icy satellites allows for the development of additional constraints and an improved understanding of the tectonics and evolution of icy satellites. The formation mechanisms for both chaos and ridges on Europa are thought to involve water as albedo changes observed in association with them imply the deposition of salt-rich water near these features. Ridges are the most ubiquitous feature on Europa and are described as central troughs flanked by two raised edifices, range in height from tens to hundreds of meters. Europan ridges can extend hundreds of km continuously along strike but are only about 2 km across. A model of a crystallizing dike--like water intrusion is able to match the overall morphology of ridges, and is consistent the long continuous strike. However, the intrusion of a large volume of water is required to match the most common heights of the ridges. Chaos on Europa is defined as a large area of disrupted ice that contain blocks of pre-existing material separated by a hummocky matrix. A proposed mechanism for the formation of Chaos is that a region of heterogeneous ice within the shell is melted and then recrystallizes. Comparing the model results with the geology of Thera Macula, a region where it has been proposed that Chaos is currently forming, suggests that additional processes may be needed to fully understand the development of Chaos. Water-rich plumes erupt from the south pole of Enceladus, suggesting the presence of a pressurized water reservoir. If a pressurized sea is located beneath the south polar terrain, its geometry and size in the ice shell would contribute to the stress state in the ice shell. The geometry and location of such an ocean, as well as the boundary conditions and thickness of an ice shell have important implications for the faulting and tectonic deformation anticipated at the surface.

Bifurcations and chaos in a parametrically damped two-well Duffing oscillator subjected to symmetric periodic pulses.

PubMed

Chacón, R; Martínez García-Hoz, A

1999-06-01

We study a parametrically damped two-well Duffing oscillator, subjected to a periodic string of symmetric pulses. The order-chaos threshold when altering solely the width of the pulses is investigated theoretically through Melnikov analysis. We show analytically and numerically that most of the results appear independent of the particular wave form of the pulses provided that the transmitted impulse is the same. By using this property, the stability boundaries of the stationary solutions are determined to first approximation by means of an elliptic harmonic balance method. Finally, the bifurcation behavior at the stability boundaries is determined numerically.

DAQ application of PC oscilloscope for chaos fiber-optic fence system based on LabVIEW

NASA Astrophysics Data System (ADS)

Lu, Manman; Fang, Nian; Wang, Lutang; Huang, Zhaoming; Sun, Xiaofei

2011-12-01

In order to obtain simultaneously high sample rate and large buffer in data acquisition (DAQ) for a chaos fiber-optic fence system, we developed a double-channel high-speed DAQ application of a digital oscilloscope of PicoScope 5203 based on LabVIEW. We accomplished it by creating call library function (CLF) nodes to call the DAQ functions in the two dynamic link libraries (DLLs) of PS5000.dll and PS5000wrap.dll provided by Pico Technology Company. The maximum real-time sample rate of the DAQ application can reach 1GS/s. We can control the resolutions of the application at the sample time and data amplitudes by changing their units in the block diagram, and also control the start and end times of the sampling operations. The experimental results show that the application has enough high sample rate and large buffer to meet the demanding DAQ requirements of the chaos fiber-optic fence system.

Astrophysics: Hidden chaos in cosmic order

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gnedin, Nickolay Y.; /Fermilab

'Galaxies, like elephants, have long memories,' says an influential article from the 1980s. Tapping into these memories has revealed some surprising facts about the history of our neighbouring Andromeda galaxy.

Astrophysics: Hidden chaos in cosmic order

NASA Astrophysics Data System (ADS)

Gnedin, Nickolay Y.

2009-09-01

``Galaxies, like elephants, have long memories,'' says an influential article from the 1980s. Tapping into these memories has revealed some surprising facts about the history of our neighbouring Andromeda galaxy.

Chaos Control of Epileptiform Bursting in the Brain

NASA Astrophysics Data System (ADS)

Slutzky, M. W.; Cvitanovic, P.; Mogul, D. J.

Epilepsy, defined as recurrent seizures, is a pathological state of the brain that afflicts over one percent of the world's population. Seizures occur as populations of neurons in the brain become overly synchronized. Although pharmacological agents are the primary treatment for preventing or reducing the incidence of these seizures, over 30% of epilepsy cases are not adequately helped by standard medical therapies. Several groups are exploring the use of electrical stimulation to terminate or prevent epileptic seizures. One experimental model used to test these algorithms is the brain slice where a select region of the brain is cut and kept viable in a well-oxygenated artificial cerebrospinal fluid. Under certain conditions, such slices may be made to spontaneously and repetitively burst, thereby providing an in vitro model of epilepsy. In this chapter, we discuss our efforts at applying chaos analysis and chaos control algorithms for manipulating this seizure-like behavior in a brain slice model. These techniques may provide a nonlinear control pathway for terminating or potentially preventing epileptic seizures in the whole brain.

Chaos control of Hastings-Powell model by combining chaotic motions.

PubMed

Danca, Marius-F; Chattopadhyay, Joydev

2016-04-01

In this paper, we propose a Parameter Switching (PS) algorithm as a new chaos control method for the Hastings-Powell (HP) system. The PS algorithm is a convergent scheme that switches the control parameter within a set of values while the controlled system is numerically integrated. The attractor obtained with the PS algorithm matches the attractor obtained by integrating the system with the parameter replaced by the averaged value of the switched parameter values. The switching rule can be applied periodically or randomly over a set of given values. In this way, every stable cycle of the HP system can be approximated if its underlying parameter value equalizes the average value of the switching values. Moreover, the PS algorithm can be viewed as a generalization of Parrondo's game, which is applied for the first time to the HP system, by showing that losing strategy can win: "losing + losing = winning." If "loosing" is replaced with "chaos" and, "winning" with "order" (as the opposite to "chaos"), then by switching the parameter value in the HP system within two values, which generate chaotic motions, the PS algorithm can approximate a stable cycle so that symbolically one can write "chaos + chaos = regular." Also, by considering a different parameter control, new complex dynamics of the HP model are revealed.

On signals of phase transitions in salmon population dynamics

PubMed Central

Krkošek, Martin; Drake, John M.

2014-01-01

Critical slowing down (CSD) reflects the decline in resilience of equilibria near a bifurcation and may reveal early warning signals (EWS) of ecological phase transitions. We studied CSD in the recruitment dynamics of 120 stocks of three Pacific salmon (Oncorhynchus spp.) species in relation to critical transitions in fishery models. Pink salmon (Oncorhynchus gorbuscha) exhibited increased variability and autocorrelation in populations that had a growth parameter, r, close to zero, consistent with EWS of extinction. However, models and data for sockeye salmon (Oncorhynchus nerka) indicate that portfolio effects from heterogeneity in age-at-maturity may obscure EWS. Chum salmon (Oncorhynchus keta) show intermediate results. The data do not reveal EWS of Ricker-type bifurcations that cause oscillations and chaos at high r. These results not only provide empirical support for CSD in some ecological systems, but also indicate that portfolio effects of age structure may conceal EWS of some critical transitions. PMID:24759855

Natural hazards impact on the technosphere from the point of view of the stability and chaos theory

NASA Astrophysics Data System (ADS)

Kudin, Valery; Petrova, Elena

2013-04-01

Technological disasters occur when the technosphere gets into the transition interval from its stable state to the chaos. Unstable state of the system is one of the possible patterns in scenario of dynamic transition to a chaotic state through a cascade of bifurcations. According to the theory of stability, the chaotic dynamics of the state is caused due to a constant supply of energy into the system from the outside. The role of external source of energy for the man-made technosphere play environmental impacts such as natural hazards or phenomena. A qualitative change in the state of the system depends on the scale and frequency of these natural impacts. Each of the major natural-technological catastrophes is associated with a long chain of triggers and effects in the unfavorable combination of many unlikely accidental circumstances and human factors. According to the classical Gaussian distribution, large deviations are so rare that they can be ignored. However, many accidents and disasters generate statistics with an exponental distribution. In this case, rare events can not be ignored, such cases are often referred to as "heavy-tailed distributions". We should address them differently than the "usual" accidents that fit the description of normal distributions. In the case of "an exponental disaster" we should expect the worst. This is a sphere in which the elements of the stability and chaos theory are of a crucial position. Nowadays scientific research related to the forecast focus on the description and prediction of rare catastrophic events. It should be noted that the asymptotic behavior of such processes before the disaster is so-called blow-up regime, where one or more variables that characterize the system, grow to infinity in a finite time. Thus, in some cases we can reffer to some generic scenarios of disasters. In some model problems, where some value changes in chaotic regime and sometimes makes giant leaps, we can identify precursors that signal danger.

Transition from order to chaos, and density limit, in magnetized plasmas.

PubMed

Carati, A; Zuin, M; Maiocchi, A; Marino, M; Martines, E; Galgani, L

2012-09-01

It is known that a plasma in a magnetic field, conceived microscopically as a system of point charges, can exist in a magnetized state, and thus remain confined, inasmuch as it is in an ordered state of motion, with the charged particles performing gyrational motions transverse to the field. Here, we give an estimate of a threshold, beyond which transverse motions become chaotic, the electrons being unable to perform even one gyration, so that a breakdown should occur, with complete loss of confinement. The estimate is obtained by the methods of perturbation theory, taking as perturbing force acting on each electron that due to the so-called microfield, i.e., the electric field produced by all the other charges. We first obtain a general relation for the threshold, which involves the fluctuations of the microfield. Then, taking for such fluctuations, the formula given by Iglesias, Lebowitz, and MacGowan for the model of a one component plasma with neutralizing background, we obtain a definite formula for the threshold, which corresponds to a density limit increasing as the square of the imposed magnetic field. Such a theoretical density limit is found to fit pretty well the empirical data for collapses of fusion machines.

Average activity of excitatory and inhibitory neural populations

NASA Astrophysics Data System (ADS)

Roulet, Javier; Mindlin, Gabriel B.

2016-09-01

We develop an extension of the Ott-Antonsen method [E. Ott and T. M. Antonsen, Chaos 18(3), 037113 (2008)] that allows obtaining the mean activity (spiking rate) of a population of excitable units. By means of the Ott-Antonsen method, equations for the dynamics of the order parameters of coupled excitatory and inhibitory populations of excitable units are obtained, and their mean activities are computed. Two different excitable systems are studied: Adler units and theta neurons. The resulting bifurcation diagrams are compared with those obtained from studying the phenomenological Wilson-Cowan model in some regions of the parameter space. Compatible behaviors, as well as higher dimensional chaotic solutions, are observed. We study numerical simulations to further validate the equations.

Average activity of excitatory and inhibitory neural populations

PubMed Central

Mindlin, Gabriel B.

2016-01-01

We develop an extension of the Ott-Antonsen method [E. Ott and T. M. Antonsen, Chaos 18(3), 037113 (2008)] that allows obtaining the mean activity (spiking rate) of a population of excitable units. By means of the Ott-Antonsen method, equations for the dynamics of the order parameters of coupled excitatory and inhibitory populations of excitable units are obtained, and their mean activities are computed. Two different excitable systems are studied: Adler units and theta neurons. The resulting bifurcation diagrams are compared with those obtained from studying the phenomenological Wilson-Cowan model in some regions of the parameter space. Compatible behaviors, as well as higher dimensional chaotic solutions, are observed. We study numerical simulations to further validate the equations. PMID:27781447

Dynamics and Collapse in a Power System Model with Voltage Variation: The Damping Effect.

PubMed

Ma, Jinpeng; Sun, Yong; Yuan, Xiaoming; Kurths, Jürgen; Zhan, Meng

2016-01-01

Complex nonlinear phenomena are investigated in a basic power system model of the single-machine-infinite-bus (SMIB) with a synchronous generator modeled by a classical third-order differential equation including both angle dynamics and voltage dynamics, the so-called flux decay equation. In contrast, for the second-order differential equation considering the angle dynamics only, it is the classical swing equation. Similarities and differences of the dynamics generated between the third-order model and the second-order one are studied. We mainly find that, for positive damping, these two models show quite similar behavior, namely, stable fixed point, stable limit cycle, and their coexistence for different parameters. However, for negative damping, the second-order system can only collapse, whereas for the third-order model, more complicated behavior may happen, such as stable fixed point, limit cycle, quasi-periodicity, and chaos. Interesting partial collapse phenomena for angle instability only and not for voltage instability are also found here, including collapse from quasi-periodicity and from chaos etc. These findings not only provide a basic physical picture for power system dynamics in the third-order model incorporating voltage dynamics, but also enable us a deeper understanding of the complex dynamical behavior and even leading to a design of oscillation damping in electric power systems.

Canards in a minimal piecewise-linear square-wave burster

DOE Office of Scientific and Technical Information (OSTI.GOV)

Desroches, M.; Krupa, M.; Fernández-García, S., E-mail: soledad@us.es

We construct a piecewise-linear (PWL) approximation of the Hindmarsh-Rose (HR) neuron model that is minimal, in the sense that the vector field has the least number of linearity zones, in order to reproduce all the dynamics present in the original HR model with classical parameter values. This includes square-wave bursting and also special trajectories called canards, which possess long repelling segments and organise the transitions between stable bursting patterns with n and n + 1 spikes, also referred to as spike-adding canard explosions. We propose a first approximation of the smooth HR model, using a continuous PWL system, and show that itsmore » fast subsystem cannot possess a homoclinic bifurcation, which is necessary to obtain proper square-wave bursting. We then relax the assumption of continuity of the vector field across all zones, and we show that we can obtain a homoclinic bifurcation in the fast subsystem. We use the recently developed canard theory for PWL systems in order to reproduce the spike-adding canard explosion feature of the HR model as studied, e.g., in Desroches et al., Chaos 23(4), 046106 (2013).« less

Magnetic Fluctuations, Precursor Phenomena, and Phase Transition in MnSi under a Magnetic Field

NASA Astrophysics Data System (ADS)

Pappas, C.; Bannenberg, L. J.; Lelièvre-Berna, E.; Qian, F.; Dewhurst, C. D.; Dalgliesh, R. M.; Schlagel, D. L.; Lograsso, T. A.; Falus, P.

2017-07-01

The reference chiral helimagnet MnSi is the first system where Skyrmion lattice correlations have been reported. At a zero magnetic field the transition at TC to the helimagnetic state is of first order. Above TC, in a region dominated by precursor phenomena, neutron scattering shows the buildup of strong chiral fluctuating correlations over the surface of a sphere with radius 2 π /ℓ, where ℓ is the pitch of the helix. It has been suggested that these fluctuating correlations drive the helical transition to first order following a scenario proposed by Brazovskii for liquid crystals. We present a comprehensive neutron scattering study under magnetic fields, which provides evidence that this is not the case. The sharp first order transition persists for magnetic fields up to 0.4 T whereas the fluctuating correlations weaken and start to concentrate along the field direction already above 0.2 T. Our results thus disconnect the first order nature of the transition from the precursor fluctuating correlations. They also show no indication for a tricritical point, where the first order transition crosses over to second order with increasing magnetic field. In this light, the nature of the first order helical transition and the precursor phenomena above TC, both of general relevance to chiral magnetism, remain an open question.

