Topological organization of (low-dimensional) chaos
International Nuclear Information System (INIS)
Tufillaro, N.B.
1992-01-01
Recent progress toward classifying low-dimensional chaos measured from time series data is described. This classification theory assigns a template to the time series once the time series is embedded in three dimensions. The template describes the primary folding and stretching mechanisms of phase space responsible for the chaotic motion. Topological invariants of the unstable periodic orbits in the closure of the strange set are calculated from the (reconstructed) template. These topological invariants must be consistent with ampersand ny model put forth to describe the time series data, and are useful in invalidating (or gaining confidence in) any model intended to describe the dynamical system generating the time series
Low-dimensional chaos in a hydrodynamic system
International Nuclear Information System (INIS)
Brandstater, A.; Swift, J.; Swinney, H.L.; Wolf, A.; Farmer, J.D.; Jen, E.; Crutchfield, J.P.
1983-01-01
Evidence is presented for low-dimensional strange attractors in Couette-Taylor flow data. Computations of the largest Lyapunov exponent and metric entropy show that the system displays sensitive dependence on initial conditions. Although the phase space is very high dimensional, analysis of experimental data shows that motion is restricted to an attractor of dimension less than 5 for Reynolds numbers up to 30% above the onset of chaos. The Lyapunov exponent, entropy, and dimension all generally increase with Reynolds number
Lack of evidence for low-dimensional chaos in heart rate variability
DEFF Research Database (Denmark)
Kanters, J K; Holstein-Rathlou, N H; Agner, E
1994-01-01
INTRODUCTION: The term chaos is used to describe erratic or apparently random time-dependent behavior in deterministic systems. It has been suggested that the variability observed in the normal heart rate may be due to chaos, but this question has not been settled. METHODS AND RESULTS: Heart rate...... in the experimental data, but the prediction error as a function of the prediction length increased at a slower rate than characteristic of a low-dimensional chaotic system. CONCLUSION: There is no evidence for low-dimensional chaos in the time series of RR intervals from healthy human subjects. However, nonlinear...
Detecting low-dimensional chaos by the “noise titration” technique: Possible problems and remedies
International Nuclear Information System (INIS)
Gao Jianbo; Hu Jing; Mao Xiang; Tung Wenwen
2012-01-01
Highlights: ► Distinguishing low-dimensional chaos from noise is an important issue. ► Noise titration technique is one of the main approaches on the issue. ► Problems of noise titration technique are systematically discussed. ► Solutions to the problems of noise titration technique are provided. - Abstract: Distinguishing low-dimensional chaos from noise is an important issue in time series analysis. Among the many methods proposed for this purpose is the noise titration technique, which quantifies the amount of noise that needs to be added to the signal to fully destroy its nonlinearity. Two groups of researchers recently have questioned the validity of the technique. In this paper, we report a broad range of situations where the noise titration technique fails, and offer solutions to fix the problems identified.
Yip, K.-P.; Marsh, D. J.; Holstein-Rathlou, N.-H.
1995-01-01
We applied a surrogate data technique to test for nonlinear structure in spontaneous fluctuations of hydrostatic pressure in renal tubules of hypertensive rats. Tubular pressure oscillates at 0.03-0.05 Hz in animals with normal blood pressure, but the fluctuations become irregular with chronic hypertension. Using time series from rats with hypertension we produced surrogate data sets to test whether they represent linearly correlated noise or ‘static’ nonlinear transforms of a linear stochastic process. The correlation dimension and the forecasting error were used as discriminating statistics to compare surrogate with experimental data. The results show that the original experimental time series can be distinguished from both linearly and static nonlinearly correlated noise, indicating that the nonlinear behavior is due to the intrinsic dynamics of the system. Together with other evidence this strongly suggests that a low dimensional chaotic attractor governs renal hemodynamics in hypertension. This appears to be the first demonstration of a transition to chaotic dynamics in an integrated physiological control system occurring in association with a pathological condition.
Chhabria, Karishma; Chakravarthy, V Srinivasa
2016-01-01
The motivation of developing simple minimal models for neuro-glio-vascular (NGV) system arises from a recent modeling study elucidating the bidirectional information flow within the NGV system having 89 dynamic equations (1). While this was one of the first attempts at formulating a comprehensive model for neuro-glio-vascular system, it poses severe restrictions in scaling up to network levels. On the contrary, low--dimensional models are convenient devices in simulating large networks that also provide an intuitive understanding of the complex interactions occurring within the NGV system. The key idea underlying the proposed models is to describe the glio-vascular system as a lumped system, which takes neural firing rate as input and returns an "energy" variable (analogous to ATP) as output. To this end, we present two models: biophysical neuro-energy (Model 1 with five variables), comprising KATP channel activity governed by neuronal ATP dynamics, and the dynamic threshold (Model 2 with three variables), depicting the dependence of neural firing threshold on the ATP dynamics. Both the models show different firing regimes, such as continuous spiking, phasic, and tonic bursting depending on the ATP production coefficient, ɛp, and external current. We then demonstrate that in a network comprising such energy-dependent neuron units, ɛp could modulate the local field potential (LFP) frequency and amplitude. Interestingly, low-frequency LFP dominates under low ɛp conditions, which is thought to be reminiscent of seizure-like activity observed in epilepsy. The proposed "neuron-energy" unit may be implemented in building models of NGV networks to simulate data obtained from multimodal neuroimaging systems, such as functional near infrared spectroscopy coupled to electroencephalogram and functional magnetic resonance imaging coupled to electroencephalogram. Such models could also provide a theoretical basis for devising optimal neurorehabilitation strategies, such as
Application of Chaos Theory to Engine Systems
Matsumoto, Kazuhiro; Diebner, Hans H.; Tsuda, Ichiro; Hosoi, Yukiharu
2008-01-01
We focus on the control issue for engine systems from the perspective of chaos theory, which is based on the fact that engine systems have a low-dimensional chaotic dynamics. Two approaches are discussed: controlling chaos and harnessing chaos, respectively. We apply Pyragas' chaos control method to an actual engine system. The experimental results show that the chaotic motion of an engine system may be stabilized to a periodic motion. Alternatively, harnessing chaos for engine systems is add...
Searching for chaos on low frequency
Nicolas Wesner
2004-01-01
A new method for detecting low dimensional chaos in small sample sets is presented. The method is applied to financial data on low frequency (annual and monthly) for which few observations are available.
Low-dimensional molecular metals
Toyota, Naoki; Muller, Jens
2007-01-01
Assimilating research in the field of low-dimensional metals, this monograph provides an overview of the status of research on quasi-one- and two-dimensional molecular metals, describing normal-state properties, magnetic field effects, superconductivity, and the phenomena of interacting p and d electrons.
Learning Low-Dimensional Metrics
Jain, Lalit; Mason, Blake; Nowak, Robert
2017-01-01
This paper investigates the theoretical foundations of metric learning, focused on three key questions that are not fully addressed in prior work: 1) we consider learning general low-dimensional (low-rank) metrics as well as sparse metrics; 2) we develop upper and lower (minimax)bounds on the generalization error; 3) we quantify the sample complexity of metric learning in terms of the dimension of the feature space and the dimension/rank of the underlying metric;4) we also bound the accuracy ...
International Nuclear Information System (INIS)
Ichikawa, Y.H.
1990-09-01
Plasma exhibits a full of variety of nonlinear phenomena. Active research in nonlinear plasma physics contributed to explore the concepts of soliton and chaos. Structure of soliton equations and dynamics of low dimensional Hamiltonian systems are discussed to emphasize the universality of these novel concepts in the wide branch of science and engineering. (author) 52 refs
Energy Technology Data Exchange (ETDEWEB)
Serletis, Apostolos [Department of Economics, University of Calgary, Calgary, Alta., T2N 1N4 (Canada)]. E-mail: Serletis@ucalgary.ca; Shahmoradi, Asghar [Faculty of Economics, University of Tehran, Tehran (Iran, Islamic Republic of)
2007-08-15
This paper uses monthly observations for the real exchange rate between Canada and the United States over the recent flexible exchange rate period (from January 1, 1973 to August 1, 2004) to test purchasing power parity between Canada and the United States using unit root and stationarity tests. Moreover, given the apparent random walk behavior in the real exchange rate, various tests from dynamical systems theory, such as for example, the Nychka et al. [Nychka DW, Ellner S, Ronald GA, McCaffrey D. Finding chaos in noisy systems. J Roy Stat Soc B 1992;54:399-426] chaos test, the Li [Li W. Absence of 1/f spectra in Dow Jones average. Int J Bifurcat Chaos 1991;1:583-97] self-organized criticality test, and the Hansen [Hansen, B.E. Inference when a nuisance parameter is not identified under the null hypothesis. Econometrica 1996;64:413-30] threshold effects test are used to distinguish between stochastic and deterministic origin for the real exchange rate.