The geologic history of Margaritifer basin, Mars

USGS Publications Warehouse

Salvatore, M. R.; Kraft, M. D.; Edwards, Christopher; Christensen, P.R.

2016-01-01

In this study, we investigate the fluvial, sedimentary, and volcanic history of Margaritifer basin and the Uzboi-Ladon-Morava (ULM) outflow channel system. This network of valleys and basins spans more than 8000 km in length, linking the fluvially dissected southern highlands and Argyre Basin with the northern lowlands via Ares Vallis. Compositionally, thermophysically, and morphologically distinct geologic units are identified and are used to place critical relative stratigraphic constraints on the timing of geologic processes in Margaritifer basin. Our analyses show that fluvial activity was separated in time by significant episodes of geologic activity, including the widespread volcanic resurfacing of Margaritifer basin and the formation of chaos terrain. The most recent fluvial activity within Margaritifer basin appears to terminate at a region of chaos terrain, suggesting possible communication between surface and subsurface water reservoirs. We conclude with a discussion of the implications of these observations on our current knowledge of Martian hydrologic evolution in this important region.

The geologic history of Margaritifer basin, Mars

NASA Astrophysics Data System (ADS)

Salvatore, M. R.; Kraft, M. D.; Edwards, C. S.; Christensen, P. R.

2016-03-01

In this study, we investigate the fluvial, sedimentary, and volcanic history of Margaritifer basin and the Uzboi-Ladon-Morava outflow channel system. This network of valleys and basins spans more than 8000 km in length, linking the fluvially dissected southern highlands and Argyre basin with the northern lowlands via Ares Vallis. Compositionally, thermophysically, and morphologically distinct geologic units are identified and are used to place critical relative stratigraphic constraints on the timing of geologic processes in Margaritifer basin. Our analyses show that fluvial activity was separated in time by significant episodes of geologic activity, including the widespread volcanic resurfacing of Margaritifer basin and the formation of chaos terrain. The most recent fluvial activity within Margaritifer basin appears to terminate at a region of chaos terrain, suggesting possible communication between surface and subsurface water reservoirs. We conclude with a discussion of the implications of these observations on our current knowledge of Martian hydrologic evolution in this important region.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Speetjens, M. F. M.; Demissie, E. A.; Metcalfe, G.

Laminar mixing by the inline-mixing principle is a key to many industrial fluids-engineering systems of size extending from micrometers to meters. However, insight into fundamental transport phenomena particularly under the realistic conditions of three-dimensionality (3D) and fluid inertia remains limited. This study addresses these issues for inline mixers with cylindrical geometries and adopts the Rotated Arc Mixer (RAM) as a representative system. Transport is investigated from a Lagrangian perspective by identifying and examining coherent structures that form in the 3D streamline portrait. 3D effects and fluid inertia introduce three key features that are not found in simplified configurations: transition zonesmore » between consecutive mixing cells of the inline-mixing flow; local upstream flow (in certain parameter regimes); transition/inertia-induced breaking of symmetries in the Lagrangian equations of motion (causing topological changes in coherent structures). Topological considerations strongly suggest that there nonetheless always exists a net throughflow region between inlet and outlet of the inline-mixing flow that is strictly separated from possible internal regions. The Lagrangian dynamics in this region admits representation by a 2D time-periodic Hamiltonian system. This establishes one fundamental kinematic structure for the present class of inline-mixing flows and implies universal behavior in that all states follow from the Hamiltonian breakdown of one common integrable state. A so-called period-doubling bifurcation is the only way to eliminate transport barriers originating from this state and thus is a necessary (yet not sufficient) condition for global chaos. Important in a practical context is that a common simplification in literature, i.e., cell-wise fully-developed Stokes flow (“2.5D approach”), retains these fundamental kinematic properties and deviates from the generic 3D inertial case only in a quantitative sense. This substantiates its suitability for (at least first exploratory) studies on (qualitative) mixing properties.« less

Gravitation waves from QCD and electroweak phase transitions

NASA Astrophysics Data System (ADS)

Chen, Yidian; Huang, Mei; Yan, Qi-Shu

2018-05-01

We investigate the gravitation waves produced from QCD and electroweak phase transitions in the early universe by using a 5-dimension holographic QCD model and a holographic technicolor model. The dynamical holographic QCD model is to describe the pure gluon system, where a first order confinement-deconfinement phase transition can happen at the critical temperature around 250 MeV. The minimal holographic technicolor model is introduced to model the strong dynamics of electroweak, it can give a first order electroweak phase transition at the critical temperature around 100-360 GeV. We find that for both GW signals produced from QCD and EW phase transitions, in the peak frequency region, the dominant contribution comes from the sound waves, while away from the peak frequency region the contribution from the bubble collision is dominant. The peak frequency of gravitation wave determined by the QCD phase transition is located around 10-7 Hz which is within the detectability of FAST and SKA, and the peak frequency of gravitational wave predicted by EW phase transition is located at 0.002 - 0.007 Hz, which might be detectable by BBO, DECIGO, LISA and ELISA.

Spontaneous CP breaking in QCD and the axion potential: an effective Lagrangian approach

NASA Astrophysics Data System (ADS)

Di Vecchia, Paolo; Rossi, Giancarlo; Veneziano, Gabriele; Yankielowicz, Shimon

2017-12-01

Using the well-known low-energy effective Lagrangian of QCD — valid for small (non-vanishing) quark masses and a large number of colors — we study in detail the regions of parameter space where CP is spontaneously broken/unbroken for a vacuum angle θ = π. In the CP broken region there are first order phase transitions as one crosses θ = π, while on the (hyper)surface separating the two regions, there are second order phase transitions signalled by the vanishing of the mass of a pseudo Nambu-Goldstone boson and by a divergent QCD topological susceptibility. The second order point sits at the end of a first order line associated with the CP spontaneous breaking, in the appropriate complex parameter plane. When the effective Lagrangian is extended by the inclusion of an axion these features of QCD imply that standard calculations of the axion potential have to be revised if the QCD parameters fall in the above mentioned CP broken region, in spite of the fact that the axion solves the strong- CP problem. These last results could be of interest for axionic dark matter calculations if the topological susceptibility of pure Yang-Mills theory falls off sufficiently fast when temperature is increased towards the QCD deconfining transition.

Gamma-radiation and isotopic effect on the critical behavior in triglycine selenate crystals

NASA Astrophysics Data System (ADS)

Kassem, M. E.; Hamed, A. E.; Abulnasr, L.; Abboudy, S.

1994-11-01

Isotopic effects in pure and γ-irradiated triglycine selenate crystals were investigated using the specific heat ( Cp) technique. The obtained results showed an interesting dependence of the critical behavior of Cp on the deuterium content. With increasing content of deuterium, the character of the phase transition changed from a second order (γ-type) to a first order transition. After γ-irradiation, the behavior of Cp around the phase transition region was essentially affected. The transition temperature, Tc, decreased and Δ Cp depressed, and the transition became broad. It was noted that the effect of γ-irradiation is opposite to the isotopic effect.

Embedded random matrix ensembles from nuclear structure and their recent applications

NASA Astrophysics Data System (ADS)

Kota, V. K. B.; Chavda, N. D.

Embedded random matrix ensembles generated by random interactions (of low body rank and usually two-body) in the presence of a one-body mean field, introduced in nuclear structure physics, are now established to be indispensable in describing statistical properties of a large number of isolated finite quantum many-particle systems. Lie algebra symmetries of the interactions, as identified from nuclear shell model and the interacting boson model, led to the introduction of a variety of embedded ensembles (EEs). These ensembles with a mean field and chaos generating two-body interaction generate in three different stages, delocalization of wave functions in the Fock space of the mean-field basis states. The last stage corresponds to what one may call thermalization and complex nuclei, as seen from many shell model calculations, lie in this region. Besides briefly describing them, their recent applications to nuclear structure are presented and they are (i) nuclear level densities with interactions; (ii) orbit occupancies; (iii) neutrinoless double beta decay nuclear transition matrix elements as transition strengths. In addition, their applications are also presented briefly that go beyond nuclear structure and they are (i) fidelity, decoherence, entanglement and thermalization in isolated finite quantum systems with interactions; (ii) quantum transport in disordered networks connected by many-body interactions with centrosymmetry; (iii) semicircle to Gaussian transition in eigenvalue densities with k-body random interactions and its relation to the Sachdev-Ye-Kitaev (SYK) model for majorana fermions.

The energy balance of the solar transition region

NASA Technical Reports Server (NTRS)

Jordan, C.

1980-01-01

It is shown how the observed distribution of the emission measure with temperature can be used to limit the range of energy deposition functions suitable for heating the solar transition region and inner corona. The minimum energy loss solution is considered in view of the work by Hearn (1975) in order to establish further scaling laws between the transition region pressure, the maximum coronal temperature and the parameter giving the absolute value of the emission measure. Also discussed is the absence of a static energy balance at the base of the transition region in terms of measurable atmospheric parameters, and the condition for a static energy balance is given. In addition, the possible role of the emission from He II in stabilizing the atmosphere by providing enhanced radiation loss is considered.

"Coherence-incoherence" transition in ensembles of nonlocally coupled chaotic oscillators with nonhyperbolic and hyperbolic attractors

NASA Astrophysics Data System (ADS)

Semenova, Nadezhda I.; Rybalova, Elena V.; Strelkova, Galina I.; Anishchenko, Vadim S.

2017-03-01

We consider in detail similarities and differences of the "coherence-incoherence" transition in ensembles of nonlocally coupled chaotic discrete-time systems with nonhyperbolic and hyperbolic attractors. As basic models we employ the Hénon map and the Lozi map. We show that phase and amplitude chimera states appear in a ring of coupled Hénon maps, while no chimeras are observed in an ensemble of coupled Lozi maps. In the latter, the transition to spatio-temporal chaos occurs via solitary states. We present numerical results for the coupling function which describes the impact of neighboring oscillators on each partial element of an ensemble with nonlocal coupling. Varying the coupling strength we analyze the evolution of the coupling function and discuss in detail its role in the "coherence-incoherence" transition in the ensembles of Hénon and Lozi maps.

Understanding The Interfacial Structure Of Aqueous Phospholipid Monolayer Films Via External Reflection FT-IR Spectroscopy.

NASA Astrophysics Data System (ADS)

Mitchell, Melody L.; Dluhy, Richard A.

1989-12-01

Monolayer films of dimyristoyl-phosphatidic-acid (DMPA) at neutral and basic pH exhibit first-order phase transitions in their pressure-area curves. In situ external reflection FT-IR studies in the CH, stretching bands over this phase transition region exhibit a --6 cm-1 shift similar to that observed in previous studies of dipalmitoyl-phosphotidylcholine (DPPC)1. The acid form of DMPA at pH 3.0 does not exhibit the first order phase transition, but a ~1cm-1 frequency shift is observed in the liquid condensed phase and is also present in the neutral pH form. A solid-solid phase transition is proposed. Examination of the polar headgroup region (1300-960 cm-1)for acidic, neutral, and basic forms of DMPA give characteristic bands of each protonation state of PO3.

Applied Chaos Level Test for Validation of Signal Conditions Underlying Optimal Performance of Voice Classification Methods.

PubMed

Liu, Boquan; Polce, Evan; Sprott, Julien C; Jiang, Jack J

2018-05-17

The purpose of this study is to introduce a chaos level test to evaluate linear and nonlinear voice type classification method performances under varying signal chaos conditions without subjective impression. Voice signals were constructed with differing degrees of noise to model signal chaos. Within each noise power, 100 Monte Carlo experiments were applied to analyze the output of jitter, shimmer, correlation dimension, and spectrum convergence ratio. The computational output of the 4 classifiers was then plotted against signal chaos level to investigate the performance of these acoustic analysis methods under varying degrees of signal chaos. A diffusive behavior detection-based chaos level test was used to investigate the performances of different voice classification methods. Voice signals were constructed by varying the signal-to-noise ratio to establish differing signal chaos conditions. Chaos level increased sigmoidally with increasing noise power. Jitter and shimmer performed optimally when the chaos level was less than or equal to 0.01, whereas correlation dimension was capable of analyzing signals with chaos levels of less than or equal to 0.0179. Spectrum convergence ratio demonstrated proficiency in analyzing voice signals with all chaos levels investigated in this study. The results of this study corroborate the performance relationships observed in previous studies and, therefore, demonstrate the validity of the validation test method. The presented chaos level validation test could be broadly utilized to evaluate acoustic analysis methods and establish the most appropriate methodology for objective voice analysis in clinical practice.

The Centaur--Jupiter Family Comet Link

NASA Astrophysics Data System (ADS)

Bailey, Brenae; Malhotra, R.

2008-09-01

The Centaurs’ orbital evolution is characterized by strong chaos and frequent planetary close encounters. We have investigated the transition between the Centaurs and the Jupiter family comets (JFCs), the latter defined as having Tisserand parameter with respect to Jupiter of 2 < TJ < 3. We find that 80% of the known sample of Centaurs spend part of their dynamical lifetimes as JFCs. The amount of time spent as a JFC is typically on the order of a few hundred thousand years, similar to the dynamical lifetimes of JFCs. We also find that the majority of these objects are "handed off” toward the inner solar system from one giant planet to the next before being ejected. In contrast, the orbital evolution of the Centaurs that spend little or no time as JFCs is either dominated by Saturn or consists largely of hopping among mean motion resonances with Uranus and Neptune. This suggests that the JFCs may originate from a dynamically distinct subset of Centaurs.

Freedom of Speech: Its Exercise and Its Interpretation

ERIC Educational Resources Information Center

Turner, David A.

2010-01-01

Professor Roy Harris (2009) criticises me for ignoring freedom of speech in order to focus on "soft" issues, such as game theory, decision theory and chaos theory. In this response, I accept most of his arguments relating to freedom of speech, but argue that, in order to develop better systems of education, we need to pay more attention to the…

Phase diagram of two-dimensional hard ellipses.

PubMed

Bautista-Carbajal, Gustavo; Odriozola, Gerardo

2014-05-28

We report the phase diagram of two-dimensional hard ellipses as obtained from replica exchange Monte Carlo simulations. The replica exchange is implemented by expanding the isobaric ensemble in pressure. The phase diagram shows four regions: isotropic, nematic, plastic, and solid (letting aside the hexatic phase at the isotropic-plastic two-step transition [E. P. Bernard and W. Krauth, Phys. Rev. Lett. 107, 155704 (2011)]). At low anisotropies, the isotropic fluid turns into a plastic phase which in turn yields a solid for increasing pressure (area fraction). Intermediate anisotropies lead to a single first order transition (isotropic-solid). Finally, large anisotropies yield an isotropic-nematic transition at low pressures and a high-pressure nematic-solid transition. We obtain continuous isotropic-nematic transitions. For the transitions involving quasi-long-range positional ordering, i.e., isotropic-plastic, isotropic-solid, and nematic-solid, we observe bimodal probability density functions. This supports first order transition scenarios.