International Nuclear Information System (INIS)
Serletis, Apostolos; Shahmoradi, Asghar
2007-01-01
This paper uses monthly observations for the real exchange rate between Canada and the United States over the recent flexible exchange rate period (from January 1, 1973 to August 1, 2004) to test purchasing power parity between Canada and the United States using unit root and stationarity tests. Moreover, given the apparent random walk behavior in the real exchange rate, various tests from dynamical systems theory, such as for example, the Nychka et al. [Nychka DW, Ellner S, Ronald GA, McCaffrey D. Finding chaos in noisy systems. J Roy Stat Soc B 1992;54:399-426] chaos test, the Li [Li W. Absence of 1/f spectra in Dow Jones average. Int J Bifurcat Chaos 1991;1:583-97] self-organized criticality test, and the Hansen [Hansen, B.E. Inference when a nuisance parameter is not identified under the null hypothesis. Econometrica 1996;64:413-30] threshold effects test are used to distinguish between stochastic and deterministic origin for the real exchange rate
Lecca, Paola; Mura, Ivan; Re, Angela; Barker, Gary C; Ihekwaba, Adaoha E C
2016-01-01
Chaotic behavior refers to a behavior which, albeit irregular, is generated by an underlying deterministic process. Therefore, a chaotic behavior is potentially controllable. This possibility becomes practically amenable especially when chaos is shown to be low-dimensional, i.e., to be attributable to a small fraction of the total systems components. In this case, indeed, including the major drivers of chaos in a system into the modeling approach allows us to improve predictability of the systems dynamics. Here, we analyzed the numerical simulations of an accurate ordinary differential equation model of the gene network regulating sporulation initiation in Bacillus subtilis to explore whether the non-linearity underlying time series data is due to low-dimensional chaos. Low-dimensional chaos is expectedly common in systems with few degrees of freedom, but rare in systems with many degrees of freedom such as the B. subtilis sporulation network. The estimation of a number of indices, which reflect the chaotic nature of a system, indicates that the dynamics of this network is affected by deterministic chaos. The neat separation between the indices obtained from the time series simulated from the model and those obtained from time series generated by Gaussian white and colored noise confirmed that the B. subtilis sporulation network dynamics is affected by low dimensional chaos rather than by noise. Furthermore, our analysis identifies the principal driver of the networks chaotic dynamics to be sporulation initiation phosphotransferase B (Spo0B). We then analyzed the parameters and the phase space of the system to characterize the instability points of the network dynamics, and, in turn, to identify the ranges of values of Spo0B and of the other drivers of the chaotic dynamics, for which the whole system is highly sensitive to minimal perturbation. In summary, we described an unappreciated source of complexity in the B. subtilis sporulation network by gathering
Optical properties of low-dimensional materials
Ogawa, T
1998-01-01
This book surveys recent theoretical and experimental studies of optical properties of low-dimensional materials. As an extended version of Optical Properties of Low-Dimensional Materials (Volume 1, published in 1995 by World Scientific), Volume 2 covers a wide range of interesting low-dimensional materials including both inorganic and organic systems, such as disordered polymers, deformable molecular crystals, dilute magnetic semiconductors, SiGe/Si short-period superlattices, GaAs quantum wires, semiconductor microcavities, and photonic crystals. There are excellent review articles by promis
Quantum Phenomena in Low-Dimensional Systems
Geller, Michael R.
2001-01-01
A brief summary of the physics of low-dimensional quantum systems is given. The material should be accessible to advanced physics undergraduate students. References to recent review articles and books are provided when possible.
International Nuclear Information System (INIS)
Sheridan, T.E.
2005-01-01
Chaotic dynamics is observed experimentally in a complex (dusty) plasma of three particles. A low-frequency sinusoidal modulation of the plasma density excites both the center-of-mass and breathing modes. Low-dimensional chaos is seen for a 1:2 resonance between these modes. A strange attractor with a dimension of 2.48±0.05 is observed. The largest Lyapunov exponent is positive
International Nuclear Information System (INIS)
Steiner, F.
1994-01-01
A short historical overview is given on the development of our knowledge of complex dynamical systems with special emphasis on ergodicity and chaos, and on the semiclassical quantization of integrable and chaotic systems. The general trace formular is discussed as a sound mathematical basis for the semiclassical quantization of chaos. Two conjectures are presented on the basis of which it is argued that there are unique fluctuation properties in quantum mechanics which are universal and, in a well defined sense, maximally random if the corresponding classical system is strongly chaotic. These properties constitute the quantum mechanical analogue of the phenomenon of chaos in classical mechanics. Thus quantum chaos has been found. (orig.)
International Nuclear Information System (INIS)
Mueller, B.
1997-01-01
The report contains viewgraphs on the following: ergodicity and chaos; Hamiltonian dynamics; metric properties; Lyapunov exponents; KS entropy; dynamical realization; lattice formulation; and numerical results
Energy Technology Data Exchange (ETDEWEB)
Mueller, B.
1997-09-22
The report contains viewgraphs on the following: ergodicity and chaos; Hamiltonian dynamics; metric properties; Lyapunov exponents; KS entropy; dynamical realization; lattice formulation; and numerical results.
Magnetic resonance of low dimensional magnetic solids
Energy Technology Data Exchange (ETDEWEB)
Gatteschi, D.; Ferraro, F.; Sessoli, R. (Florence Univ. (Italy))
1994-06-01
The utility of EPR and NMR in the study of low-dimensional magnetic solids is shown. A short summary of the basis of magnetic resonance in these systems is reported, and the importance of spin-diffusion and magnetic anisotropy evidenced. Some results from experiments on metal-radical chains and clusters are presented. (authors). 37 refs., 7 figs.
Magnetic resonance of low dimensional magnetic solids
International Nuclear Information System (INIS)
Gatteschi, D.; Ferraro, F.; Sessoli, R.
1994-01-01
The utility of EPR and NMR in the study of low-dimensional magnetic solids is shown. A short summary of the basis of magnetic resonance in these systems is reported, and the importance of spin-diffusion and magnetic anisotropy evidenced. Some results from experiments on metal-radical chains and clusters are presented. (authors). 37 refs., 7 figs
Physics of low-dimensional systems
International Nuclear Information System (INIS)
Anon.
1989-01-01
The physics of low-dimensional systems has developed in a remarkable way over the last decade and has accelerated over the last few years, in particular because of the discovery of the new high temperature superconductors. The new developments started more than fifteen years ago with the discovery of the unexpected quasi-one-dimensional character of the TTF-TCNQ. Since then the field of conducting quasi-one-dimensional organic system have been rapidly growing. Parallel to the experimental work there has been an important theoretical development of great conceptual importance, such as charge density waves, soliton-like excitations, fractional charges, new symmetry properties etc. A new field of fundamental importance was the discovery of the Quantum Hall Effect in 1980. This field is still expanding with new experimental and theoretical discoveries. In 1986, then, came the totally unexpected discovery of high temperature superconductivity which started an explosive development. The three areas just mentioned formed the main themes of the Symposium. They do not in any way exhaust the progress in low-dimensional physics. We should mention the recent important development with both two-dimensional and one-dimensional and even zero-dimensional structures (quantum dots). The physics of mesoscopic systems is another important area where the low dimensionality is a key feature. Because of the small format of this Symposium we could unfortunately not cover these areas
Chaos in plasma simulation and experiment
International Nuclear Information System (INIS)
Watts, C.; Sprott, J.C.
1993-09-01
We investigate the possibility that chaos and simple determinism are governing the dynamics of reversed field pinch (RFP) plasmas using data from both numerical simulations and experiment. A large repertoire of nonlinear analysis techniques is used to identify low dimensional chaos. These tools include phase portraits and Poincard sections, correlation dimension, the spectrum of Lyapunov exponents and short term predictability. In addition, nonlinear noise reduction techniques are applied to the experimental data in an attempt to extract any underlying deterministic dynamics. Two model systems are used to simulate the plasma dynamics. These are -the DEBS code, which models global RFP dynamics, and the dissipative trapped electron mode (DTEM) model, which models drift wave turbulence. Data from both simulations show strong indications of low,dimensional chaos and simple determinism. Experimental data were obtained from the Madison Symmetric Torus RFP and consist of a wide array of both global and local diagnostic signals. None of the signals shows any indication of low dimensional chaos or other simple determinism. Moreover, most of the analysis tools indicate the experimental system is very high dimensional with properties similar to noise. Nonlinear noise reduction is unsuccessful at extracting an underlying deterministic system
Chaos in plasma simulation and experiment
Energy Technology Data Exchange (ETDEWEB)
Watts, C. [Texas Univ., Austin, TX (United States). Fusion Research Center; Newman, D.E. [Oak Ridge National Lab., TN (United States); Sprott, J.C. [Wisconsin Univ., Madison, WI (United States). Plasma Physics Research
1993-09-01
We investigate the possibility that chaos and simple determinism are governing the dynamics of reversed field pinch (RFP) plasmas using data from both numerical simulations and experiment. A large repertoire of nonlinear analysis techniques is used to identify low dimensional chaos. These tools include phase portraits and Poincard sections, correlation dimension, the spectrum of Lyapunov exponents and short term predictability. In addition, nonlinear noise reduction techniques are applied to the experimental data in an attempt to extract any underlying deterministic dynamics. Two model systems are used to simulate the plasma dynamics. These are -the DEBS code, which models global RFP dynamics, and the dissipative trapped electron mode (DTEM) model, which models drift wave turbulence. Data from both simulations show strong indications of low,dimensional chaos and simple determinism. Experimental data were obtained from the Madison Symmetric Torus RFP and consist of a wide array of both global and local diagnostic signals. None of the signals shows any indication of low dimensional chaos or other simple determinism. Moreover, most of the analysis tools indicate the experimental system is very high dimensional with properties similar to noise. Nonlinear noise reduction is unsuccessful at extracting an underlying deterministic system.