Chaos, Complexity and Deterrence

DTIC Science & Technology

2000-04-19

populations of adversary countries but which seldom affect their leadership . Conclusion The jury is still out on the applicability of chaos theory to...Advent of Chaos Chaos theory in the West (considerable work on chaos was also conducted in the Soviet Union) developed from the 1960s work of...predicted by his model over time.1 This discovery, sensitivity to initial conditions, is one of the fundamental characteristics of chaos theory . Lorenz

Topical Meeting on Optical Bistability Held at Rochester, New York on 15-17 June 1983.

DTIC Science & Technology

1983-01-01

distortion of their initial directions of polarization : both of the beams are linearly polarized , with their electric vectors either (i)parallel to...New Zealand. ChSAM aIB ct Multistability, self-oscillation, and chaos in a model for polarization I Chas mnd Optlcal Bltabillty: Blfuraton...second circularly polarized pumping beam has been observed, transition sequence arises that is consistent with recent observ- Sense of response

Particle transport in a wave spectrum with a thermal distribution of Larmor radii

NASA Astrophysics Data System (ADS)

Martinell, Julio; Kryukov, Nikolay; Del Castillo-Negrete, Diego

2017-10-01

Test particle E × B transport is studied due to an infinite spectrum of drift waves in two dimensions using a Hamiltonian approach, which can be reduced to a 2D mapping. Finite Larmor radius (FLR) effects are included taking a gyroaverage. When the wave amplitude is increased there is a gradual transition to chaos but the chaos level is reduced when FLR grows, implying that fast particles are better confined. The fraction of confined particles is found to be reduced as the wave amplitude rises. The statistical properties of transport are studied finding that, in the absence of a background flow, it is diffusive with a Gaussian PDF, when all particles have the same FLR. In contrast, for a thermal FLR distribution, the PDF is non-Gaussian but the transport remains diffusive. A theoretical explanation of this is given showing that a superposition of Gaussians produces a PDF with long tails. When a background flow is introduced that varies monotonically with radius, the transport becomes strongly super-diffusive due to the appearance of long Levy flights which dominate the particles. The PDF develops long tails as the flow strength is increased. The particle variance scales as σ t3 for chaotic regime but reduces to ballistic ( t2) for low chaos. Work funded by PAPIIT-UNAM project IN109115.

Attractors of relaxation discrete-time systems with chaotic dynamics on a fast time scale

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maslennikov, Oleg V.; Nekorkin, Vladimir I.

In this work, a new type of relaxation systems is considered. Their prominent feature is that they comprise two distinct epochs, one is slow regular motion and another is fast chaotic motion. Unlike traditionally studied slow-fast systems that have smooth manifolds of slow motions in the phase space and fast trajectories between them, in this new type one observes, apart the same geometric objects, areas of transient chaos. Alternating periods of slow regular motions and fast chaotic ones as well as transitions between them result in a specific chaotic attractor with chaos on a fast time scale. We formulate basicmore » properties of such attractors in the framework of discrete-time systems and consider several examples. Finally, we provide an important application of such systems, the neuronal electrical activity in the form of chaotic spike-burst oscillations.« less

Line tension controls liquid-disordered + liquid-ordered domain size transition in lipid bilayers

DOE PAGES

Usery, Rebecca D.; Enoki, Thais A.; Wickramasinghe, Sanjula P.; ...

2017-04-11

To better understand animal cell plasma membranes, we studied simplified models, namely four-component lipid bilayer mixtures. Here we describe the domain size transition in the region of coexisting liquid-disordered (Ld) + liquid-ordered (Lo) phases. This transition occurs abruptly in composition space with domains increasing in size by two orders of magnitude, from tens of nanometers to microns. We measured the line tension between coexisting Ld and Lo domains close to the domain size transition for a variety of lipid mixtures, finding that in every case the transition occurs at a line tension of ~0.3 pN. A computational model incorporating linemore » tension and dipole repulsion indicated that even small changes in line tension can result in domains growing in size by several orders of magnitude, consistent with experimental observations. Lastly, we find that other properties of the coexisting Ld and Lo phases do not change significantly in the vicinity of the abrupt domain size transition.« less

Line tension controls liquid-disordered + liquid-ordered domain size transition in lipid bilayers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Usery, Rebecca D.; Enoki, Thais A.; Wickramasinghe, Sanjula P.

To better understand animal cell plasma membranes, we studied simplified models, namely four-component lipid bilayer mixtures. Here we describe the domain size transition in the region of coexisting liquid-disordered (Ld) + liquid-ordered (Lo) phases. This transition occurs abruptly in composition space with domains increasing in size by two orders of magnitude, from tens of nanometers to microns. We measured the line tension between coexisting Ld and Lo domains close to the domain size transition for a variety of lipid mixtures, finding that in every case the transition occurs at a line tension of ~0.3 pN. A computational model incorporating linemore » tension and dipole repulsion indicated that even small changes in line tension can result in domains growing in size by several orders of magnitude, consistent with experimental observations. Lastly, we find that other properties of the coexisting Ld and Lo phases do not change significantly in the vicinity of the abrupt domain size transition.« less

Orientational order in bipolar nematic microdroplets close to the phase transition

NASA Astrophysics Data System (ADS)

Vilfan, I.; Vilfan, M.; Žumer, S.

1989-10-01

The ordering in bipolar liquid-crystal droplets close to the nematic-paranematic phase translation is studied. Here, ``paranematic'' refers to the phase above the nematic-isotropic transition temperature. The structure of spherical droplets is obtained after the minimization of the Landau-de Gennes-type free energy assuming a constant value of the surface order parameter and strong anchoring of the molecules parallel to the surface. Disordered defect regions caused by elastic deformations are found close to the poles. The defect regions grow into the droplet as the coexistence temperature between the paranematic and nematic phases is approached from below. The temperature-radius phase diagram shows the first-order coexistence curve terminating in the critical point and a pronounced decrease of the coexistence temperature on approaching the critical radius.

U-Pb zircon and CHIME monazite dating of granitoids and high-grade metamorphic rocks from the Eastern and Peninsular Thailand - A new report of Early Paleozoic granite

NASA Astrophysics Data System (ADS)

Kawakami, T.; Nakano, N.; Higashino, F.; Hokada, T.; Osanai, Y.; Yuhara, M.; Charusiri, P.; Kamikubo, H.; Yonemura, K.; Hirata, T.

2014-07-01

In order to understand the age and tectonic framework of Eastern to Peninsular Thailand from the viewpoint of basement (metamorphic and plutonic) geology, the LA-ICP-MS U-Pb zircon dating and the chemical Th-U-total Pb isochron method (CHIME) monazite dating were performed in the Khao Chao, Hub-Kapong to Pran Buri, and Khanom areas in Eastern to Peninsular Thailand. The LA-ICP-MS U-Pb zircon dating of the garnet-hornblende gneiss from the Khao Chao area gave 229 ± 3 Ma representing the crystallization age of the gabbro, and that of the garnet-biotite gneisses gave 193 ± 4 Ma representing the timing of an upper amphibolite facies metamorphism. The CHIME monazite dating of pelitic gneiss from the Khao Chao gneiss gave scattered result of 68 ± 22 Ma, due to low PbO content and rejuvenation of older monazite grains during another metamorphism in the Late Cretaceous to Tertiary time. The U-Pb ages of zircon from the Hua Hin gneissic granite in the Hub-Kapong to Pran Buri area scatter from 250 Ma to 170 Ma on the concordia. Granite crystallization was at 219 ± 2 Ma, followed by the sillimanite-grade regional metamorphism at 185 ± 2 Ma. Monazite in the pelitic gneiss from this area also preserves Early to Middle Jurassic metamorphism and rejuvenation by later contact metamorphism by non-foliated granite or by another fluid infiltration event in the Late Cretaceous to Tertiary time. The Khao Dat Fa granite from the Khanom area of Peninsular Thailand gave a U-Pb zircon age of 477 ± 7 Ma. This is the second oldest granite pluton ever reported from Thailand, and is a clear evidence for the Sibumasu block having a crystalline basement that was formed during the Pan-African Orogeny. The Khao Pret granite gives U-Pb zircon concordia age of 67.5 ± 1.3 Ma, which represents the timing of zircon crystallization from the granitic melt and accompanied sillimanite-grade contact metamorphism against surrounding metapelites and gneisses. Metamorphic rocks in the Doi Inthanon area also share the similar plutono-metamorphic history with the Khanom and the Hub-Kapong to Pran Buri areas. This suggests that these three areas belong to the Sibumasu block, and the Sibumasu block records similar plutono-metamorphic history from Northern to Peninsular Thailand. Relative abundance of oceanic components in the Khao Chao gneiss, their Late Triassic magmatic ages, and the Early Jurassic metamorphic ages prefer the interpretation that the Khao Chao gneiss belongs to the Sukhothai Arc.

In Search of Determinism-Sensitive Region to Avoid Artefacts in Recurrence Plots

NASA Astrophysics Data System (ADS)

Wendi, Dadiyorto; Marwan, Norbert; Merz, Bruno

As an effort to reduce parameter uncertainties in constructing recurrence plots, and in particular to avoid potential artefacts, this paper presents a technique to derive artefact-safe region of parameter sets. This technique exploits both deterministic (incl. chaos) and stochastic signal characteristics of recurrence quantification (i.e. diagonal structures). It is useful when the evaluated signal is known to be deterministic. This study focuses on the recurrence plot generated from the reconstructed phase space in order to represent many real application scenarios when not all variables to describe a system are available (data scarcity). The technique involves random shuffling of the original signal to destroy its original deterministic characteristics. Its purpose is to evaluate whether the determinism values of the original and the shuffled signal remain closely together, and therefore suggesting that the recurrence plot might comprise artefacts. The use of such determinism-sensitive region shall be accompanied by standard embedding optimization approaches, e.g. using indices like false nearest neighbor and mutual information, to result in a more reliable recurrence plot parameterization.

Chaotic dynamics in nanoscale NbO2 Mott memristors for analogue computing

NASA Astrophysics Data System (ADS)

Kumar, Suhas; Strachan, John Paul; Williams, R. Stanley

2017-08-01

At present, machine learning systems use simplified neuron models that lack the rich nonlinear phenomena observed in biological systems, which display spatio-temporal cooperative dynamics. There is evidence that neurons operate in a regime called the edge of chaos that may be central to complexity, learning efficiency, adaptability and analogue (non-Boolean) computation in brains. Neural networks have exhibited enhanced computational complexity when operated at the edge of chaos, and networks of chaotic elements have been proposed for solving combinatorial or global optimization problems. Thus, a source of controllable chaotic behaviour that can be incorporated into a neural-inspired circuit may be an essential component of future computational systems. Such chaotic elements have been simulated using elaborate transistor circuits that simulate known equations of chaos, but an experimental realization of chaotic dynamics from a single scalable electronic device has been lacking. Here we describe niobium dioxide (NbO2) Mott memristors each less than 100 nanometres across that exhibit both a nonlinear-transport-driven current-controlled negative differential resistance and a Mott-transition-driven temperature-controlled negative differential resistance. Mott materials have a temperature-dependent metal-insulator transition that acts as an electronic switch, which introduces a history-dependent resistance into the device. We incorporate these memristors into a relaxation oscillator and observe a tunable range of periodic and chaotic self-oscillations. We show that the nonlinear current transport coupled with thermal fluctuations at the nanoscale generates chaotic oscillations. Such memristors could be useful in certain types of neural-inspired computation by introducing a pseudo-random signal that prevents global synchronization and could also assist in finding a global minimum during a constrained search. We specifically demonstrate that incorporating such memristors into the hardware of a Hopfield computing network can greatly improve the efficiency and accuracy of converging to a solution for computationally difficult problems.

Competitive Modes for the Detection of Chaotic Parameter Regimes in the General Chaotic Bilinear System of Lorenz Type

NASA Astrophysics Data System (ADS)

Mallory, Kristina; van Gorder, Robert A.

We study chaotic behavior of solutions to the bilinear system of Lorenz type developed by Celikovsky and Vanecek [1994] through an application of competitive modes. This bilinear system of Lorenz type is one possible canonical form holding the Lorenz equation as a special case. Using a competitive modes analysis, which is a completely analytical method allowing one to identify parameter regimes for which chaos may occur, we are able to demonstrate a number of parameter regimes which admit a variety of distinct chaotic behaviors. Indeed, we are able to draw some interesting conclusions which relate the behavior of the mode frequencies arising from writing the state variables for the Celikovsky-Vanecek model as coupled oscillators, and the types of emergent chaotic behaviors observed. The competitive modes analysis is particularly useful if all but one of the model parameters are fixed, and the remaining free parameter is used to modify the chaos observed, in a manner analogous to a bifurcation parameter. Through a thorough application of the method, we are able to identify several parameter regimes which give new dynamics (such as specific forms of chaos) which were not observed or studied previously in the Celikovsky-Vanecek model. Therefore, the results demonstrate the advantage of the competitive modes approach for detecting new parameter regimes leading to chaos in third-order dynamical systems.

The nameless father in the poetry and life of Francis Webb.

PubMed

Powell, C

1998-08-01

A brief biographical review of the poet Francis Webb was carried out, with reference to his mental illness and recurring themes in his poetry. Material is drawn from a recent biography and the author's personal encounters with the poet. Reference is also made to Lacan's theory of psychosis and Winnicott's construct of the 'transitional object'. The poetry may be seen in part as a transitional object whereby the poet sought to repair deficits in the structure of the self and contain psychotic chaos. The poems have a beauty and power beyond any psychoanalytic theorising, but may also be read as a vital striving toward self-healing on the part of the poet.

Emplacement of Widespread Fe/Mg Phyllosilicate Layer in West Margaritifer Terra, Mars

NASA Astrophysics Data System (ADS)

Seelos, K. D.; Maxwell, R. E.; Seelos, F. P.; Buczkowski, D.; Viviano-Beck, C. E.

2017-12-01

West Margaritifer Terra is located at the eastern end of Valles Marineris at the complex intersection of chaos terrains, cratered highlands, and multiple generations of outflow channels. Adjacent regions host layered phyllosilicates thought to indicate early Mars pedogenic and/or ground water-based alteration (e.g., Le Deit et al., 2012), and indeed, hydrologic modeling supports prolonged aqueous activity in the Noachian and Hesperian eras (Andrews-Hanna and Lewis, 2011). The remnant high-standing plateaus in West Margaritifer (0-15°S, 325-345°E) host numerous phyllosilicate-bearing outcrops as well and are the focus of this study. Here, we performed a systematic mapping and characterization of mineralogy and morphology of these deposits in order to assess similarity to other layered phyllosilicates and evaluate potential formation mechanisms. Utilizing multiple remote sensing datasets, we identified three types of phyllosilicate exposures distributed throughout the region: 1) along upper chaos fracture walls, 2) in erosional windows on the plains, and 3) in crater walls and ejecta. Outcrops are spectrally indicative of Fe/Mg smectite (most similar to saponite) and only rare, isolated occurrences of Al-phyllosilicate were observed. Morphologically, the layer is a few to 10 m thick, light-toned, polygonally fractured at decameter scales, and vertical subparallel banding is evident in places. These characteristics were used along with spatial distribution, elevation, and geologic context to evaluate 4 potential formation mechanisms: fluvio-lacustrine, pedogenesis, diagenesis, and hydrothermal alteration. We find that the widespread distribution and spectral homogeneity of the layer favors formation via groundwater alteration and/or pedogenic weathering. This is consistent with interpretations of similar layered phyllosilicates in NW Noachis Terra and the Valles Marineris plains to the west, and significantly extends the area over which these aqueous processes operated in Noachian times.

Historical transition of eco-structure in a tidal flat caused by expansion of sewerage treatment area.

PubMed

Tatsumoto, Hideki; Ishii, Yuichi; Machida, Motoi; Taki, Kazuo

2004-05-11

An artificial tidal flat was prepared for the mitigation tool on coastal environment. However, it is considered that most of the flat was not restored to the sufficient amenities for aquatic living things, migratory birds, etc. because none of the ecological mechanisms were understood or planned for. It is therefore investigated in this paper that historical transition factors in ecosystem structure are selected and traced with the diffusion of a public sewerage system, and with environmental factors such as water quality, sediment condition, and aquatic producers in the Yatsu Tidal Flat. As a result, it can be defined that the tidal flat, just like a lagoon, was formed artificially with reclamation and development of its circumference at the first step of transition; the water quality and sediment condition gradually became brackish water and muddy sediment conditions, interactively. The ecosystem pyramid forming orderly layers according to trophic level appeared as a high-bio-production potential in its tidal flat. In the second step, i.e., in recent years, the characteristics of water quality and sediment conditions evolved into a foreshore tidal flat, namely, conditions in the flat observed were that the progression of water included a high concentration of chloride ion as seawater and sediment conditions became sandy. Because of that, the inflowing fresh water and organic mater from the land area decreased with the improvement of the public sewerage system. The ecosystem pyramid was distorted into a chaos pyramid, with inversion of Ulva spp.

Ordering Chaos: Eva Miller--Multnomah County Library, Portland, OR

ERIC Educational Resources Information Center

Library Journal, 2004

2004-01-01

Eva Miller has a knack for creating order out of disorder. She single-handedly brought Oregon's virtual reference service, Answerland, live in just under 90 days, says Rivkah Sass, now director of the Omaha Public Library. Miller created its web site, designed the graphics, developed marketing materials, and recruited and trained librarians--all…

Modelling Mass Movements for Planetary Studies

NASA Technical Reports Server (NTRS)

Bulmer, M. H.; Glaze, L.; Barnouin-Jha, O.; Murphy, W.; Neumann, G.

2002-01-01

Use of an empirical model in conjunction with data from the Chaos Jumbles rock avalanches constrain to first order their flow behavior, and provide a method to interpret rock/debris avalanche emplacement on Mars. Additional information is contained in the original extended abstract.

On dynamics of integrate-and-fire neural networks with conductance based synapses.

PubMed

Cessac, Bruno; Viéville, Thierry

2008-01-01

We present a mathematical analysis of networks with integrate-and-fire (IF) neurons with conductance based synapses. Taking into account the realistic fact that the spike time is only known within some finite precision, we propose a model where spikes are effective at times multiple of a characteristic time scale delta, where delta can be arbitrary small (in particular, well beyond the numerical precision). We make a complete mathematical characterization of the model-dynamics and obtain the following results. The asymptotic dynamics is composed by finitely many stable periodic orbits, whose number and period can be arbitrary large and can diverge in a region of the synaptic weights space, traditionally called the "edge of chaos", a notion mathematically well defined in the present paper. Furthermore, except at the edge of chaos, there is a one-to-one correspondence between the membrane potential trajectories and the raster plot. This shows that the neural code is entirely "in the spikes" in this case. As a key tool, we introduce an order parameter, easy to compute numerically, and closely related to a natural notion of entropy, providing a relevant characterization of the computational capabilities of the network. This allows us to compare the computational capabilities of leaky and IF models and conductance based models. The present study considers networks with constant input, and without time-dependent plasticity, but the framework has been designed for both extensions.

Bounding the space of holographic CFTs with chaos

DOE PAGES

Perlmutter, Eric

2016-10-13

In this study, thermal states of quantum systems with many degrees of freedom are subject to a bound on the rate of onset of chaos, including a bound on the Lyapunov exponent, λ L ≤ 2π/β. We harness this bound to constrain the space of putative holographic CFTs and their would-be dual theories of AdS gravity. First, by studying out-of-time-order four-point functions, we discuss how λ L = 2π/β in ordinary two-dimensional holographic CFTs is related to properties of the OPE at strong coupling. We then rule out the existence of unitary, sparse two-dimensional CFTs with large central charge andmore » a set of higher spin currents of bounded spin; this implies the inconsistency of weakly coupled AdS 3 higher spin gravities without infinite towers of gauge fields, such as the SL(N) theories. This fits naturally with the structure of higher-dimensional gravity, where finite towers of higher spin fields lead to acausality. On the other hand, unitary CFTs with classical W ∞[λ] symmetry, dual to 3D Vasiliev or hs[λ] higher spin gravities, do not violate the chaos bound, instead exhibiting no chaos: λ L = 0. Independently, we show that such theories violate unitarity for |λ| > 2. These results encourage a tensionless string theory interpretation of the 3D Vasiliev theory.« less

Frequency-locked chaotic opto-RF oscillator.

PubMed

Thorette, Aurélien; Romanelli, Marco; Brunel, Marc; Vallet, Marc

2016-06-15

A driven opto-RF oscillator, consisting of a dual-frequency laser (DFL) submitted to frequency-shifted feedback, is experimentally and numerically studied in a chaotic regime. Precise control of the reinjection strength and detuning permits isolation of a parameter region of bounded-phase chaos, where the opto-RF oscillator is frequency-locked to the master oscillator, in spite of chaotic phase and intensity oscillations. Robust experimental evidence of this synchronization regime is found, and phase noise spectra allow us to compare phase-locking and bounded-phase chaos regimes. In particular, it is found that the long-term phase stability of the master oscillator is well transferred to the opto-RF oscillator, even in the chaotic regime.

AMD-stability in the presence of first-order mean motion resonances

NASA Astrophysics Data System (ADS)

Petit, A. C.; Laskar, J.; Boué, G.

2017-11-01

The angular momentum deficit (AMD)-stability criterion allows to discriminate between a priori stable planetary systems and systems for which the stability is not granted and needs further investigations. AMD-stability is based on the conservation of the AMD in the averaged system at all orders of averaging. While the AMD criterion is rigorous, the conservation of the AMD is only granted in absence of mean-motion resonances (MMR). Here we extend the AMD-stability criterion to take into account mean-motion resonances, and more specifically the overlap of first-order MMR. If the MMR islands overlap, the system will experience generalized chaos leading to instability. The Hamiltonian of two massive planets on coplanar quasi-circular orbits can be reduced to an integrable one degree of freedom problem for period ratios close to a first-order MMR. We use the reduced Hamiltonian to derive a new overlap criterion for first-order MMR. This stability criterion unifies the previous criteria proposed in the literature and admits the criteria obtained for initially circular and eccentric orbits as limit cases. We then improve the definition of AMD-stability to take into account the short term chaos generated by MMR overlap. We analyze the outcome of this improved definition of AMD-stability on selected multi-planet systems from the Extrasolar Planets Encyclopædia.

Pretransitional diffuse neutron scattering in the mixed perovskite relaxor K1-xLixTaO3

NASA Astrophysics Data System (ADS)

Yong, Grace; Toulouse, Jean; Erwin, Ross; Shapiro, Stephen M.; Hennion, Bernard

2000-12-01

Several previous studies of K1-xLixTaO3 (KLT) have revealed the presence, above the structural transition, of polar nanoregions. Recently, these have been shown to play an essential role in the relaxor behavior of KLT. In order to characterize these regions, we have performed a neutron-scattering study of KLT crystals with different lithium concentrations, both above and below the critical concentration. This study reveals the existence of diffuse scattering that appears upon formation of these regions. The rodlike distribution of the diffuse scattering along cubic directions indicates that the regions form in the shape of discs in the various cubic planes. From the width of the diffuse scattering we extract values for a correlation length or size of the regions as a function of temperature. Finally, on the basis of the reciprocal lattice points around which the diffuse scattering is most intense, we conclude that the regions have tetragonal symmetry. The large increase in Bragg intensities at the first-order transition suggests that the polar regions freeze to form large structural domains and the transition is triggered by the percolation of strain fields through the crystals.

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

NASA Astrophysics Data System (ADS)

Lundqvist, Stig

1985-01-01

The physics of non-linear phenomena has developed in a remarkable way over the last couple of decades and has accelerated over the last few years, in particular because of the recent progress in the study of chaotic behaviour. In particular the discovery of the universal properties of the transition into chaos for certain classes of systems has stimulated much recent work in different directions both theoretically and experimentally. Chaos theory has become a real challenge to physicists in many different fields and also in many other disciplines such as astronomy, chemistry, medicine, meteorology and economics and social theory. The study of chaos-related phenomena has a truly interdisciplinary character and makes use of important concepts and methods from other disciplines. For the description of chaotic structures one needs a new, recently developed geometry called fractal geometry. For the discussion of the enormous richness of ordered structures which appear, one uses the theory of pattern recognition. In order to study even the simplest theoretical models describing chaos, a computer is essential. It should finally be mentioned that important aspects of computer science are related to the theory of order and chaos. A Nobel Symposium provides an excellent opportunity to bring together a group of prominent scientists for a stimulating exchange of new ideas and results. The Nobel Symposia are very small meetings by invitation only and the number of key participants is typically in the range 20-40. These symposia are organized through a special Nobel Symposium Committee after proposals from individuals. This symposium was sponsored by the Nobel Foundation through its Nobel Symposium Fund with grants from The Tercentenary Fund of the Bank of Sweden and The Knut Alice Wallenberg Foundation. Additional support was obtained from the Royal Academy of Sciences, The Nordic Institute for Theoretical Atomic Physics (NORDITA), Chalmers University of Technology and Gothenburg University. The idea to arrange a Nobel symposium on the physics of chaos and related problems came up more than three years ago. The rapid progress in the field since then seemed a bit frightening, to say the least, in view of the small format of the meeting. Nevertheless, we found the idea attractive - provided that we could restrict the programme to a few selected topics of current interest in order to generate a strong interaction between the participants and produce an intensive discussion. I feel that I need to express my apologies to all prominent scientists who could not be invited as a result of our planning. In the first place we did not attempt to review areas which seemed to be well established and have reached a certain level of maturity or saturation, irrespective of how great the individual contributions might have been. We decided firmly to concentrate on just a few of the recent developments which seemed to be in the focus of interest, deliberately leaving out important areas equally exciting. These proceedings contain practically all the material presented in the papers given at the Symposium. We felt that some participants might have found it inconvenient to prepare a full-length paper, which in some cases would have been merely modified versions of material due to appear in regular journals. We therefore took a liberal attitude and accepted everything from a brief abstract with some key references, up to a full-length paper. We would like to place on record our sincere thanks to all the participants who have contributed substantially in the planning of the Symposium by making valuable comments and suggestions about participants and topics. In particular, Jerry Gollub and Pierre Hohenberg helped me in organizing the programme and they also did a beautiful job with the concluding session and the conference summary. My co-organizers played a crucial role in the planning and during the Symposium week and always seemed to show an outstanding patience with my often rather chaotic actions. Our secretary, Yvonne Steen, deserves very special thanks for her outstanding work for the symposium on top of all her regular duties. I would finally like to say something about Gräftåvallen and our hosts, Annica and Tommy Hagström. We decided to take this symposium out of the cities and away from the academic environment and found this charming tiny mountain resort on a mountain slope in the northern Swedish mountains about 20 miles from the nearest village. Annica and Tommy Hagström welcomed us with such a warm hospitality and offered us throughout the week the best of the local mountain specialities such as reindeer, bear and beaver and a variety of mountain fishes. Also the local community greeted us as some very special guests and arranged an afternoon programme at a nearby shieling with goats, sheep, dairy maids, folk music and folk dancing. They also arranged a wonderful concert in their beautiful church from the 12th century. Altogether it was a very special week also outside the lecture room. We, the organizers, experienced this symposium as an unforgettable scientific event thanks to the outstanding contributions of our participants. We hope that these proceedings will convey to the reader something of the excitement felt by the participants during the symposium week.

Three-dimensional instabilities of natural convection between two differentially heated vertical plates: Linear and nonlinear complementary approaches

NASA Astrophysics Data System (ADS)

Gao, Zhenlan; Podvin, Berengere; Sergent, Anne; Xin, Shihe; Chergui, Jalel

2018-05-01

The transition to the chaos of the air flow between two vertical plates maintained at different temperatures is studied in the Boussinesq approximation. After the first bifurcation at critical Rayleigh number Rac, the flow consists of two-dimensional (2D) corotating rolls. The stability of the 2D rolls is examined, confronting linear predictions with nonlinear integration. In all cases the 2D rolls are destabilized in the spanwise direction. Efficient linear stability analysis based on an Arnoldi method shows competition between two eigenmodes, corresponding to different spanwise wavelengths and different types of roll distortion. Nonlinear integration shows that the lower-wave-number mode is always dominant. A partial route to chaos is established through the nonlinear simulations. The flow becomes temporally chaotic for Ra =1.05 Rac , but remains characterized by the spatial patterns identified by linear stability analysis. This highlights the complementary role of linear stability analysis and nonlinear simulation.

Uncertainty Propagation for Turbulent, Compressible Flow in a Quasi-1D Nozzle Using Stochastic Methods

NASA Technical Reports Server (NTRS)

Zang, Thomas A.; Mathelin, Lionel; Hussaini, M. Yousuff; Bataille, Francoise

2003-01-01

This paper describes a fully spectral, Polynomial Chaos method for the propagation of uncertainty in numerical simulations of compressible, turbulent flow, as well as a novel stochastic collocation algorithm for the same application. The stochastic collocation method is key to the efficient use of stochastic methods on problems with complex nonlinearities, such as those associated with the turbulence model equations in compressible flow and for CFD schemes requiring solution of a Riemann problem. Both methods are applied to compressible flow in a quasi-one-dimensional nozzle. The stochastic collocation method is roughly an order of magnitude faster than the fully Galerkin Polynomial Chaos method on the inviscid problem.

Maintenance and suppression of chaos by weak harmonic perturbations: a unified view.

PubMed

Chacón, R

2001-02-26

General results concerning maintenance or enhancement of chaos are presented for dissipative systems subjected to two harmonic perturbations (one chaos inducing and the other chaos enhancing). The connection with previous results on chaos suppression is also discussed in a general setting. It is demonstrated that, in general, a second harmonic perturbation can reliably play an enhancer or inhibitor role by solely adjusting its initial phase. Numerical results indicate that general theoretical findings concerning periodic chaos-inducing perturbations also work for aperiodic chaos-inducing perturbations, and in arrays of identical chaotic coupled oscillators.