Hunt, Brian R; Ott, Edward
2015-09-01
In this paper, we propose, discuss, and illustrate a computationally feasible definition of chaos which can be applied very generally to situations that are commonly encountered, including attractors, repellers, and non-periodically forced systems. This definition is based on an entropy-like quantity, which we call "expansion entropy," and we define chaos as occurring when this quantity is positive. We relate and compare expansion entropy to the well-known concept of topological entropy to which it is equivalent under appropriate conditions. We also present example illustrations, discuss computational implementations, and point out issues arising from attempts at giving definitions of chaos that are not entropy-based.
Low dimensional modeling of wall turbulence
Aubry, Nadine
2015-11-01
In this talk we will review the original low dimensional dynamical model of the wall region of a turbulent boundary layer [Aubry, Holmes, Lumley and Stone, Journal of Fluid Dynamics 192, 1988] and discuss its impact on the field of fluid dynamics. We will also invite a few researchers who would like to make brief comments on the influence Lumley had on their research paths. In collaboration with Philip Holmes, Program in Applied and Computational Mathematics and Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ.
An introduction to chaos theory in CFD
Pulliam, Thomas H.
1990-01-01
The popular subject 'chaos theory' has captured the imagination of a wide variety of scientists and engineers. CFD has always been faced with nonlinear systems and it is natural to assume that nonlinear dynamics will play a role at sometime in such work. This paper will attempt to introduce some of the concepts and analysis procedures associated with nonlinear dynamics theory. In particular, results from computations of an airfoil at high angle of attack which exhibits a sequence of bifurcations for single frequency unsteady shedding through period doublings cascading into low dimensional chaos are used to present and demonstrate various aspects of nonlinear dynamics in CFD.
Chaos in an imperfectly premixed model combustor.
Kabiraj, Lipika; Saurabh, Aditya; Karimi, Nader; Sailor, Anna; Mastorakos, Epaminondas; Dowling, Ann P; Paschereit, Christian O
2015-02-01
This article reports nonlinear bifurcations observed in a laboratory scale, turbulent combustor operating under imperfectly premixed mode with global equivalence ratio as the control parameter. The results indicate that the dynamics of thermoacoustic instability correspond to quasi-periodic bifurcation to low-dimensional, deterministic chaos, a route that is common to a variety of dissipative nonlinear systems. The results support the recent identification of bifurcation scenarios in a laminar premixed flame combustor (Kabiraj et al., Chaos: Interdiscip. J. Nonlinear Sci. 22, 023129 (2012)) and extend the observation to a practically relevant combustor configuration.
Nee, Sean
2018-05-01
Survival analysis in biology and reliability theory in engineering concern the dynamical functioning of bio/electro/mechanical units. Here we incorporate effects of chaotic dynamics into the classical theory. Dynamical systems theory now distinguishes strong and weak chaos. Strong chaos generates Type II survivorship curves entirely as a result of the internal operation of the system, without any age-independent, external, random forces of mortality. Weak chaos exhibits (a) intermittency and (b) Type III survivorship, defined as a decreasing per capita mortality rate: engineering explicitly defines this pattern of decreasing hazard as 'infant mortality'. Weak chaos generates two phenomena from the normal functioning of the same system. First, infant mortality- sensu engineering-without any external explanatory factors, such as manufacturing defects, which is followed by increased average longevity of survivors. Second, sudden failure of units during their normal period of operation, before the onset of age-dependent mortality arising from senescence. The relevance of these phenomena encompasses, for example: no-fault-found failure of electronic devices; high rates of human early spontaneous miscarriage/abortion; runaway pacemakers; sudden cardiac death in young adults; bipolar disorder; and epilepsy.
An efficient chaos embedded hybrid approach for hydro-thermal unit commitment problem
International Nuclear Information System (INIS)
Yuan, Xiaohui; Ji, Bin; Yuan, Yanbin; Ikram, Rana M.; Zhang, Xiaopan; Huang, Yuehua
2015-01-01
Highlights: • Thermal unit commitment is considered in hydrothermal generation scheduling (SHTGS). • Two newly proposed promising optimization algorithms are combined to solving SHTGS. • The proposed method is enhanced by integrating a chaotic local search strategy. • Heuristic search strategies are applied to handle the constraints of the SHTGS. • The results verify the proposed method is feasible and efficient for handling SHTGS. - Abstract: This paper establishes a model to deal with the short-term hydrothermal generation scheduling (SHTGS) problem. The problem is composed of three interconnected parts: short-term hydrothermal coordination, thermal unit commitment and economic load dispatch. An efficient hybrid method composed of chaotic backtracking search optimization algorithm and binary charged system search algorithm (CBSA–BCSS) is proposed to solve this problem. In order to analyze the effect of the chaotic map on the performance of the method, three different chaotic maps are adopted to integrate into the proposed method and the corresponding consequences are achieved. Furthermore, efficient heuristic search strategies are adopted to handle with the complicated constraints of the SHTGS system. Finally, a hydrothermal unit commitment system is utilized to verify the feasibility and effectiveness of the proposed method. The results demonstrate the efficiency of the hybrid optimization method and the appropriation of the constraint handling strategies. The comparison of the solutions achieved by different methods shows that the proposed method has higher efficiency in terms of solving SHTGS problem
International Nuclear Information System (INIS)
Cejnar, P.
2007-01-01
Chaos is a name given in physics to a branch which, within classical mechanics, studies the consequences of sensitive dependences of the behavior of physical systems on the starting conditions, i.e., the 'butterfly wing effect'. However, how to describe chaotic behavior in the world of quantum particles? It appears that quantum mechanics does not admit the sensitive dependence on the starting conditions, and moreover, predicts a substantial suppression of chaos also at the macroscopic level. Still, the quantum properties of systems that are chaotic in terms of classical mechanics differ basically from the properties of classically arranged systems. This topic is studied by a field of physics referred to as quantum chaos. (author)
A low dimensional dynamical system for the wall layer
Aubry, N.; Keefe, L. R.
1987-01-01
Low dimensional dynamical systems which model a fully developed turbulent wall layer were derived.The model is based on the optimally fast convergent proper orthogonal decomposition, or Karhunen-Loeve expansion. This decomposition provides a set of eigenfunctions which are derived from the autocorrelation tensor at zero time lag. Via Galerkin projection, low dimensional sets of ordinary differential equations in time, for the coefficients of the expansion, were derived from the Navier-Stokes equations. The energy loss to the unresolved modes was modeled by an eddy viscosity representation, analogous to Heisenberg's spectral model. A set of eigenfunctions and eigenvalues were obtained from direct numerical simulation of a plane channel at a Reynolds number of 6600, based on the mean centerline velocity and the channel width flow and compared with previous work done by Herzog. Using the new eigenvalues and eigenfunctions, a new ten dimensional set of ordinary differential equations were derived using five non-zero cross-stream Fourier modes with a periodic length of 377 wall units. The dynamical system was integrated for a range of the eddy viscosity prameter alpha. This work is encouraging.
Indian Academy of Sciences (India)
It lurks in the fluctuations of stock prices. ... This attracting ellipse, on which the motion ... 'strange' because it is both attracting and chaotic (Box 2). .... the low dimensional state space, wind around forever without intersecting itself or closing on ...
Anticipatory synchronization via low-dimensional filters
International Nuclear Information System (INIS)
Pyragiene, T.; Pyragas, K.
2017-01-01
An anticipatory chaotic synchronization scheme based on a low-order all-pass filter is proposed. The filter is designed as a Padé approximation to the transfer function of an ideal delay line, which is used in a standard Voss scheme. We show that despite its simplicity, the filter works in an anticipatory scheme as well as an ideal delay line. It provides extremely small synchronization error in the whole interval of anticipation time where the anticipatory manifold is stable. The efficacy of our scheme is explained by an analytically solvable model of unidirectionally coupled unstable spirals and confirmed numerically by an example of unidirectionally coupled chaotic Rössler systems. - Highlights: • A new coupling scheme for anticipating chaotic synchronization is proposed. • The scheme consists of a drive system coupled to a low-dimensional filter. • Long-term anticipation is achieved without using time-delay terms. • An analytical treatment estimates the maximum anticipation time. • The method is verified for the Rössler system.
Anticipatory synchronization via low-dimensional filters
Energy Technology Data Exchange (ETDEWEB)
Pyragiene, T., E-mail: tatjana.pyragiene@ftmc.lt; Pyragas, K.
2017-06-15
An anticipatory chaotic synchronization scheme based on a low-order all-pass filter is proposed. The filter is designed as a Padé approximation to the transfer function of an ideal delay line, which is used in a standard Voss scheme. We show that despite its simplicity, the filter works in an anticipatory scheme as well as an ideal delay line. It provides extremely small synchronization error in the whole interval of anticipation time where the anticipatory manifold is stable. The efficacy of our scheme is explained by an analytically solvable model of unidirectionally coupled unstable spirals and confirmed numerically by an example of unidirectionally coupled chaotic Rössler systems. - Highlights: • A new coupling scheme for anticipating chaotic synchronization is proposed. • The scheme consists of a drive system coupled to a low-dimensional filter. • Long-term anticipation is achieved without using time-delay terms. • An analytical treatment estimates the maximum anticipation time. • The method is verified for the Rössler system.
Low Dimensionality Effects in Complex Magnetic Oxides
Kelley, Paula J. Lampen
Complex magnetic oxides represent a unique intersection of immense technological importance and fascinating physical phenomena originating from interwoven structural, electronic and magnetic degrees of freedom. The resulting energetically close competing orders can be controllably selected through external fields. Competing interactions and disorder represent an additional opportunity to systematically manipulate the properties of pure magnetic systems, leading to frustration, glassiness, and other novel phenomena while finite sample dimension plays a similar role in systems with long-range cooperative effects or large correlation lengths. A rigorous understanding of these effects in strongly correlated oxides is key to manipulating their functionality and device performance, but remains a challenging task. In this dissertation, we examine a number of problems related to intrinsic and extrinsic low dimensionality, disorder, and competing interactions in magnetic oxides by applying a unique combination of standard magnetometry techniques and unconventional magnetocaloric effect and transverse susceptibility measurements. The influence of dimensionality and disorder on the nature and critical properties of phase transitions in manganites is illustrated in La0.7 Ca0.3MnO3, in which both size reduction to the nanoscale and chemically-controlled quenched disorder are observed to induce a progressive weakening of the first-order nature of the transition, despite acting through the distinct mechanisms of surface effects and site dilution. In the second-order material La0.8Ca0.2MnO3, a strong magnetic field is found to drive the system toward its tricritical point as competition between exchange interactions in the inhomogeneous ground state is suppressed. In the presence of large phase separation stabilized by chemical disorder and long-range strain, dimensionality has a profound effect. With the systematic reduction of particle size in microscale-phase-separated (La, Pr
2005-01-01
[figure removed for brevity, see original site] Context image for PIA03200 Iani Chaos This VIS image of Iani Chaos shows the layered deposit that occurs on the floor. It appears that the layers were deposited after the chaos was formed. Image information: VIS instrument. Latitude 2.3S, Longitude 342.3E. 17 meter/pixel resolution. Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time. NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.
Quantum Fluctuations of Low Dimensional Bose-Einstein ...
African Journals Online (AJOL)
A system of low dimensional condensed ultracold atomic gases inside a field of a laser-driven optical cavity exhibits dispersive optical bistability. During such a process the system also shows quantum fluctuations. Condensate fluctuations are highly manifested particularly in low dimensional systems. In this paper we have ...
On the efficiency of chaos optimization algorithms for global optimization
International Nuclear Information System (INIS)
Yang Dixiong; Li Gang; Cheng Gengdong
2007-01-01
Chaos optimization algorithms as a novel method of global optimization have attracted much attention, which were all based on Logistic map. However, we have noticed that the probability density function of the chaotic sequences derived from Logistic map is a Chebyshev-type one, which may affect the global searching capacity and computational efficiency of chaos optimization algorithms considerably. Considering the statistical property of the chaotic sequences of Logistic map and Kent map, the improved hybrid chaos-BFGS optimization algorithm and the Kent map based hybrid chaos-BFGS algorithm are proposed. Five typical nonlinear functions with multimodal characteristic are tested to compare the performance of five hybrid optimization algorithms, which are the conventional Logistic map based chaos-BFGS algorithm, improved Logistic map based chaos-BFGS algorithm, Kent map based chaos-BFGS algorithm, Monte Carlo-BFGS algorithm, mesh-BFGS algorithm. The computational performance of the five algorithms is compared, and the numerical results make us question the high efficiency of the chaos optimization algorithms claimed in some references. It is concluded that the efficiency of the hybrid optimization algorithms is influenced by the statistical property of chaotic/stochastic sequences generated from chaotic/stochastic algorithms, and the location of the global optimum of nonlinear functions. In addition, it is inappropriate to advocate the high efficiency of the global optimization algorithms only depending on several numerical examples of low-dimensional functions
Energy Technology Data Exchange (ETDEWEB)
Bohigas, Oriol [Laboratoire de Physique Theorique et Modeles Statistiques, Orsay (France)
2005-04-18
Are there quantum signatures, for instance in the spectral properties, of the underlying regular or chaotic nature of the corresponding classical motion? Are there universality classes? Within this framework the merging of two at first sight seemingly disconnected fields, namely random matrix theories (RMT) and quantum chaos (QC), is briefly described. Periodic orbit theory (POT) plays a prominent role. Emphasis is given to compound nucleus resonances and binding energies, whose shell effects are examined from this perspective. Several aspects are illustrated with Riemann's {zeta}-function, which has become a testing ground for RMT, QC, POT, and their relationship.
International Nuclear Information System (INIS)
Bohigas, Oriol
2005-01-01
Are there quantum signatures, for instance in the spectral properties, of the underlying regular or chaotic nature of the corresponding classical motion? Are there universality classes? Within this framework the merging of two at first sight seemingly disconnected fields, namely random matrix theories (RMT) and quantum chaos (QC), is briefly described. Periodic orbit theory (POT) plays a prominent role. Emphasis is given to compound nucleus resonances and binding energies, whose shell effects are examined from this perspective. Several aspects are illustrated with Riemann's ζ-function, which has become a testing ground for RMT, QC, POT, and their relationship
Chaos in reversed-field-pinch plasma simulation and experiment
International Nuclear Information System (INIS)
Watts, C.; Newman, D.E.; Sprott, J.C.
1994-01-01
We investigate the possibility that chaos and simple determinism are governing the dynamics of reversed-field-pinch (RFP) plasmas using data from both numerical simulations and experiment. A large repertoire of nonlinear-analysis techniques is used to identify low-dimensional chaos. These tools include phase portraits and Poincare sections, correlation dimension, the spectrum of Lyapunov exponents, and short-term predictability. In addition, nonlinear-noise-reduction techniques are applied to the experimental data in an attempt to extract any underlying deterministic dynamics. Two model systems are used to simulate the plasma dynamics. These are the DEBS computer code, which models global RFP dynamics, and the dissipative trapped-electron-mode model, which models drift-wave turbulence. Data from both simulations show strong indications of low-dimensional chaos and simple determinism. Experimental data were obtained from the Madison Symmetric Torus RFP and consist of a wide array of both global and local diagnostic signals. None of the signals shows any indication of low-dimensional chaos or other simple determinism. Moreover, most of the analysis tools indicate that the experimental system is very high dimensional with properties similar to noise. Nonlinear noise reduction is unsuccessful at extracting an underlying deterministic system
Mechanical properties of low dimensional materials
Saini, Deepika
Recent advances in low dimensional materials (LDMs) have paved the way for unprecedented technological advancements. The drive to reduce the dimensions of electronics has compelled researchers to devise newer techniques to not only synthesize novel materials, but also tailor their properties. Although micro and nanomaterials have shown phenomenal electronic properties, their mechanical robustness and a thorough understanding of their structure-property relationship are critical for their use in practical applications. However, the challenges in probing these mechanical properties dramatically increase as their dimensions shrink, rendering the commonly used techniques inadequate. This dissertation focuses on developing techniques for accurate determination of elastic modulus of LDMs and their mechanical responses under tensile and shear stresses. Fibers with micron-sized diameters continuously undergo tensile and shear deformations through many phases of their processing and applications. Significant attention has been given to their tensile response and their structure-tensile properties relations are well understood, but the same cannot be said about their shear responses or the structure-shear properties. This is partly due to the lack of appropriate instruments that are capable of performing direct shear measurements. In an attempt to fill this void, this dissertation describes the design of an inexpensive tabletop instrument, referred to as the twister, which can measure the shear modulus (G) and other longitudinal shear properties of micron-sized individual fibers. An automated system applies a pre-determined twist to the fiber sample and measures the resulting torque using a sensitive optical detector. The accuracy of the instrument was verified by measuring G for high purity copper and tungsten fibers. Two industrially important fibers, IM7 carbon fiber and KevlarRTM 119, were found to have G = 17 and 2.4 GPa, respectively. In addition to measuring the shear
The bane of low-dimensionality clustering
DEFF Research Database (Denmark)
Cohen-Addad, Vincent; de Mesmay, Arnaud; Rotenberg, Eva
2018-01-01
geometric problems such as the traveling salesman problem, or computing an independent set of unit spheres. While these problems benefit from the so-called (limited) blessing of dimensionality, as they can be solved in time nO(k1--1/d) or 2
Control of collective network chaos.
Wagemakers, Alexandre; Barreto, Ernest; Sanjuán, Miguel A F; So, Paul
2014-06-01
Under certain conditions, the collective behavior of a large globally-coupled heterogeneous network of coupled oscillators, as quantified by the macroscopic mean field or order parameter, can exhibit low-dimensional chaotic behavior. Recent advances describe how a small set of "reduced" ordinary differential equations can be derived that captures this mean field behavior. Here, we show that chaos control algorithms designed using the reduced equations can be successfully applied to imperfect realizations of the full network. To systematically study the effectiveness of this technique, we measure the quality of control as we relax conditions that are required for the strict accuracy of the reduced equations, and hence, the controller. Although the effects are network-dependent, we show that the method is effective for surprisingly small networks, for modest departures from global coupling, and even with mild inaccuracy in the estimate of network heterogeneity.