Scaling with System Size of the Lyapunov Exponents for the Hamiltonian Mean Field Model

NASA Astrophysics Data System (ADS)

Manos, Thanos; Ruffo, Stefano

2011-12-01

The Hamiltonian Mean Field model is a prototype for systems with long-range interactions. It describes the motion of N particles moving on a ring, coupled with an infinite-range potential. The model has a second-order phase transition at the energy density Uc =3/4 and its dynamics is exactly described by the Vlasov equation in the N→∞ limit. Its chaotic properties have been investigated in the past, but the determination of the scaling with N of the Lyapunov Spectrum (LS) of the model remains a challenging open problem. Here we show that the N -1/3 scaling of the Maximal Lyapunov Exponent (MLE), found in previous numerical and analytical studies, extends to the full LS; scaling is "precocious" for the LS, meaning that it becomes manifest for a much smaller number of particles than the one needed to check the scaling for the MLE. Besides that, the N -1/3 scaling appears to be valid not only for U>Uc , as suggested by theoretical approaches based on a random matrix approximation, but also below a threshold energy Ut ≈0.2. Using a recently proposed method (GALI) devised to rapidly check the chaotic or regular nature of an orbit, we find that Ut is also the energy at which a sharp transition from weak to strong chaos is present in the phase-space of the model. Around this energy the phase of the vector order parameter of the model becomes strongly time dependent, inducing a significant untrapping of particles from a nonlinear resonance.

Eos Chaos Rocks

NASA Technical Reports Server (NTRS)

2006-01-01

11 January 2006 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows light-toned, layered rock outcrops in Eos Chaos, located near the east end of the Valles Marineris trough system. The outcrops occur in the form of a distinct, circular butte (upper half of image) and a high slope (lower half of image). The rocks might be sedimentary rocks, similar to those found elsewhere exposed in the Valles Marineris system and the chaotic terrain to the east of the region.

Location near: 12.9oS, 49.5oW Image width: 3 km (1.9 mi) Illumination from: lower left Season: Southern Summer

Adaptation to the edge of chaos in a self-starting Kerr-lens mode-locked laser

NASA Astrophysics Data System (ADS)

Hsu, C. C.; Lin, J. H.; Hsieh, W. F.

2009-08-01

We experimentally and numerically demonstrated that self-focusing acts as a slow-varying control parameter that suppresses the transient chaos to reach a stable mode-locking (ML) state in a self-starting Kerr-lens mode-locked Ti:sapphire laser without external modulation and feedback control. Based on Fox-Li’s approach, including the self-focusing effect, the theoretical simulation reveals that the self-focusing effect is responsible for the self-adaptation. The self-adaptation occurs at the boundary between the chaotic and continuous output regions in which the laser system begins with a transient chaotic state with fractal correlation dimension, and then evolves with reducing dimension into the stable ML state.

Singlet-catalyzed electroweak phase transitions in the 100 TeV frontier

NASA Astrophysics Data System (ADS)

Kotwal, Ashutosh V.; Ramsey-Musolf, Michael J.; No, Jose Miguel; Winslow, Peter

2016-08-01

We study the prospects for probing a gauge singlet scalar-driven strong first-order electroweak phase transition with a future proton-proton collider in the 100 TeV range. Singlet-Higgs mixing enables resonantly enhanced di-Higgs production, potentially aiding discovery prospects. We perform Monte Carlo scans of the parameter space to identify regions associated with a strong first-order electroweak phase transition, analyze the corresponding di-Higgs signal, and select a set of benchmark points that span the range of di-Higgs signal strengths. For the b b ¯γ γ and 4 τ final states, we investigate discovery prospects for each benchmark point for the high-luminosity phase of the Large Hadron Collider and for a future p p collider with √{s }=50 , 100, or 200 TeV. We find that any of these future collider scenarios could significantly extend the reach beyond that of the high-luminosity LHC, and that with √{s }=100 TeV (200 TeV) and 30 ab-1 , the full region of parameter space favorable to strong first-order electroweak phase transitions is almost fully (fully) discoverable.

Household chaos, sociodemographic risk, coparenting, and parent-infant relations during infants' first year.

PubMed

Whitesell, Corey J; Teti, Douglas M; Crosby, Brian; Kim, Bo-Ram

2015-04-01

Household chaos is a construct often overlooked in studies of human development, despite its theoretical links with the integrity of individual well-being, family processes, and child development. The present longitudinal study examined relations between household chaos and well-established correlates of chaos (sociodemographic risk, major life events, and personal distress) and several constructs that, to date, are theoretically linked with chaos but never before assessed as correlates (quality of coparenting and emotional availability with infants at bedtime). In addressing this aim, we introduce a new measure of household chaos (the Descriptive In-home Survey of Chaos--Observer ReporteD, or DISCORD), wholly reliant on independent observer report, which draws from household chaos theory and prior empirical work but extends the measurement of chaos to include information about families' compliance with a home visiting protocol. Household chaos was significantly associated with socioeconomic risk, negative life events, less favorable coparenting, and less emotionally available bedtime parenting, but not with personal distress. These findings emphasize the need to examine household chaos as a direct and indirect influence on child and family outcomes, as a moderator of intervention attempts to improving parenting and child development, and as a target of intervention in its own right. (c) 2015 APA, all rights reserved).

Pairing transition, coherence transition, and the irreversibility line in granular GdBa2Cu3O7-δ

NASA Astrophysics Data System (ADS)

Roa-Rojas, J.; Menegotto Costa, R.; Pureur, P.; Prieto, P.

2000-05-01

We report on electrical magnetoconductivity experiments near the superconducting transition of a granular sample of GdBa2Cu3O7-δ. The measurements were performed in magnetic fields ranging from 0 to 500 Oe applied parallel to the current orientation. The results show that the transition proceeds in two steps. When the temperature is decreased we first observe the pairing transition, which stabilizes superconductivity within the grains at a temperature practically coincident with the bulk critical temperature Tc. Analysis of the fluctuation contributions to the conductivity shows that the universality class for this transition is that of the three dimensional (3D)-XY model in the ordered case, with dynamic critical exponent z=3/2. Close to the zero-resistance state, the measurements reveal the occurrence of a coherence transition, where the phases of the order parameter in individual grains become long-range ordered. The critical temperature Tco for this transition is close to the point where the resistivity vanishes. A strong enlargement of the fluctuation interval preceding the coherence transition is caused by the applied magnetic field. In this region, a 3D-Gaussian regime and an asymptotic critical regime were clearly identified. The critical conductivity behavior for the coherence transition is interpreted within a 3D-XY model where disorder and frustration are relevant. The irreversibility line is determined from magnetoconductivity measurements performed according to the zero-field-cooled (ZFC) and field-cooled data collected on cooling (FCC) recipes. The locus of this line coincides with the upper temperature limit for the fluctuation region above the coherence transition. The irreversibility line is interpreted as an effect of the formation of small clusters with closed loops of Josephson-coupled grains.

Effusive silicic volcanism in the Central Andes: The Chao dacite and other young lavas of the Altiplano-Puna Volcanic Complex

NASA Technical Reports Server (NTRS)

De Silva, S. L.; Self, S.; Francis, P. W.; Drake, R. E.; Ramirez, Carlos R.

1994-01-01

The largest known Quaternary silicic lava body in the world is Cerro Chao in north Chile, a 14-km-long coulee with a volume of at least 26 cu km. It is the largest of a group of several closely similar dacitic lavas erupted during a recent (less than 100,000 year old) magmatic episode in the Altiplano-Puna Volcanic Complex (APVC; 21-24 deg S) of the Centra; Andean Volcanic Zone. The eruption of Chao proceeded in three phases. Phase 1 was explosive and produced approximately 1 cu km of coarse, nonwelded dacitic pumice deposits and later block and ash flows that form an apron in front of the main lava body. Phase 2 was dominantly effusive and erupted approximately 22.5 cu km of magma in the form of a composite coulee covering approximately 53 sq km with a 400-m-high flow front and a small cone of poorly expanded pumice around the vent. The lava is homogeneous with rare flow banding and vesicular tops and selvages. Ogives (flow ridges) reaching heights of 30 m form prominent features on its surface. Phase 3 produced a 6-km-long, 3-km-wide flow that emanated from a collapsed dome. Ogives are subdued, and the lava is glassier than that produced in previous phases. All the Chao products are crystal-rich high-K dacites and rhyodacites with phenocrysts of plagioclase, quartz, hornblende, biotite, sphene, rare snidine, and oxides. Phenocryst contents reach 40-60 vol % (vesicle free) in the main phase 2 lavas but are lower in the phase 1 (20-25%) and phase 3 (approximately 40%) lavas. Ovoid andesitic inclusions with vesicular interiors and chilled margins up to 10 cm are found in the later stages of phase 2 and compose up to 5% of the phase 3 lava. There is little evidence for preeruptive zonation of the magma body in composition, temperature (approximately 840 C), fO2 (19(exp -11), or water content, so we propose that eruption of the Chao complex was driven by intrusion of fresh, hot andesitic magma into a crystallizing and largely homogeneous body of dacitic magma. Morphological measurements suggest that the Chao lavas had internal plastic viscosities of 10(exp 10) to 10(exp 12) Pa s, apparent viscosities of 10(exp 9) Pa s, surface viscosities of 10(exp 15) to 10(exp 24) Pa s, and a yield strength of 8 x 10(exp 5) Pa. These estimates indicate that Chao would have exhibited largely similar rheological properties to other silicic lava extrusions, notwithstanding its high phenocryst content. We suggest that Chao's anomalous size is a function of both the relatively steep local slope (20 deg to 3 deg) and the available volume of magma. The eruption duration for Chao's emplacement is thought to have been about 100 to 150 years, with maximum effusion rates of about 25 cu m/s for short periods. Four other lavas in the vicinity with volumes of approximately 5 cu km closely resemble Chao and are probably comagnetic. The suite as a whole shares a petrologic and chemical similarity with the voluminous regional Tertiary to Pleistocene ignimbrites of the APVC and may be derived from a zone of silicic magmatism that is thought to have been active since the late Tertiary. Chao and the other young lavas may represent either the waning of this system or a new episode fueled by intrusions of mafic magma.

Spread of a disease and its effect on population dynamics in an eco-epidemiological system

NASA Astrophysics Data System (ADS)

Upadhyay, Ranjit Kumar; Roy, Parimita

2014-12-01

In this paper, an eco-epidemiological model with simple law of mass action and modified Holling type II functional response has been proposed and analyzed to understand how a disease may spread among natural populations. The proposed model is a modification of the model presented by Upadhyay et al. (2008) [1]. Existence of the equilibria and their stability analysis (linear and nonlinear) has been studied. The dynamical transitions in the model have been studied by identifying the existence of backward Hopf-bifurcations and demonstrated the period-doubling route to chaos when the death rate of predator (μ1) and the growth rate of susceptible prey population (r) are treated as bifurcation parameters. Our studies show that the system exhibits deterministic chaos when some control parameters attain their critical values. Chaotic dynamics is depicted using the 2D parameter scans and bifurcation analysis. Possible implications of the results for disease eradication or its control are discussed.

Nonlinear convective pulsation models of type II Cepheids

NASA Astrophysics Data System (ADS)

Smolec, Radoslaw

2015-08-01

We present a grid of nonlinear convective pulsation models of type-II Cepheids: BL Her stars, W Vir stars and RV Tau stars. The models cover a wide range of masses, luminosities, effective temperatures and chemical compositions. The most interesting result is detection of deterministic chaos in the models. Different routes to chaos are detected (period doubling, intermittent route) as well as variety of phenomena intrinsic to chaotic dynamics (periodic islands within chaotic bands, crisis bifurcation, type-I and type-III intermittency). Some of the phenomena (period doubling in BL Her and in RV Tau stars, irregular pulsation of RV Tau stars) are well known in the pulsation of type-II Cepheids. Prospects of discovering the other are briefly discussed. Transition from BL Her type pulsation through W Vir type till RV Tau type is analysed. In the most luminous models a dynamical instability is detected, which indicates that pulsation driven mass loss is important process occurring in type-II Cepheids.

Finite-temperature phase transitions of third and higher order in gauge theories at large N

DOE PAGES

Nishimura, Hiromichi; Pisarski, Robert D.; Skokov, Vladimir V.

2018-02-15

We study phase transitions in SU(∞) gauge theories at nonzero temperature using matrix models. Our basic assumption is that the effective potential is dominated by double trace terms for the Polyakov loops. As a function of the various parameters, related to terms linear, quadratic, and quartic in the Polyakov loop, the phase diagram exhibits a universal structure. In a large region of this parameter space, there is a continuous phase transition whose order is larger than second. This is a generalization of the phase transition of Gross, Witten, and Wadia (GWW). Depending upon the detailed form of the matrix model,more » the eigenvalue density and the behavior of the specific heat near the transition differ drastically. Here, we speculate that in the pure gauge theory, that although the deconfining transition is thermodynamically of first order, it can be nevertheless conformally symmetric at infnite N.« less

Finite-temperature phase transitions of third and higher order in gauge theories at large N

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nishimura, Hiromichi; Pisarski, Robert D.; Skokov, Vladimir V.

We study phase transitions in SU(∞) gauge theories at nonzero temperature using matrix models. Our basic assumption is that the effective potential is dominated by double trace terms for the Polyakov loops. As a function of the various parameters, related to terms linear, quadratic, and quartic in the Polyakov loop, the phase diagram exhibits a universal structure. In a large region of this parameter space, there is a continuous phase transition whose order is larger than second. This is a generalization of the phase transition of Gross, Witten, and Wadia (GWW). Depending upon the detailed form of the matrix model,more » the eigenvalue density and the behavior of the specific heat near the transition differ drastically. Here, we speculate that in the pure gauge theory, that although the deconfining transition is thermodynamically of first order, it can be nevertheless conformally symmetric at infnite N.« less

Action Research: Order Out of Chaos.

ERIC Educational Resources Information Center

Geffen, Mitzi

2002-01-01

Describes on Israeli English-as-a-Foreign-Language teacher's action research project that focused on how to teach reading comprehension in English to a class of ninth grade boys. Outlines the teacher's goals, implementation of the project, and thoughts on the outcomes. (Author/VWL)

There is Diversity in Disorder-"In all Chaos there is a Cosmos, in all Disorder a Secret Order".

PubMed

Nielsen, Jakob T; Mulder, Frans A A

2016-01-01

The protein universe consists of a continuum of structures ranging from full order to complete disorder. As the structured part of the proteome has been intensively studied, stably folded proteins are increasingly well documented and understood. However, proteins that are fully, or in large part, disordered are much less well characterized. Here we collected NMR chemical shifts in a small database for 117 protein sequences that are known to contain disorder. We demonstrate that NMR chemical shift data can be brought to bear as an exquisite judge of protein disorder at the residue level, and help in validation. With the help of secondary chemical shift analysis we demonstrate that the proteins in the database span the full spectrum of disorder, but still, largely segregate into two classes; disordered with small segments of order scattered along the sequence, and structured with small segments of disorder inserted between the different structured regions. A detailed analysis reveals that the distribution of order/disorder along the sequence shows a complex and asymmetric distribution, that is highly protein-dependent. Access to ratified training data further suggests an avenue to improving prediction of disorder from sequence.

The circum-Chryse region as a possible example of a hydrologic cycle on Mars: Geologic observations and theoretical evaluation

NASA Technical Reports Server (NTRS)

Moore, Jeffrey M.; Clow, Gary D.; Davis, Wanda L.; Gulick, Virginia C.; Janke, David R.; Mckay, Christopher P.; Stoker, Carol R.; Zent, Aaron P.

1995-01-01

The transection and superposition relationships among channels, chaos, surface materials units, and other features in the circum-Chryse region of Mars were used to evaluate relative age relationships and evolution of flood events. Channels and chaos in contact (with one another) were treated as single discrete flood-carved systems. Some outflow channel systems form networks and are inferred to have been created by multiple flood events. Within some outflow channel networks, several separate individual channel systems can be traced to a specific chaos which acted as flood-source area to that specific flood channel. Individual flood-carved systems were related to widespread materials units or other surface features that served as stratigraphic horizons. Chryse outflow channels are inferred to have formed over most of the perceivable history of Mars. Outflow channels are inferred to become younger with increasing proximity to the Chryse basin. The relationship of subsequent outflow channel sources to the sources of earlier floods is inferred to disfavor episodic flooding due to the progresssive tapping of a juvenile near-surface water supply. Instead, we propose the circum-Chryse region as a candidate site of past hydrological recycling. The discharge rates necessary to carve the circum-Chryse outflow channels would have inevitably formed temporary standing bodies of H2O on the Martian surface where the flood-waters stagnated and pooled (the Chryse basin is topographically enclosed). These observations and inferences have led us to formulate and evaluate two hypotheses. Our numerical evaluations indicate that of these two hypotheses formulated, the groundwater seep cycle seems by far the more viable. Further observations from forthcoming missions may permit the determination of which mechanisms may have operated to recycle the Chryse flood-waters.

Symmetry restoring bifurcations and quasiperiodic chaos induced by a new intermittency in a vibro-impact system.

PubMed

Yue, Yuan; Miao, Pengcheng; Xie, Jianhua; Celso, Grebogi

2016-11-01

Quasiperiodic chaos (QC), which is a combination of quasiperiodic sets and a chaotic set, is uncovered in the six dimensional Poincaré map of a symmetric three-degree of freedom vibro-impact system. Accompanied by symmetry restoring bifurcation, this QC is the consequence of a novel intermittency that occurs between two conjugate quasiperiodic sets and a chaotic set. The six dimensional Poincaré map P is the 2-fold composition of another virtual implicit map Q, yielding the symmetry of the system. Map Q can capture two conjugate attractors, which is at the core of the dynamics of the vibro-impact system. Three types of symmetry restoring bifurcations are analyzed in detail. First, if two conjugate chaotic attractors join together, the chaos-chaos intermittency induced by attractor-merging crisis takes place. Second, if two conjugate quasiperiodic sets are suddenly embedded in a chaotic one, QC is induced by a new intermittency between the three attractors. Third, if two conjugate quasiperiodic attractors connect with each other directly, they merge to form a single symmetric quasiperiodic one. For the second case, the new intermittency is caused by the collision of two conjugate quasiperiodic attractors with an unstable symmetric limit set. As the iteration number is increased, the largest finite-time Lyapunov exponent of the QC does not converge to a constant, but fluctuates in the positive region.

Bounds on strain in large Tertiary shear zones of SE Asia from boudinage restoration

NASA Astrophysics Data System (ADS)

Lacassin, R.; Leloup, P. H.; Tapponnier, P.

1993-06-01

We have used surface-balanced restoration of stretched, boudinaged layers to estimate minimum amounts of finite strain in the mylonitic gneisses of the Oligo-Miocene Red River-Ailao Shan shear zone (Yunnan, China) and of the Wang Chao shear zone (Thailand). The layer-parallel extension values thus obtained range between 250 and 870%. We discuss how to use such extension values to place bounds on amounts of finite shear strain in these large crustal shear zones. Assuming simple shear, these values imply minimum total and late shear strains of, respectively, 33 ± 6 and 7 ± 3 at several sites along the Red River-Ailao Shan shear zone. For the Wang Chao shear zone a minimum shear strain of 7 ± 4 is deduced. Assuming homogeneous shear would imply that minimum strike-slip displacements along these two left-lateral shear zones, which have been interpreted to result from the India-Asia collision, have been of the order of 330 ± 60 km (Red River-Ailao Shan) and 35 ± 20 km (Wang Chao).

Convergent chaos

NASA Astrophysics Data System (ADS)

Pradas, Marc; Pumir, Alain; Huber, Greg; Wilkinson, Michael

2017-07-01

Chaos is widely understood as being a consequence of sensitive dependence upon initial conditions. This is the result of an instability in phase space, which separates trajectories exponentially. Here, we demonstrate that this criterion should be refined. Despite their overall intrinsic instability, trajectories may be very strongly convergent in phase space over extremely long periods, as revealed by our investigation of a simple chaotic system (a realistic model for small bodies in a turbulent flow). We establish that this strong convergence is a multi-facetted phenomenon, in which the clustering is intense, widespread and balanced by lacunarity of other regions. Power laws, indicative of scale-free features, characterize the distribution of particles in the system. We use large-deviation and extreme-value statistics to explain the effect. Our results show that the interpretation of the ‘butterfly effect’ needs to be carefully qualified. We argue that the combination of mixing and clustering processes makes our specific model relevant to understanding the evolution of simple organisms. Lastly, this notion of convergent chaos, which implies the existence of conditions for which uncertainties are unexpectedly small, may also be relevant to the valuation of insurance and futures contracts.

The Cycles of Snow Cover in Pyrenees Mountain and Mont Lebanon Analyzed Using the Global Modeling Technique.

NASA Astrophysics Data System (ADS)

Drapeau, L.; Mangiarotti, S.; Le Jean, F.; Gascoin, S.; Jarlan, L.

2014-12-01

The global modeling technique provides a way to obtain ordinary differential equations from single time series1. This technique, initiated in the 1990s, could be applied successfully to numerous theoretic and experimental systems. More recently it could be applied to environmental systems2,3. Here this technique is applied to seasonal snow cover area in the Pyrenees mountain (Europe) and Mont Lebanon (Mediterranean region). The snowpack evolution is complex because it results from combination of processes driven by physiography (elevation, slope, land cover...) and meteorological variables (precipitation, temperature, wind speed...), which are highly heterogeneous in such regions. Satellite observations in visible bands offer a powerful tool to monitor snow cover areas at global scale, with large resolutions range. Although this observable does not directly inform about snow water equivalent, its dynamical behavior strongly relies on it. Therefore, snow cover area is likely to be a good proxy of the global dynamics and global modeling technique a well adapted approach. The MOD10A2 product (500m) generated from MODIS by the NASA is used after a pretreatment is applied to minimize clouds effect. The global modeling technique is then applied using two packages4,5. The analysis is performed with two time series for the whole period (2000-2012) and year by year. Low-dimensional chaotic models are obtained in many cases. Such models provide a strong argument for chaos since involving the two necessary conditions in a synthetic way: determinism and strong sensitivity to initial conditions. The models comparison suggests important non-stationnarities at interannual scale which prevent from detecting long term changes. 1: Letellier et al 2009. Frequently asked questions about global modeling, Chaos, 19, 023103. 2: Maquet et al 2007. Global models from the Canadian lynx cycles as a direct evidence for chaos in real ecosystems. J. of Mathematical Biology, 55 (1), 21-39 3: Mangiarotti et al 2014. Two chaotic global models for cereal crops cycles observed from satellite in Northern Morocco. Chaos, 24, 023130. 4 : Mangiarotti et al 2012. Polynomial search and Global modelling: two algorithms for modeling chaos. Physical Review E, 86(4), 046205. 5: http://cran.r-project.org/web/packages/PoMoS/index.html.

Controlling transient chaos in deterministic flows with applications to electrical power systems and ecology

NASA Astrophysics Data System (ADS)

Dhamala, Mukeshwar; Lai, Ying-Cheng

1999-02-01

Transient chaos is a common phenomenon in nonlinear dynamics of many physical, biological, and engineering systems. In applications it is often desirable to maintain sustained chaos even in parameter regimes of transient chaos. We address how to sustain transient chaos in deterministic flows. We utilize a simple and practical method, based on extracting the fundamental dynamics from time series, to maintain chaos. The method can result in control of trajectories from almost all initial conditions in the original basin of the chaotic attractor from which transient chaos is created. We apply our method to three problems: (1) voltage collapse in electrical power systems, (2) species preservation in ecology, and (3) elimination of undesirable bursting behavior in a chemical reaction system.

Margaret Wheatley on Leadership for Change.

ERIC Educational Resources Information Center

Steinberger, Elizabeth Donohoe

1995-01-01

Wheatley's 1992 bestseller, "Leadership and the New Science," argues that across scientific disciplines, our rational, systematic quest for order, control, stability, and predictability are yielding to a deeper appreciation for chaos, complexity, uncertainty, and change. In this interview, Wheatley shows how breakthroughs in biology,…

Beleaguered by Bains and Bureaucrats

ERIC Educational Resources Information Center

Rowan, Patricia

1977-01-01

The Bains Report was meant to produce order out of chaos in local government. But Avon's corporate management row last autumn suggested it may have done more harm than good. This article, the first in a two-part series, reports on its impact elsewhere. (Editor/RK)

A new simple technique for improving the random properties of chaos-based cryptosystems

NASA Astrophysics Data System (ADS)

Garcia-Bosque, M.; Pérez-Resa, A.; Sánchez-Azqueta, C.; Celma, S.

2018-03-01

A new technique for improving the security of chaos-based stream ciphers has been proposed and tested experimentally. This technique manages to improve the randomness properties of the generated keystream by preventing the system to fall into short period cycles due to digitation. In order to test this technique, a stream cipher based on a Skew Tent Map algorithm has been implemented on a Virtex 7 FPGA. The randomness of the keystream generated by this system has been compared to the randomness of the keystream generated by the same system with the proposed randomness-enhancement technique. By subjecting both keystreams to the National Institute of Standards and Technology (NIST) tests, we have proved that our method can considerably improve the randomness of the generated keystreams. In order to incorporate our randomness-enhancement technique, only 41 extra slices have been needed, proving that, apart from effective, this method is also efficient in terms of area and hardware resources.

High-sensitivity optical sensing of axial strain based on microfiber with microarched transition region

NASA Astrophysics Data System (ADS)

Xia, Liang; Xing, Zengshan; Yu, Jianhui; Lu, Huihui; Guan, Heyuan; Zhong, Yongchun; Chen, Zhe

2017-11-01

We demonstrated strain sensing of a microfiber with a microarched transition region, which was fabricated by flame heated tapering. Due to multimode interference of different propagation modes of microfiber, two main transmission dips were observed at 1215.0 and 1469.8 nm. Enhanced by the microarched transition region, the depth of the dip was up to 19 dB at 1215.0 nm. The position of the dip red-shifted while the axial strain changed from 0 to 1166.2 μɛ. The axial strain sensitivity was up to 56.6 pm/μɛ, which was one order of magnitude higher than that of the traditional optical strain sensor based on microfiber or fiber Bragg grating. The linear correlation coefficient was 98.21%. This kind of microfiber with a microarched transition region can be widely used in various physical, chemical, and biological sensing and detection fields.

Eliminate the "Bounce"!

ERIC Educational Resources Information Center

Leigh, Susan

2016-01-01

The "bounce" (coined by students at Susan Leigh's last campus) refers to the amount of time students spent chasing signatures and removing often-unnecessary registration "holds" in order to attend their classes. Leigh explains that all this chaos from complex, separately housed transactional business processes has led to the…

The geomagnetic jerk of 2003.5-characterisation with regional observatory secular variation data

NASA Astrophysics Data System (ADS)

Feng, Yan; Holme, Richard; Cox, Grace Alexandra; Jiang, Yi

2018-05-01

The 2003.5 geomagnetic jerk was identified in geomagnetic records from satellite data, and a matching feature reported in variations in length-of-day (ΔLOD), but detailed study has been hampered by lack of geomagnetic observatory data where it appears strongest. Here we examine secular variation (annual differences of monthly means) based on a new resource of 43 Chinese observatory records for 1998 until the present, focusing on 10 series of particularly high quality and consistency. To obtain a clean series, we calculate the covariance matrix of residuals between measurements and a state-of-the-art field model, CHAOS-6, and use eigenvalue analysis to remove noisy contributions from the uncorrected data. The magnitude of the most significant eigenvector correlates well with Dcx (corrected, extended Dst), suggesting the noise originates from unmodelled external magnetic field. Removal of this noise eliminates much coherent misfit around 2003-2005; nevertheless, the 2003.5 jerk is seen clearly in the first time derivative of the East component in Chinese data, and is also seen in the first time derivative of the vertical component in European data. Estimates of the jerk time are centred on 2003.5, but with some spatial variation; this variation can be eliminated if we allow a discontinuity in the secular variation as well as its temporal gradient. Both regions also provide evidence for a jerk around 2014, although less clearly than 2003.5. We create a new field model based on new data and CHAOS-6 to further examine the regional signals. The new model is close to CHAOS-6, but better fits Chinese data, although modelling also identifies some data features as unphysical.

Bifurcation scenarios for bubbling transition.

PubMed

Zimin, Aleksey V; Hunt, Brian R; Ott, Edward

2003-01-01

Dynamical systems with chaos on an invariant submanifold can exhibit a type of behavior called bubbling, whereby a small random or fixed perturbation to the system induces intermittent bursting. The bifurcation to bubbling occurs when a periodic orbit embedded in the chaotic attractor in the invariant manifold becomes unstable to perturbations transverse to the invariant manifold. Generically the periodic orbit can become transversely unstable through a pitchfork, transcritical, period-doubling, or Hopf bifurcation. In this paper a unified treatment of the four types of bubbling bifurcation is presented. Conditions are obtained determining whether the transition to bubbling is soft or hard; that is, whether the maximum burst amplitude varies continuously or discontinuously with variation of the parameter through its critical value. For soft bubbling transitions, the scaling of the maximum burst amplitude with the parameter is derived. For both hard and soft transitions the scaling of the average interburst time with the bifurcation parameter is deduced. Both random (noise) and fixed (mismatch) perturbations are considered. Results of numerical experiments testing our theoretical predictions are presented.

Formation and degradation of chaotic terrain in the Galaxias regions of Mars: implications for near-surface storage of ice

NASA Astrophysics Data System (ADS)

Gallagher, Colman; Balme, Matt; Soare, Richard; Conway, Susan J.