2002-01-01
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.
Quantum Fluctuations of Low Dimensional Bose-Einstein ...
African Journals Online (AJOL)
Tadesse
that low dimensional quantum gases exhibit not only highly fascinating .... 2009; Marquardt and Girvin, 2009; Law, 1995; Vitali et al., 2007). ... ideal playground to test correlations between light and mesoscopic objects, to understand the.
Hyperchaos and chaotic hierarchy in low-dimensional chemical systems
Baier, Gerold; Sahle, Sven
1994-06-01
Chemical reaction chains with feedback of one of the products on the source of the chain are considered. A strategy is presented in terms of ordinary differential equations which creates one, two, and three positive Lyapunov exponents as the finite dimension of the system is increased. In particular, a nonlinear inhibition loop in a chemical reaction sequence controls the type of chaos. The bifurcation scenarios are studied and chaos and hyperchaos are found for broad regions of bifurcation parameter. Some implications for the occurrence of higher chaos in real systems are discussed.
Common phase diagram for low-dimensional superconductors
International Nuclear Information System (INIS)
Michalak, Rudi
2003-01-01
A phenomenological phase diagram which has been derived for high-temperature superconductors from NMR Knight-shift measurements of the pseudogap is compared to the phase diagram that is obtained for organic superconductors and spin-ladder superconductors, both low-dimensional systems. This is contrasted to the phase diagram of some Heavy Fermion superconductors, i.e. superconductors not constrained to a low dimensionality
CT Image Reconstruction in a Low Dimensional Manifold
Cong, Wenxiang; Wang, Ge; Yang, Qingsong; Hsieh, Jiang; Li, Jia; Lai, Rongjie
2017-01-01
Regularization methods are commonly used in X-ray CT image reconstruction. Different regularization methods reflect the characterization of different prior knowledge of images. In a recent work, a new regularization method called a low-dimensional manifold model (LDMM) is investigated to characterize the low-dimensional patch manifold structure of natural images, where the manifold dimensionality characterizes structural information of an image. In this paper, we propose a CT image reconstruc...
PREFACE: Dynamics of low-dimensional systems Dynamics of low-dimensional systems
Bernasconi, M.; Miret-Artés, S.; Toennies, J. P.
2012-03-01
With the development of techniques for high-resolution inelastic helium atom scattering (HAS), electron scattering (EELS) and neutron spin echo spectroscopy, it has become possible, within approximately the last thirty years, to measure the dispersion curves of surface phonons in insulators, semiconductors and metals. In recent years, the advent of new experimental techniques such as 3He spin-echo spectroscopy, scanning inelastic electron tunnel spectroscopy, inelastic x-ray scattering spectroscopy and inelastic photoemission have extended surface phonon spectroscopy to a variety of systems. These include ultra-thin metal films, adsorbates at surface and elementary processes where surface phonons play an important role. Other important directions have been actively pursued in the past decade: the dynamics of stepped surfaces and clusters grown on metal surfaces, due to their relevance in many dynamical and chemical processes at surfaces, including heterogeneous catalysis; clusters; diffusion etc. The role of surface effects in these processes has been conjectured since the early days of surface dynamics, although only now is the availability of ab initio approaches providing those conjectures with a microscopic basis. Last but not least, the investigation of non-adiabatic effects, originating for instance from the hybridization (avoided crossing) of the surface phonons branches with the quasi 1D electron-hole excitation branch, is also a challenging new direction. Furthermore, other elementary oscillations such as surface plasmons are being actively investigated. The aforementioned experimental breakthroughs have been accompanied by advances in the theoretical study of atom-surface interaction. In particular, in the past decade first principles calculations based on density functional perturbation theory have boosted the theoretical study of the dynamics of low-dimensional systems. Phonon dispersion relations of clean surfaces, the dynamics of adsorbates, and the
Symbolic dynamics of noisy chaos
Energy Technology Data Exchange (ETDEWEB)
Crutchfield, J P; Packard, N H
1983-05-01
One model of randomness observed in physical systems is that low-dimensional deterministic chaotic attractors underly the observations. A phenomenological theory of chaotic dynamics requires an accounting of the information flow fromthe observed system to the observer, the amount of information available in observations, and just how this information affects predictions of the system's future behavior. In an effort to develop such a description, the information theory of highly discretized observations of random behavior is discussed. Metric entropy and topological entropy are well-defined invariant measures of such an attractor's level of chaos, and are computable using symbolic dynamics. Real physical systems that display low dimensional dynamics are, however, inevitably coupled to high-dimensional randomness, e.g. thermal noise. We investigate the effects of such fluctuations coupled to deterministic chaotic systems, in particular, the metric entropy's response to the fluctuations. It is found that the entropy increases with a power law in the noise level, and that the convergence of the entropy and the effect of fluctuations can be cast as a scaling theory. It is also argued that in addition to the metric entropy, there is a second scaling invariant quantity that characterizes a deterministic system with added fluctuations: I/sub 0/, the maximum average information obtainable about the initial condition that produces a particular sequence of measurements (or symbols). 46 references, 14 figures, 1 table.
2003-01-01
[figure removed for brevity, see original site] Released 11 November 2003Aureum Chaos is a large crater that was filled with sediment after its formation. After the infilling of sediment, something occurred that caused the sediment to be broken up into large, slumped blocks and smaller knobs. Currently, it is believed that the blocks and knobs form when material is removed from the subsurface, creating void space. Subsurface ice was probably heated, and the water burst out to the surface, maybe forming a temporary lake. Other areas of chaos terrain have large outflow channels that emanate from them, indicating that a tremendous amount of water was released.Image information: VIS instrument. Latitude -3.2, Longitude 331 East (29 West). 19 meter/pixel resolution.Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time. NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.
2003-01-01
[figure removed for brevity, see original site] At the easternmost end of Valles Marineris, a rugged, jumbled terrain known as chaos displays a stratigraphy that could be described as precarious. Perched on top of the jumbled blocks is another layer of sedimentary material that is in the process of being eroded off the top. This material is etched by the wind into yardangs before it ultimately is stripped off to reveal the existing chaos.Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time.NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.Image information: VIS instrument. Latitude -7.8, Longitude 19.1 East (340.9 West). 19 meter/pixel resolution.
Quantum signatures of chaos or quantum chaos?
Energy Technology Data Exchange (ETDEWEB)
Bunakov, V. E., E-mail: bunakov@VB13190.spb.edu [St. Petersburg State University (Russian Federation)
2016-11-15
A critical analysis of the present-day concept of chaos in quantum systems as nothing but a “quantum signature” of chaos in classical mechanics is given. In contrast to the existing semi-intuitive guesses, a definition of classical and quantum chaos is proposed on the basis of the Liouville–Arnold theorem: a quantum chaotic system featuring N degrees of freedom should have M < N independent first integrals of motion (good quantum numbers) specified by the symmetry of the Hamiltonian of the system. Quantitative measures of quantum chaos that, in the classical limit, go over to the Lyapunov exponent and the classical stability parameter are proposed. The proposed criteria of quantum chaos are applied to solving standard problems of modern dynamical chaos theory.
Quantum signatures of chaos or quantum chaos?
International Nuclear Information System (INIS)
Bunakov, V. E.
2016-01-01
A critical analysis of the present-day concept of chaos in quantum systems as nothing but a “quantum signature” of chaos in classical mechanics is given. In contrast to the existing semi-intuitive guesses, a definition of classical and quantum chaos is proposed on the basis of the Liouville–Arnold theorem: a quantum chaotic system featuring N degrees of freedom should have M < N independent first integrals of motion (good quantum numbers) specified by the symmetry of the Hamiltonian of the system. Quantitative measures of quantum chaos that, in the classical limit, go over to the Lyapunov exponent and the classical stability parameter are proposed. The proposed criteria of quantum chaos are applied to solving standard problems of modern dynamical chaos theory.
Dynamic colloidal assembly pathways via low dimensional models
Energy Technology Data Exchange (ETDEWEB)
Yang, Yuguang; Bevan, Michael A., E-mail: mabevan@jhu.edu [Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, Maryland 21218 (United States); Thyagarajan, Raghuram; Ford, David M. [Chemical Engineering, University of Massachusetts, Amherst, Massachusetts 01003 (United States)
2016-05-28
Here we construct a low-dimensional Smoluchowski model for electric field mediated colloidal crystallization using Brownian dynamic simulations, which were previously matched to experiments. Diffusion mapping is used to infer dimensionality and confirm the use of two order parameters, one for degree of condensation and one for global crystallinity. Free energy and diffusivity landscapes are obtained as the coefficients of a low-dimensional Smoluchowski equation to capture the thermodynamics and kinetics of microstructure evolution. The resulting low-dimensional model quantitatively captures the dynamics of different assembly pathways between fluid, polycrystal, and single crystals states, in agreement with the full N-dimensional data as characterized by first passage time distributions. Numerical solution of the low-dimensional Smoluchowski equation reveals statistical properties of the dynamic evolution of states vs. applied field amplitude and system size. The low-dimensional Smoluchowski equation and associated landscapes calculated here can serve as models for predictive control of electric field mediated assembly of colloidal ensembles into two-dimensional crystalline objects.
2002-01-01
[figure removed for brevity, see original site] Collapsed terrain in Hydapsis Chaos.This is the source terrain for several outflow channels. Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time.NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.VIS Instrument. Latitude 3.2, Longitude 333.2 East. 19 meter/pixel resolution.
Huwe, Terence K.
2009-01-01
"Embracing the chaos" is an ongoing challenge for librarians. Embracing the chaos means librarians must have a plan for responding to the flood of new products, widgets, web tools, and gizmos that students use daily. In this article, the author argues that library instruction and access services have been grappling with that chaos with…
Scientific data interpolation with low dimensional manifold model
Zhu, Wei; Wang, Bao; Barnard, Richard; Hauck, Cory D.; Jenko, Frank; Osher, Stanley
2018-01-01
We propose to apply a low dimensional manifold model to scientific data interpolation from regular and irregular samplings with a significant amount of missing information. The low dimensionality of the patch manifold for general scientific data sets has been used as a regularizer in a variational formulation. The problem is solved via alternating minimization with respect to the manifold and the data set, and the Laplace-Beltrami operator in the Euler-Lagrange equation is discretized using the weighted graph Laplacian. Various scientific data sets from different fields of study are used to illustrate the performance of the proposed algorithm on data compression and interpolation from both regular and irregular samplings.
Scientific data interpolation with low dimensional manifold model
International Nuclear Information System (INIS)
Zhu, Wei; Wang, Bao; Barnard, Richard C.; Hauck, Cory D.
2017-01-01
Here, we propose to apply a low dimensional manifold model to scientific data interpolation from regular and irregular samplings with a significant amount of missing information. The low dimensionality of the patch manifold for general scientific data sets has been used as a regularizer in a variational formulation. The problem is solved via alternating minimization with respect to the manifold and the data set, and the Laplace–Beltrami operator in the Euler–Lagrange equation is discretized using the weighted graph Laplacian. Various scientific data sets from different fields of study are used to illustrate the performance of the proposed algorithm on data compression and interpolation from both regular and irregular samplings.
Quantum confinement effects in low-dimensional systems
Indian Academy of Sciences (India)
2015-06-03
Jun 3, 2015 ... Quantum confinement effects in low-dimensional systems. Figure 5. (a) Various cuts of the three-dimensional data showing energy vs. momen- tum dispersion relations for Ag film of 17 ML thickness on Ge(111). (b) Photo- emission intensity maps along ¯M– ¯ – ¯K direction. (c) Substrate bands replotted ...
Low-dimensional chaotic attractors in drift wave turbulence
International Nuclear Information System (INIS)
Persson, M.; Nordman, H.
1991-01-01
Simulation results of toroidal η i -mode turbulence are analyzed using mathematical tools of nonlinear dynamics. Low-dimensional chaotic attractors are found in the strongly nonlinear regime while in the weakly interacting regime the dynamics is high dimensional. In both regimes, the solutions are found to display sensitive dependence on initial conditions, characterized by a positive largest Liapunov exponent. (au)
Shape control synthesis of low-dimensional calcium sulfate
Indian Academy of Sciences (India)
Shape control synthesis of low-dimensional calcium sulfate .... C in mixed solvents of 50 mL ethanol and 30 mL water for different reaction times was characterized by .... Duan X, Huang Y, Cui Y, Wang J and Lieber C M 2001 Nature 409 66.
Confinement Effects in Low-Dimensional Lead Iodide Perovskite Hybrids
Kamminga, Machteld E.; Fang, Honghua; Filip, Marina R.; Giustino, Feliciano; Baas, Jacobus; Blake, Graeme R.; Loi, Maria Antonietta; Palstra, Thomas T. M.
2016-01-01
We use a layered solution crystal growth technique to synthesize high-quality single crystals of phenylalkylammonium lead iodide organic/inorganic hybrid compounds. Single-crystal X-ray diffraction reveals low-dimensional structures consisting of inorganic sheets separated by bilayers of the organic
Neutron scattering studies of low dimensional magnetic systems
DEFF Research Database (Denmark)
Hansen, Ursula Bengård
investigated at low temperaturesand in a longitudinal magnetic eld using neutron spectroscopy. Here we observe thehybridisation of the magnon bound states, inherent to the low dimensional nature ofCoCl2 · 2D2O.At higher temperature, signatures which can be attributed to Magnetic Bloch Oscillationsis observed...
2004-01-01
[figure removed for brevity, see original site] Released 7 May 2004 This daytime visible color image was collected on May 30, 2002 during the Southern Fall season in Atlantis Chaos. The THEMIS VIS camera is capable of capturing color images of the martian surface using its five different color filters. In this mode of operation, the spatial resolution and coverage of the image must be reduced to accommodate the additional data volume produced from the use of multiple filters. To make a color image, three of the five filter images (each in grayscale) are selected. Each is contrast enhanced and then converted to a red, green, or blue intensity image. These three images are then combined to produce a full color, single image. Because the THEMIS color filters don't span the full range of colors seen by the human eye, a color THEMIS image does not represent true color. Also, because each single-filter image is contrast enhanced before inclusion in the three-color image, the apparent color variation of the scene is exaggerated. Nevertheless, the color variation that does appear is representative of some change in color, however subtle, in the actual scene. Note that the long edges of THEMIS color images typically contain color artifacts that do not represent surface variation. Image information: VIS instrument. Latitude -34.5, Longitude 183.6 East (176.4 West). 38 meter/pixel resolution. Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time. NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D
2005-01-01
[figure removed for brevity, see original site] The THEMIS VIS camera is capable of capturing color images of the Martian surface using five different color filters. In this mode of operation, the spatial resolution and coverage of the image must be reduced to accommodate the additional data volume produced from using multiple filters. To make a color image, three of the five filter images (each in grayscale) are selected. Each is contrast enhanced and then converted to a red, green, or blue intensity image. These three images are then combined to produce a full color, single image. Because the THEMIS color filters don't span the full range of colors seen by the human eye, a color THEMIS image does not represent true color. Also, because each single-filter image is contrast enhanced before inclusion in the three-color image, the apparent color variation of the scene is exaggerated. Nevertheless, the color variation that does appear is representative of some change in color, however subtle, in the actual scene. Note that the long edges of THEMIS color images typically contain color artifacts that do not represent surface variation. This false color image was collected during Southern Fall and shows part of the Aureum Chaos. Image information: VIS instrument. Latitude -3.6, Longitude 332.9 East (27.1 West). 35 meter/pixel resolution. Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time. NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS
Low dimensional chaotic models for the plague epidemic in Bombay (1896–1911)
International Nuclear Information System (INIS)
Mangiarotti, Sylvain
2015-01-01
A plague epidemic broke out in Bombay in 1896 and became endemic. From 1905 to 1911, the epidemic was closely monitored by an Advisory Committee appointed to investigate the causes of the disease in any way. An impressive quantity of information was gathered, analyzed and published. Published data include records of the number of people who died from plague, and of the two main populations of rodents which were infected by plague in Bombay city. In the present paper, these data are revisited using a global modeling technique. This technique is applied to both single and multivariate observational time series. Several models are obtained for which a chaotic behavior can be observed. Obtaining such models proves that the dynamics of plague can be approximated by low-dimensional deterministic systems that can produce chaos. The multivariate models give a strong argument for interactive couplings between the epidemic and the epizootics of the two main species of rat. An interpretation of this coupling is given.
Erçetin, Şefika; Tekin, Ali
2014-01-01
The present work investigates global politics and political implications of social science and management with the aid of the latest complexity and chaos theories. Until now, deterministic chaos and nonlinear analysis have not been a focal point in this area of research. This book remedies this deficiency by utilizing these methods in the analysis of the subject matter. The authors provide the reader a detailed analysis on politics and its associated applications with the help of chaos theory, in a single edited volume.
National Research Council Canada - National Science Library
Morris, Jr, Gerald W
2007-01-01
.... The study investigates whether chaos theory, part of complexity science, can extract information from Katrina contracting data to help managers make better logistics decisions during disaster relief operations...
Murphy, David
2011-01-01
About 20 years ago, while lost in the midst of his PhD research, the author mused over proposed titles for his thesis. He was pretty pleased with himself when he came up with "Chaos Rules" (the implied double meaning was deliberate), or more completely, "Chaos Rules: An Exploration of the Work of Instructional Designers in Distance Education." He…
Chaos Modelling with Computers
Indian Academy of Sciences (India)
Chaos is one of the major scientific discoveries of our times. In fact many scientists ... But there are other natural phenomena that are not predictable though ... characteristics of chaos. ... The position and velocity are all that are needed to determine the motion of a .... a system of equations that modelled the earth's weather ...
Are low-dimensional dynamics typical in magnetically confined plasmas?
International Nuclear Information System (INIS)
Ball, R.; Dewar, R.L.