2018-07-01

Galaxias Chaos is a region of low plateaus separated by narrow fractures - a chaotic terrain. Galaxias Mensae and Galaxias Colles are characterised by mesa and knobby terrains of individual landforms, or small assemblages, separated by plains. Galaxias Chaos has been attributed to ground disturbance due to sublimation in shallow subsurface ice-rich deposits, Galaxias Mensae and Galaxias Colles to sublimation and degradation of icy surface materials, without production of chaotic terrain. Liquid water has not been regarded as a product of the degradation of these icy terrains. This paper asks two research questions: (1) what was the total extent of the different modes of landscape degradation, especially chaotic terrain, involved in producing the present landscapes of Galaxias Chaos and Galaxias Mensae-Colles; (2) can the generation of liquid water as a product of landscape degradation be ruled-out? Using a morphological-statistical approach, including power spectrum analysis of relief, our observations and analyses show that present mesa-knobby terrains of Galaxias Mensae-Colles evolved from a landscape that had the same directional pattern and relief as presently found in Galaxias Chaos. This terrain extended across ∼440,000 km2 but ∼22,000 km3 (average thickness, 77 m) have been lost across ∼285,000 km2. This represents a significant loss of ice-bearing deposits. Moreover, this surface degradation was spatially partitioned by landforms associated with elevated ground heating and the transmission of a fluid in the shallow subsurface towards a distal channel. In answer to research question 2, it cannot be determined definitively if the fluid involved was groundwater, generated by the thermal destabilisation of the icy deposits, or low viscosity lava. However, it is likely that the degradation of Galaxias Mensae-Colles was not a consequence of sublimation alone. These findings underscore the significance of cryo-volcanic interactions in the cycling of water between the Martian surface and the atmosphere.

Numerical investigation of hypersonic flat-plate boundary layer transition mechanism induced by different roughness shapes

NASA Astrophysics Data System (ADS)

Zhou, Yunlong; Zhao, Yunfei; Xu, Dan; Chai, Zhenxia; Liu, Wei

2016-10-01

The roughness-induced laminar-turbulent boundary layer transition is significant for high-speed aerospace applications. The transition mechanism is closely related to the roughness shape. In this paper, high-order numerical method is used to investigate the effect of roughness shape on the flat-plate laminar-to-turbulent boundary layer transition. Computations are performed in both the supersonic and hypersonic regimes (free-stream Mach number from 3.37 up to 6.63) for the square, cylinder, diamond and hemisphere roughness elements. It is observed that the square and diamond roughness elements are more effective in inducing transition compared with the cylinder and hemisphere ones. The square roughness element has the longest separated region in which strong unsteadiness exists and the absolute instability is formed, thus resulting in the earliest transition. The diamond roughness element has a maximum width of the separated region leading to the widest turbulent wake region far downstream. Furthermore, transition location moves backward as the Mach number increases, which indicates that the compressibility significantly suppresses the roughness-induced boundary layer transition.

Detection of chaos: New approach to atmospheric pollen time-series analysis

NASA Astrophysics Data System (ADS)

Bianchi, M. M.; Arizmendi, C. M.; Sanchez, J. R.

1992-09-01

Pollen and spores are biological particles that are ubiquitous to the atmosphere and are pathologically significant, causing plant diseases and inhalant allergies. One of the main objectives of aerobiological surveys is forecasting. Prediction models are required in order to apply aerobiological knowledge to medical or agricultural practice; a necessary condition of these models is not to be chaotic. The existence of chaos is detected through the analysis of a time series. The time series comprises hourly counts of atmospheric pollen grains obtained using a Burkard spore trap from 1987 to 1989 at Mar del Plata. Abraham's method to obtain the correlation dimension was applied. A low and fractal dimension shows chaotic dynamics. The predictability of models for atomspheric pollen forecasting is discussed.

Dissipation processes in the insulating skyrmion compound Cu2OSeO3

NASA Astrophysics Data System (ADS)

Levatić, I.; Šurija, V.; Berger, H.; Živković, I.

2014-12-01

We present a detailed study of the phase diagram surrounding the skyrmion lattice (SkL) phase of Cu2OSe2O3 using high-precision magnetic ac susceptibility measurements. An extensive investigation of transition dynamics around the SkL phase using the imaginary component of the susceptibility revealed that at the conical-to-SkL transition a broad dissipation region exists with a complex frequency dependence. The analysis of the observed behavior within the SkL phase indicates a distribution of relaxation times intrinsically related to SkL. At the SkL-to-paramagnet transition a narrow first-order peak is found that exhibits a strong frequency and magnetic field dependence. Surprisingly, very similar dependence has been discovered for the first-order transition below the SkL phase, i.e., where the system enters the helical and conical state(s), indicating similar processes across the order-disorder transition.

Adventures in order and chaos : a scientific autobiography

NASA Astrophysics Data System (ADS)

Contopoulos, George

The field of Order and Chaos had a remarkable expansion in the last 50 years. The main reason was the use of computers, and the development of new theoretical methods that we call now 'the theory of chaos'. The author describes this fascinating period in a relaxed and sometimes humorous autobiographical way. He relates his interactions with many people in dynamical astronomy and he quotes several anecdotes from these interactions. He refers also to his experiences when he served in various international positions, such as general secretary of the IAU and chairman of the journal Astronomy and Astrophysics. In recent years the theory of chaos has been extended to new areas, like relativity, cosmology and quantum mechanics and it continues expanding in almost all branches of physics. The book describes many important ideas in this field in a simple way. It refers also to problems of more general interest, like writing papers and giving lectures and the interaction of authors and referees. Finally it gives some useful prospects for the future of dynamical astronomy and related fields. George Contopoulos, PhD U.Athens1953; Professor of Astronomy U.Thessaloniki 1957-75; U.Athens 1975-96; Emeritus 1996-; Member, Academy of Athens 1997-. Visiting Professor Yale U., Harvard U., MIT, Cornell U., U.Chicago, U.Maryland, U. Florida, Florida State U., U. Milan; Res. Associate, Yerkes Obs., Inst.Adv.Study Princeton, Inst.Space Studies, Goddard Flight Center, Columbia U., ESO. Author or Editor of 15 books, and about 250 papers on Galactic Dynamics, Relativity and Celestial Mechanics. Positions held: Gen.Secretary of the IAU; Director General Nat.Obs.of Greece, Pres.Hellenic Astron.Soc.; Nat.Representative of Greece in NATO, etc. Distinctions: Amer. Astron.Soc. Brouwer Prize; U.Chicago, Honorary Doctor's Degree; IAU, Pres. Commission 33 (Galaxy); Member Academia Europaea; Associate Royal Astron. Soc.; Chairman of the European Journal "Astronomy and Astrophysics"; Assoc. Editor of "Cel. Mech. Dyn. Astron."; Over 4500 citations and 300 acknowledgements.

Continuous Isotropic-Nematic Transition in Amyloid Fibril Suspensions Driven by Thermophoresis.

PubMed

Vigolo, Daniele; Zhao, Jianguo; Handschin, Stephan; Cao, Xiaobao; deMello, Andrew J; Mezzenga, Raffaele

2017-04-27

The isotropic and nematic (I + N) coexistence for rod-like colloids is a signature of the first-order thermodynamics nature of this phase transition. However, in the case of amyloid fibrils, the biphasic region is too small to be experimentally detected, due to their extremely high aspect ratio. Herein, we study the thermophoretic behaviour of fluorescently labelled β-lactoglobulin amyloid fibrils by inducing a temperature gradient across a microfluidic channel. We discover that fibrils accumulate towards the hot side of the channel at the temperature range studied, thus presenting a negative Soret coefficient. By exploiting this thermophoretic behaviour, we show that it becomes possible to induce a continuous I-N transition with the I and N phases at the extremities of the channel, starting from an initially single N phase, by generating an appropriate concentration gradient along the width of the microchannel. Accordingly, we introduce a new methodology to control liquid crystal phase transitions in anisotropic colloidal suspensions. Because the induced order-order transitions are achieved under stationary conditions, this may have important implications in both applied colloidal science, such as in separation and fractionation of colloids, as well as in fundamental soft condensed matter, by widening the accessibility of target regions in the phase diagrams.

Bifurcations and degenerate periodic points in a three dimensional chaotic fluid flow

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smith, L. D., E-mail: lachlan.smith@monash.edu; CSIRO Mineral Resources, Clayton, Victoria 3800; Rudman, M.

2016-05-15

Analysis of the periodic points of a conservative periodic dynamical system uncovers the basic kinematic structure of the transport dynamics and identifies regions of local stability or chaos. While elliptic and hyperbolic points typically govern such behaviour in 3D systems, degenerate (parabolic) points also play an important role. These points represent a bifurcation in local stability and Lagrangian topology. In this study, we consider the ramifications of the two types of degenerate periodic points that occur in a model 3D fluid flow. (1) Period-tripling bifurcations occur when the local rotation angle associated with elliptic points is reversed, creating a reversalmore » in the orientation of associated Lagrangian structures. Even though a single unstable point is created, the bifurcation in local stability has a large influence on local transport and the global arrangement of manifolds as the unstable degenerate point has three stable and three unstable directions, similar to hyperbolic points, and occurs at the intersection of three hyperbolic periodic lines. The presence of period-tripling bifurcation points indicates regions of both chaos and confinement, with the extent of each depending on the nature of the associated manifold intersections. (2) The second type of bifurcation occurs when periodic lines become tangent to local or global invariant surfaces. This bifurcation creates both saddle–centre bifurcations which can create both chaotic and stable regions, and period-doubling bifurcations which are a common route to chaos in 2D systems. We provide conditions for the occurrence of these tangent bifurcations in 3D conservative systems, as well as constraints on the possible types of tangent bifurcation that can occur based on topological considerations.« less

Analysis of multiple time scales in a transistor amplifier.

PubMed

Armstead, Douglas N; Carroll, Thomas L

2005-03-01

It was shown previously in an experiment that when high frequency signals (on the order of 1 MHz) were injected into this low frequency amplifier, the nonlinearities of the pn junctions caused period doubling, chaos, and very low frequency oscillations (on the order of 1 Hz). In this paper we present theory and simulations to explain the existence of the low frequency oscillations.

Predictability analysis and validation of a low-dimensional model - an application to the dynamics of cereal crops observed from satellite

NASA Astrophysics Data System (ADS)

Mangiarotti, Sylvain; Drapeau, Laurent

2013-04-01

The global modeling approach aims to obtain parsimonious models of observed dynamics from few or single time series (Letellier et al. 2009). Specific algorithms were developed and validated for this purpose (Mangiarotti et al. 2012a). This approach was applied to the dynamics of cereal crops in semi-arid region using the vegetation index derived from satellite data as a proxy of the dynamics. A low-dimensional autonomous model could be obtained. The corresponding attractor is characteristic of weakly dissipative chaos and exhibits a toroidal-like structure. At present, only few theoretical cases of such chaos are known, and none was obtained from real world observations. Under smooth conditions, a robust validation of three-dimensional chaotic models can be usually performed based on the topological approach (Gilmore 1998). Such approach becomes more difficult for weakly dissipative systems, and almost impossible under noisy observational conditions. For this reason, another validation approach is developed which consists in comparing the forecasting skill of the model to other forecasts for which no dynamical model is required. A data assimilation process is associated to the model to estimate the model's skill; several schemes are tested (simple re-initialization, Extended and Ensemble Kalman Filters and Back and Forth Nudging). Forecasts without model are performed based on the search of analogous states in the phase space (Mangiarotti et al. 2012b). The comparison reveals the quality of the model's forecasts at short to moderate horizons and contributes to validate the model. These results suggest that the dynamics of cereal crops can be reasonably approximated by low-dimensional chaotic models, and also bring out powerful arguments for chaos. Chaotic models have often been used as benchmark to test data assimilation schemes; the present work shows that such tests may not only have a theoretical interest, but also almost direct applicative potential. Moreover, other global models could be obtained for other regions. The model considered here is not a particular case which highlights the usefulness to investigate and to widen this field of modeling and research. References: Letellier, C., Aguirre, L.A., Freitas, U.S., 2009. Frequently asked questions about global modeling. Chaos, 19, doi:10.1063/1.3125705. Gilmore R., 1998. Topological analysis of chaotic dynamical systems. Review of Modern Physics, 70, 1455-1530. Mangiarotti, S., Coudret, R., Drapreau, L., Jarlan, L., 2012a. Polynomial Search and Global Modeling - two algorithms for modelling chaos. Physical Review E, 86(4), 046205. Mangiarotti, S., Mazzega, P., Mougin, E., Hiernaux, P., 2012b. Predictability of vegetation cycles over the semi-arid region of Gourma (Mali) from forecasts of AVHRR-NDVI signals. Remote Sensing of Environment, 123, 246-257.

Topological order and thermal equilibrium in polariton condensates

NASA Astrophysics Data System (ADS)

Caputo, Davide; Ballarini, Dario; Dagvadorj, Galbadrakh; Sánchez Muñoz, Carlos; de Giorgi, Milena; Dominici, Lorenzo; West, Kenneth; Pfeiffer, Loren N.; Gigli, Giuseppe; Laussy, Fabrice P.; Szymańska, Marzena H.; Sanvitto, Daniele

2018-02-01

The Berezinskii-Kosterlitz-Thouless phase transition from a disordered to a quasi-ordered state, mediated by the proliferation of topological defects in two dimensions, governs seemingly remote physical systems ranging from liquid helium, ultracold atoms and superconducting thin films to ensembles of spins. Here we observe such a transition in a short-lived gas of exciton-polaritons, bosonic light-matter particles in semiconductor microcavities. The observed quasi-ordered phase, characteristic for an equilibrium two-dimensional bosonic gas, with a decay of coherence in both spatial and temporal domains with the same algebraic exponent, is reproduced with numerical solutions of stochastic dynamics, proving that the mechanism of pairing of the topological defects (vortices) is responsible for the transition to the algebraic order. This is made possible thanks to long polariton lifetimes in high-quality samples and in a reservoir-free region. Our results show that the joint measurement of coherence both in space and time is required to characterize driven-dissipative phase transitions and enable the investigation of topological ordering in open systems.

Chaos in a 4D dissipative nonlinear fermionic model

NASA Astrophysics Data System (ADS)

Aydogmus, Fatma

2015-12-01

Gursey Model is the only possible 4D conformally invariant pure fermionic model with a nonlinear self-coupled spinor term. It has been assumed to be similar to the Heisenberg's nonlinear generalization of Dirac's equation, as a possible basis for a unitary description of elementary particles. Gursey Model admits particle-like solutions for the derived classical field equations and these solutions are instantonic in character. In this paper, the dynamical nature of damped and forced Gursey Nonlinear Differential Equations System (GNDES) are studied in order to get more information on spinor type instantons. Bifurcation and chaos in the system are observed by constructing the bifurcation diagrams and Poincaré sections. Lyapunov exponent and power spectrum graphs of GNDES are also constructed to characterize the chaotic behavior.

Hero's journey in bifurcation diagram

NASA Astrophysics Data System (ADS)

Monteiro, L. H. A.; Mustaro, P. N.

2012-06-01

The hero's journey is a narrative structure identified by several authors in comparative studies on folklore and mythology. This storytelling template presents the stages of inner metamorphosis undergone by the protagonist after being called to an adventure. In a simplified version, this journey is divided into three acts separated by two crucial moments. Here we propose a discrete-time dynamical system for representing the protagonist's evolution. The suffering along the journey is taken as the control parameter of this system. The bifurcation diagram exhibits stationary, periodic and chaotic behaviors. In this diagram, there are transition from fixed point to chaos and transition from limit cycle to fixed point. We found that the values of the control parameter corresponding to these two transitions are in quantitative agreement with the two critical moments of the three-act hero's journey identified in 10 movies appearing in the list of the 200 worldwide highest-grossing films.