2000-01-01
Full text: Since 1988 there have been many serious attempts to construct low-dimensional dynamical systems that model L-H transitions and associated oscillatory phenomena in magnetically confined plasmas. Such models usually consist of coupled ordinary differential equations in a few dynamical state variables and several parameters that represent physical properties or external controls. The advantages of a unified, low-dimensional approach to modelling plasma behaviour are multifold. Most importantly, the qualitative analysis of nonlinear ODE and algebraic systems is supported by a substantial body of theory. The toolkits of singularity and stability theory are well-developed and accessible, and contain the right tools for the job of charting the state and parameter space. One of the driving forces behind the development of low-dimensional dynamical models is the predictive potential of a parameter map. For example, a model that talks of the shape and extent of hysteresis in the L-H transition would help engineers who are interested in controlling access to H-mode. We can express this problem another way: given the enormous number of variables and parameters that could be varied around a hysteretic regime, it would be cheaper to know in advance which ones actually do influence the quality and quantity of the hysteresis. The quest for a low-dimensional state space that contains the qualitative dynamics of L-H transitions also introduces other problems. We need to identify the essential (few) dynamical variables and the essential (few) independent parameter groups, clarify the mechanisms for the feedback that is modelled by nonlinear terms, and identify symmetries in the physics. Before jumping the gun on these questions the fundamental issue should be addressed of whether a confined plasma, having many important length and time scales, steep gradients, strong anisotropy, and an uncountable multiplicity of states, can indeed exhibit low-dimensional dynamics. In this
Low-dimensional filiform Lie algebras over finite fields
Falcón Ganfornina, Óscar Jesús; Núñez Valdés, Juan; Pacheco Martínez, Ana María; Villar Liñán, María Trinidad; Vasek, Vladimir (Coordinador); Shmaliy, Yuriy S. (Coordinador); Trcek, Denis (Coordinador); Kobayashi, Nobuhiko P. (Coordinador); Choras, Ryszard S. (Coordinador); Klos, Zbigniew (Coordinador)
2011-01-01
In this paper we use some objects of Graph Theory to classify low-dimensional filiform Lie algebras over finite fields. The idea lies in the representation of each Lie algebra by a certain type of graphs. Then, some properties on Graph Theory make easier to classify the algebras. As results, which can be applied in several branches of Physics or Engineering, for instance, we find out that there exist, up to isomorphism, six 6-dimensional filiform Lie algebras over Z/pZ, for p = 2, 3, 5. Pl...
Magnetometry of low-dimensional electron and hole systems
Energy Technology Data Exchange (ETDEWEB)
Usher, A [School of Physics, University of Exeter, Stocker Road, Exeter EX4 4QL (United Kingdom); Elliott, M [School of Physics and Astronomy, Cardiff University, Queens Buildings, Cardiff CF24 3AA (United Kingdom)], E-mail: a.usher@exeter.ac.uk, E-mail: elliottm@cf.ac.uk
2009-03-11
The high-magnetic-field, low-temperature magnetic properties of low-dimensional electron and hole systems reveal a wealth of fundamental information. Quantum oscillations of the thermodynamic equilibrium magnetization yield the total density of states, a central quantity in understanding the quantum Hall effect in 2D systems. The magnetization arising from non-equilibrium circulating currents reveals details, not accessible with traditional measurements, of the vanishingly small longitudinal resistance in the quantum Hall regime. We review how the technique of magnetometry has been applied to these systems, the most important discoveries that have been made, and their theoretical significance. (topical review)
Low dimensional field theories and condensed matter physics
International Nuclear Information System (INIS)
Nagaoka, Yosuke
1992-01-01
This issue is devoted to the Proceedings of the Fourth Yukawa International Seminar (YKIS '91) on Low Dimensional Field Theories and Condensed Matter Physics, which was held on July 28 to August 3 in Kyoto. In recent years there have been great experimental discoveries in the field of condensed matter physics: the quantum Hall effect and the high temperature superconductivity. Theoretical effort to clarify mechanisms of these phenomena revealed that they are deeply related to the basic problem of many-body systems with strong correlation. On the other hand, there have been important developments in field theory in low dimensions: the conformal field theory, the Chern-Simons gauge theory, etc. It was found that these theories work as a powerful method of approach to the problems in condensed matter physics. YKIS '91 was devoted to the study of common problems in low dimensional field theories and condensed matter physics. The 17 of the presented papers are collected in this issue. (J.P.N.)
Future device applications of low-dimensional carbon superlattice structures
Bhattacharyya, Somnath
2005-03-01
We observe superior transport properties in low-dimensional amorphous carbon (a-C) and superlattice structures fabricated by a number of different techniques. Low temperature conductivity of these materials is explained using argument based on the crossover of dimensionality of weak localization and electron-electron interactions along with a change of sign of the magneto-resistance. These trends are significantly different from many other well characterized ordered or oriented carbon structures, and, show direct evidence of high correlation length, mobility and an effect of the dimensionality in low-dimensional a-C films. We show routes to prepare bespoke features by tuning the phase relaxation time in order to make high-speed devices over large areas. The artificially grown multi-layer superlattice structures of diamond-like amorphous carbon films show high-frequency resonance and quantum conductance suggesting sufficiently high values of phase coherence length in the present disordered a-C system that could lead to fast switching multi-valued logic.
International Nuclear Information System (INIS)
Friedrich, H.
1992-01-01
Rapid growth in the study of nonlinear dynamics and chaos in classical mechanics, has led physicists to reappraise their abandonment of this definition of atomic theory in favour of quantum mechanics adopted earlier this century. The concept of chaos in classical mechanics is examined in this paper and manifestations of chaos in quantum mechanics are explored. While quantum mechanics teaches that atomic particles must not be pictured as moving sharply in defined orbits, these precise orbits can be used to describe essential features of the measurable quantum mechanical spectra. (UK)
Chaos applications in telecommunications
Stavroulakis, Peter
2005-01-01
IntroductionPeter StavroulakisChaotic Signal Generation and Transmission Antonio Cândido Faleiros,Waldecir João Perrella,TâniaNunes Rabello,Adalberto Sampaio Santos, andNeiYoshihiro SomaChaotic Transceiver Design Arthur Fleming-DahlChaos-Based Modulation and DemodulationTechniques Francis C.M. Lau and Chi K. TseA Chaos Approach to Asynchronous DS-CDMASystems S. Callegari, G. Mazzini, R. Rovatti, and G. SettiChannel Equalization in Chaotic CommunicationSystems Mahmut CiftciOptical Communications using ChaoticTechniques Gregory D. VanWiggerenAPPENDIX AFundamental Concepts of the Theory ofChaos a
Energy Technology Data Exchange (ETDEWEB)
Maldacena, Juan [School of Natural Sciences, Institute for Advanced Study,1 Einstein Drive, Princeton, NJ (United States); Shenker, Stephen H. [Stanford Institute for Theoretical Physics and Department of Physics, Stanford University,382 Via Pueblo Mall, Stanford, CA (United States); Stanford, Douglas [School of Natural Sciences, Institute for Advanced Study,1 Einstein Drive, Princeton, NJ (United States)
2016-08-17
We conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order correlation function closely related to the commutator of operators separated in time. We conjecture that the influence of chaos on this correlator can develop no faster than exponentially, with Lyapunov exponent λ{sub L}≤2πk{sub B}T/ℏ. We give a precise mathematical argument, based on plausible physical assumptions, establishing this conjecture.
DEFF Research Database (Denmark)
Lindberg, Erik
1996-01-01
The chaotic behaviour of the Colpitts oscillator reported by M.P. Kennedy is further investigated by means of PSpice simulations. Chaos is also observed with the default Ebers-Moll BJT transistor model with no memory. When the model is extended with memory and losses chaos do not occur and a 3'rd...... order limit cycle is found. If the the forward Early voltage parameter is added chaos is observed again. An examination of the eigenvalues of the oscillator with the simple memoryless Ebers-Moll BJT injection model is presented. By adding bulk resistors to the model stable limit cycles of orders 1, 2, 3...
Campbell, David
1987-11-01
I provide a brief overview of the current status of the field of deterministic "chaos" stressing its interrelations and applications to other fields and suggesting a number of important open problems for future study.
Quantum manifestations of chaos
International Nuclear Information System (INIS)
Borondo, F.; Benito, R.M.
1998-01-01
The correspondence between classical and quantum mechanics is considered both in the regular and chaotic regimes, and the main results regarding the quantum manifestations of chaos are reviewed. (Author) 16 refs
Energy Technology Data Exchange (ETDEWEB)
Bolotin, IU L; Gonchar, V IU; Truten, V I; Shulga, N F
1986-01-01
It is shown that axial channeling of relativistic electrons can give rise to the effect of dynamic chaos which involves essentially chaotic motion of a particle in the channel. The conditions leading to the effect of dynamic chaos and the manifestations of this effect in physical processes associated with the passage of particles through a crystal are examined using a silicon crystal as an example. 7 references.
Exploiting chaos for applications
Energy Technology Data Exchange (ETDEWEB)
Ditto, William L., E-mail: wditto@hawaii.edu [Department of Physics and Astronomy, University of Hawaii at Mānoa, Honolulu, Hawaii 96822 (United States); Sinha, Sudeshna, E-mail: sudeshna@iisermohali.ac.in [Indian Institute of Science Education and Research (IISER), Mohali, Knowledge City, Sector 81, SAS Nagar, PO Manauli 140306, Punjab (India)
2015-09-15
We discuss how understanding the nature of chaotic dynamics allows us to control these systems. A controlled chaotic system can then serve as a versatile pattern generator that can be used for a range of application. Specifically, we will discuss the application of controlled chaos to the design of novel computational paradigms. Thus, we present an illustrative research arc, starting with ideas of control, based on the general understanding of chaos, moving over to applications that influence the course of building better devices.