Household chaos and family sleep during infants' first year.

PubMed

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

2018-05-21

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

Dielectric properties of ferroelectric betaine phosphite crystals with a high degree of deuteration

NASA Astrophysics Data System (ADS)

Balashova, E. V.; Krichevtsov, B. B.; Yurko, E. I.; Svinarev, F. B.; Pankova, G. A.

2015-12-01

The dielectric properties of deuterated betaine phosphite crystals with a high degree of deuteration in the region of the antiferrodistorsive (at T = T c1) and ferroelectric (at T = T c2) phase transitions have been investigated. The temperature behavior of the dielectric permittivity of betaine phosphite and deuterated betaine phosphite has been described within the framework of the Landau thermodynamic model taking into account the biquadratic coupling between the polar order parameter of the ferroelectric transition and the nonpolar order parameter of the antiferrodistorsive phase transition. It has been shown that an increase in the degree of deuteration leads to a decrease in the coupling between the order parameters. An increase in the temperature of the ferroelectric phase transition due to the deuteration of betaine phosphite is caused by an increase in the dielectric permittivity in the symmetric phase above the temperature of the antiferrodistorsive phase transition.

Liquid-liquid phase transition in an ionic model of silica

NASA Astrophysics Data System (ADS)

Chen, Renjie; Lascaris, Erik; Palmer, Jeremy C.

2017-06-01

Recent equation of state calculations [E. Lascaris, Phys. Rev. Lett. 116, 125701 (2016)] for an ionic model of silica suggest that it undergoes a density-driven, liquid-liquid phase transition (LLPT) similar to the controversial transition hypothesized to exist in deeply supercooled water. Here, we perform extensive free energy calculations to scrutinize the model's low-temperature phase behavior and confirm the existence of a first-order phase transition between two liquids with identical compositions but different densities. The low-density liquid (LDL) exhibits tetrahedral order, which is partially disrupted in the high-density liquid (HDL) by the intrusion of additional particles into the primary neighbor shell. Histogram reweighting methods are applied to locate conditions of HDL-LDL coexistence and the liquid spinodals that bound the two-phase region. Spontaneous liquid-liquid phase separation is also observed directly in large-scale molecular dynamics simulations performed inside the predicted two-phase region. Given its clear LLPT, we anticipate that this model may serve as a paradigm for understanding whether similar transitions occur in water and other tetrahedral liquids.

Building CHAOS: An Operating System for Livermore Linux Clusters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garlick, J E; Dunlap, C M

2003-02-21

The Livermore Computing (LC) Linux Integration and Development Project (the Linux Project) produces and supports the Clustered High Availability Operating System (CHAOS), a cluster operating environment based on Red Hat Linux. Each CHAOS release begins with a set of requirements and ends with a formally tested, packaged, and documented release suitable for use on LC's production Linux clusters. One characteristic of CHAOS is that component software packages come from different sources under varying degrees of project control. Some are developed by the Linux Project, some are developed by other LC projects, some are external open source projects, and some aremore » commercial software packages. A challenge to the Linux Project is to adhere to release schedules and testing disciplines in a diverse, highly decentralized development environment. Communication channels are maintained for externally developed packages in order to obtain support, influence development decisions, and coordinate/understand release schedules. The Linux Project embraces open source by releasing locally developed packages under open source license, by collaborating with open source projects where mutually beneficial, and by preferring open source over proprietary software. Project members generally use open source development tools. The Linux Project requires system administrators and developers to work together to resolve problems that arise in production. This tight coupling of production and development is a key strategy for making a product that directly addresses LC's production requirements. It is another challenge to balance support and development activities in such a way that one does not overwhelm the other.« less

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

PubMed

Rosen, Diane

2016-01-01

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

Least squares polynomial chaos expansion: A review of sampling strategies

NASA Astrophysics Data System (ADS)

Hadigol, Mohammad; Doostan, Alireza

2018-04-01

As non-institutive polynomial chaos expansion (PCE) techniques have gained growing popularity among researchers, we here provide a comprehensive review of major sampling strategies for the least squares based PCE. Traditional sampling methods, such as Monte Carlo, Latin hypercube, quasi-Monte Carlo, optimal design of experiments (ODE), Gaussian quadratures, as well as more recent techniques, such as coherence-optimal and randomized quadratures are discussed. We also propose a hybrid sampling method, dubbed alphabetic-coherence-optimal, that employs the so-called alphabetic optimality criteria used in the context of ODE in conjunction with coherence-optimal samples. A comparison between the empirical performance of the selected sampling methods applied to three numerical examples, including high-order PCE's, high-dimensional problems, and low oversampling ratios, is presented to provide a road map for practitioners seeking the most suitable sampling technique for a problem at hand. We observed that the alphabetic-coherence-optimal technique outperforms other sampling methods, specially when high-order ODE are employed and/or the oversampling ratio is low.

Multifractal analysis of a GCM climate

NASA Astrophysics Data System (ADS)

Carl, P.

2003-04-01

Multifractal analysis using the Wavelet Transform Modulus Maxima (WTMM) approach is being applied to the climate of a Mintz--Arakawa type, coarse resolution, two--layer AGCM. The model shows a backwards running period multiplication scenario throughout the northern summer, subsequent to a 'hard', subcritical Hopf bifurcation late in spring. This 'route out of chaos' (seen in cross sections of a toroidal phase space structure) is born in the planetary monsoon system which inflates the seasonal 'cycle' into these higher order structures and is blamed for the pronounced intraseasonal--to--centennial model climate variability. Previous analyses of the latter using advanced modal decompositions showed regularity based patterns in the time--frequency plane which are qualitatively similar to those obtained from the real world. The closer look here at the singularity structures, as a fundamental diagnostic supplement, aims at both more complete understanding (and quantification) of the model's qualitative dynamics and search for further tools of model intercomparison and verification in this respect. Analysing wavelet is the 10th derivative of the Gaussian which might suffice to suppress regular patterns in the data. Intraseasonal attractors, studied in time series of model precipitation over Central India, show shifting and braodening singularity spectra towards both more violent extreme events (premonsoon--monsoon transition) and weaker events (late summer to postmonsoon transition). Hints at a fractal basin boundary are found close to transition from period--2 to period--1 in the monsoon activity cycle. Interannual analyses are provided for runs with varied solar constants. To address the (in--)stationarity issue, first results are presented with a windowed multifractal analysis of longer--term runs ("singularity spectrogram").

Using chaos theory: the implications for nursing.

PubMed

Haigh, Carol

2002-03-01

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

Demodulation of acoustic telemetry binary phase shift keying signal based on high-order Duffing system

NASA Astrophysics Data System (ADS)

Yan, Bing-Nan; Liu, Chong-Xin; Ni, Jun-Kang; Zhao, Liang

2016-10-01

In order to grasp the downhole situation immediately, logging while drilling (LWD) technology is adopted. One of the LWD technologies, called acoustic telemetry, can be successfully applied to modern drilling. It is critical for acoustic telemetry technology that the signal is successfully transmitted to the ground. In this paper, binary phase shift keying (BPSK) is used to modulate carrier waves for the transmission and a new BPSK demodulation scheme based on Duffing chaos is investigated. Firstly, a high-order system is given in order to enhance the signal detection capability and it is realized through building a virtual circuit using an electronic workbench (EWB). Secondly, a new BPSK demodulation scheme is proposed based on the intermittent chaos phenomena of the new Duffing system. Finally, a system variable crossing zero-point equidistance method is proposed to obtain the phase difference between the system and the BPSK signal. Then it is determined that the digital signal transmitted from the bottom of the well is ‘0’ or ‘1’. The simulation results show that the demodulation method is feasible. Project supported by the National Natural Science Foundation of China (Grant No. 51177117) and the National Key Science & Technology Special Projects, China (Grant No. 2011ZX05021-005).

Effortful control and school adjustment: The moderating role of classroom chaos.

PubMed

Berger, Rebecca H; Valiente, Carlos; Eisenberg, Nancy; Hernandez, Maciel M; Thompson, Marilyn; Spinrad, Tracy; VanSchyndel, Sarah; Silva, Kassondra; Southworth, Jody

2017-11-01

Guided by the person by environment framework, the primary goal of this study was to determine whether classroom chaos moderated the relation between effortful control and kindergarteners' school adjustment. Classroom observers reported on children's ( N = 301) effortful control in the fall. In the spring, teachers reported on classroom chaos and school adjustment outcomes (teacher-student relationship closeness and conflict, and school liking and avoidance). Cross-level interactions between effortful control and classroom chaos predicting school adjustment outcomes were assessed. A consistent pattern of interactions between effortful control and classroom chaos indicated that the relations between effortful control and the school adjustment outcomes were strongest in high chaos classrooms. Post-hoc analyses indicated that classroom chaos was associated with poor school adjustment when effortful control was low, suggesting that the combination of high chaos and low effortful control was associated with the poorest school outcomes.

Agent Learning for Mixed-Initiative Knowledge Acquisition

DTIC Science & Technology

2010-02-28

philosopher of science Stephen Toulmin (1963), and the evidence professor David Schum (1987, 2001a). This approach uses expert knowledge and evidence to...Change, Forward to Ilya Prigogine and Isabelle Stengers. Order Out of Chaos: Man’s New Dialogue with Nature. Bantam Books, 1984. Toulmin , S. E., The

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

PubMed

Hirata, Yoshito; Oku, Makito; Aihara, Kazuyuki

2012-12-01

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

Galileo disposal strategy: stability, chaos and predictability

NASA Astrophysics Data System (ADS)

Rosengren, Aaron J.; Daquin, Jérôme; Tsiganis, Kleomenis; Alessi, Elisa Maria; Deleflie, Florent; Rossi, Alessandro; Valsecchi, Giovanni B.

2017-02-01

Recent studies have shown that the medium-Earth orbit (MEO) region of the global navigation satellite systems is permeated by a devious network of lunisolar secular resonances, which can interact to produce chaotic and diffusive motions. The precarious state of the four navigation constellations, perched on the threshold of instability, makes it understandable why all past efforts to define stable graveyard orbits, especially in the case of Galileo, were bound to fail; the region is far too complex to allow for an adoption of the simple geosynchronous disposal strategy. We retrace one such recent attempt, funded by ESA's General Studies Programme in the frame of the GreenOPS initiative, that uses a systematic parametric approach and the straightforward maximum-eccentricity method to identify long-term-stable regions, suitable for graveyards, as well as large-scale excursions in eccentricity, which can be used for post-mission deorbiting of constellation satellites. We then apply our new results on the stunningly rich dynamical structure of the MEO region towards the analysis of these disposal strategies for Galileo, and discuss the practical implications of resonances and chaos in this regime. We outline how the identification of the hyperbolic and elliptic fixed points of the resonances near Galileo can lead to explicit criteria for defining optimal disposal strategies.

Study of chaos in chaotic satellite systems

NASA Astrophysics Data System (ADS)

Khan, Ayub; Kumar, Sanjay

2018-01-01

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

Chaos and Order in Weakly Coupled Systems of Nonlinear Oscillators

NASA Astrophysics Data System (ADS)

Bruhn, B.

1987-01-01

We consider in this paper perturbations of two degree of freedom Hamiltonian systems which contain periodic and heteroclinic orbits. The Melnikov-Keener condition is used to proof the existence of horseshoes in the dynamics. The same condition is applied to prove a high degree of order in the motion of the swinging Atwood's machine. For some selected parameter values the theoretical predictions are checked by numerical calculations.

Moscow meltdown: Can Russia survive

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stern, J.E.

Western intelligence analysts and policy makers should pay closer attention to the centrifugal forces in Russia for two primary reasons: nuclear weapons are located in some of the most volatile regions, and central control of the armed forces is eroding. If Russia were to fragment, thousands of weapons and tons of fissile materials would be dispersed to new states with little safeguards infrastructure and little experience in controlling borders, a situation potentially far more dangerous than the breakup of the Soviet Union. Nuclear research, production, maintenance, and dismantlement facilities, plus uranium enrichment and plutonium separation facilities, could be inherited bymore » new, unstable states. Further devolution of political authority could loosen control over sensitive exports and increase the risk of terrorist acquisition of fissile materials. This article discusses the confusion over the legitimacy of the physical and political boundaries of the Russian Federation; then, the economic incentives for regionalism in Russia; next, the main ethnic groups in Russia and the roots of ethnic nationalism in the Russian Federation. It then discusses political disarray in the center and in the regions, and the lack of unity among order-enforcing entities; focuses in somewhat more detail on the Volga-Ural region, where there is a concentration of nuclear weapons and facilities, and which is especially volatile politically. These factors taken together call into question Russia's viability as a state. In post-communist Russia, chaos has replaced order; license has replaced terror. Order-enforcing entities are eviscerated or in conflict. Neither economic shock therapy nor Group of Seven funds can help with these problems; Russia will not be a state until new unifying institutions are created, whether they are democratic or authoritarian.« less

Psychotherapy Is Chaotic—(Not Only) in a Computational World

PubMed Central

Schiepek, Günter K.; Viol, Kathrin; Aichhorn, Wolfgang; Hütt, Marc-Thorsten; Sungler, Katharina; Pincus, David; Schöller, Helmut J.

2017-01-01

Objective: The aim of this article is to outline the role of chaotic dynamics in psychotherapy. Besides some empirical findings of chaos at different time scales, the focus is on theoretical modeling of change processes explaining and simulating chaotic dynamics. It will be illustrated how some common factors of psychotherapeutic change and psychological hypotheses on motivation, emotion regulation, and information processing of the client's functioning can be integrated into a comprehensive nonlinear model of human change processes. Methods: The model combines 5 variables (intensity of emotions, problem intensity, motivation to change, insight and new perspectives, therapeutic success) and 4 parameters into a set of 5 coupled nonlinear difference equations. The results of these simulations are presented as time series, as phase space embedding of these time series (i.e., attractors), and as bifurcation diagrams. Results: The model creates chaotic dynamics, phase transition-like phenomena, bi- or multi-stability, and sensibility of the dynamic patterns on parameter drift. These features are predicted by chaos theory and by Synergetics and correspond to empirical findings. The spectrum of these behaviors illustrates the complexity of psychotherapeutic processes. Conclusion: The model contributes to the development of an integrative conceptualization of psychotherapy. It is consistent with the state of scientific knowledge of common factors, as well as other psychological topics, such as: motivation, emotion regulation, and cognitive processing. The role of chaos theory is underpinned, not only in the world of computer simulations, but also in practice. In practice, chaos demands technologies capable of real-time monitoring and reporting on the nonlinear features of the ongoing process (e.g., its stability or instability). Based on this monitoring, a client-centered, continuous, and cooperative process of feedback and control becomes possible. By contrast, restricted predictability and spontaneous changes challenge the usefulness of prescriptive treatment manuals or other predefined programs of psychotherapy. PMID:28484401