Exploiting chaos for applications.
Ditto, William L; Sinha, Sudeshna
2015-09-01
We discuss how understanding the nature of chaotic dynamics allows us to control these systems. A controlled chaotic system can then serve as a versatile pattern generator that can be used for a range of application. Specifically, we will discuss the application of controlled chaos to the design of novel computational paradigms. Thus, we present an illustrative research arc, starting with ideas of control, based on the general understanding of chaos, moving over to applications that influence the course of building better devices.
Low dimensional neutron moderators for enhanced source brightness
DEFF Research Database (Denmark)
Mezei, Ferenc; Zanini, Luca; Takibayev, Alan
2014-01-01
In a recent numerical optimization study we have found that liquid para-hydrogen coupled cold neutron moderators deliver 3–5 times higher cold neutron brightness at a spallation neutron source if they take the form of a flat, quasi 2-dimensional disc, in contrast to the conventional more voluminous...... for cold neutrons. This model leads to the conclusions that the optimal shape for high brightness para-hydrogen neutron moderators is the quasi 1-dimensional tube and these low dimensional moderators can also deliver much enhanced cold neutron brightness in fission reactor neutron sources, compared...... to the much more voluminous liquid D2 or H2 moderators currently used. Neutronic simulation calculations confirm both of these theoretical conclusions....
Low-dimensional geometry from euclidean surfaces to hyperbolic knots
Bonahon, Francis
2009-01-01
The study of 3-dimensional spaces brings together elements from several areas of mathematics. The most notable are topology and geometry, but elements of number theory and analysis also make appearances. In the past 30 years, there have been striking developments in the mathematics of 3-dimensional manifolds. This book aims to introduce undergraduate students to some of these important developments. Low-Dimensional Geometry starts at a relatively elementary level, and its early chapters can be used as a brief introduction to hyperbolic geometry. However, the ultimate goal is to describe the very recently completed geometrization program for 3-dimensional manifolds. The journey to reach this goal emphasizes examples and concrete constructions as an introduction to more general statements. This includes the tessellations associated to the process of gluing together the sides of a polygon. Bending some of these tessellations provides a natural introduction to 3-dimensional hyperbolic geometry and to the theory o...
Low Dimensional Semiconductor Structures Characterization, Modeling and Applications
Horing, Norman
2013-01-01
Starting with the first transistor in 1949, the world has experienced a technological revolution which has permeated most aspects of modern life, particularly over the last generation. Yet another such revolution looms up before us with the newly developed capability to control matter on the nanometer scale. A truly extraordinary research effort, by scientists, engineers, technologists of all disciplines, in nations large and small throughout the world, is directed and vigorously pressed to develop a full understanding of the properties of matter at the nanoscale and its possible applications, to bring to fruition the promise of nanostructures to introduce a new generation of electronic and optical devices. The physics of low dimensional semiconductor structures, including heterostructures, superlattices, quantum wells, wires and dots is reviewed and their modeling is discussed in detail. The truly exceptional material, Graphene, is reviewed; its functionalization and Van der Waals interactions are included h...
Nonlinear Spatio-Temporal Dynamics and Chaos in Semiconductors
Schöll, Eckehard
2005-08-01
Nonlinear transport phenomena are an increasingly important aspect of modern semiconductor research. This volume deals with complex nonlinear dynamics, pattern formation, and chaotic behavior in such systems. It bridges the gap between two well-established fields: the theory of dynamic systems and nonlinear charge transport in semiconductors. This unified approach helps reveal important electronic transport instabilities. The initial chapters lay a general framework for the theoretical description of nonlinear self-organized spatio-temporal patterns, such as current filaments, field domains, fronts, and analysis of their stability. Later chapters consider important model systems in detail: impact ionization induced impurity breakdown, Hall instabilities, superlattices, and low-dimensional structures. State-of-the-art results include chaos control, spatio-temporal chaos, multistability, pattern selection, activator-inhibitor kinetics, and global coupling, linking fundamental issues to electronic device applications. This book will be of great value to semiconductor physicists and nonlinear scientists alike.
Generalized Statistical Mechanics at the Onset of Chaos
Directory of Open Access Journals (Sweden)
Alberto Robledo
2013-11-01
Full Text Available Transitions to chaos in archetypal low-dimensional nonlinear maps offer real and precise model systems in which to assess proposed generalizations of statistical mechanics. The known association of chaotic dynamics with the structure of Boltzmann–Gibbs (BG statistical mechanics has suggested the potential verification of these generalizations at the onset of chaos, when the only Lyapunov exponent vanishes and ergodic and mixing properties cease to hold. There are three well-known routes to chaos in these deterministic dissipative systems, period-doubling, quasi-periodicity and intermittency, which provide the setting in which to explore the limit of validity of the standard BG structure. It has been shown that there is a rich and intricate behavior for both the dynamics within and towards the attractors at the onset of chaos and that these two kinds of properties are linked via generalized statistical-mechanical expressions. Amongst the topics presented are: (i permanently growing sensitivity fluctuations and their infinite family of generalized Pesin identities; (ii the emergence of statistical-mechanical structures in the dynamics along the routes to chaos; (iii dynamical hierarchies with modular organization; and (iv limit distributions of sums of deterministic variables. The occurrence of generalized entropy properties in condensed-matter physical systems is illustrated by considering critical fluctuations, localization transition and glass formation. We complete our presentation with the description of the manifestations of the dynamics at the transitions to chaos in various kinds of complex systems, such as, frequency and size rank distributions and complex network images of time series. We discuss the results.
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
Nonlinear chaos control and synchronization
Huijberts, H.J.C.; Nijmeijer, H.; Schöll, E.; Schuster, H.G.
2007-01-01
This chapter contains sections titled: Introduction Nonlinear Geometric Control Some Differential Geometric Concepts Nonlinear Controllability Chaos Control Through Feedback Linearization Chaos Control Through Input-Output Linearization Lyapunov Design Lyapunov Stability and Lyapunov's First Method
Stochastic Estimation via Polynomial Chaos
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
Enlightenment philosophers’ ideas about chaos
Directory of Open Access Journals (Sweden)
A. V. Kulik
2014-07-01
It is grounded that the philosopher and enlightener Johann Gottfried von Herder advanced an idea of objectivity of process of transformation chaos into order. It is shown that idea of «The law of nature» existing as for ordering chaos opened farreaching prospects for researches of interaction with chaos.
Kasimov, Aslan R.; Faria, Luiz; Rosales, Rodolfo R.
2013-01-01
: steady traveling wave solutions, instability of such solutions, and the onset of chaos. Our model is the first (to our knowledge) to describe chaos in shock waves by a scalar first-order partial differential equation. The chaos arises in the equation
Low Dimensional Representation of Fisher Vectors for Microscopy Image Classification.
Song, Yang; Li, Qing; Huang, Heng; Feng, Dagan; Chen, Mei; Cai, Weidong
2017-08-01
Microscopy image classification is important in various biomedical applications, such as cancer subtype identification, and protein localization for high content screening. To achieve automated and effective microscopy image classification, the representative and discriminative capability of image feature descriptors is essential. To this end, in this paper, we propose a new feature representation algorithm to facilitate automated microscopy image classification. In particular, we incorporate Fisher vector (FV) encoding with multiple types of local features that are handcrafted or learned, and we design a separation-guided dimension reduction method to reduce the descriptor dimension while increasing its discriminative capability. Our method is evaluated on four publicly available microscopy image data sets of different imaging types and applications, including the UCSB breast cancer data set, MICCAI 2015 CBTC challenge data set, and IICBU malignant lymphoma, and RNAi data sets. Our experimental results demonstrate the advantage of the proposed low-dimensional FV representation, showing consistent performance improvement over the existing state of the art and the commonly used dimension reduction techniques.
Electronic properties and phase transitions in low-dimensional semiconductors
International Nuclear Information System (INIS)
Panich, A M
2008-01-01
We present the first review of the current state of the literature on electronic properties and phase transitions in TlX and TlMX 2 (M = Ga, In; X = Se, S, Te) compounds. These chalcogenides belong to a family of the low-dimensional semiconductors possessing chain or layered structure. They are of significant interest because of their highly anisotropic properties, semi- and photoconductivity, nonlinear effects in their I-V characteristics (including a region of negative differential resistance), switching and memory effects, second harmonic optical generation, relaxor behavior and potential applications for optoelectronic devices. We review the crystal structure of TlX and TlMX 2 compounds, their transport properties under ambient conditions, experimental and theoretical studies of the electronic structure, transport properties and semiconductor-metal phase transitions under high pressure, and sequences of temperature-induced structural phase transitions with intermediate incommensurate states. The electronic nature of the ferroelectric phase transitions in the above-mentioned compounds, as well as relaxor behavior, nanodomains and possible occurrence of quantum dots in doped and irradiated crystals is discussed. (topical review)
Low-Dimensional Feature Representation for Instrument Identification
Ihara, Mizuki; Maeda, Shin-Ichi; Ikeda, Kazushi; Ishii, Shin
For monophonic music instrument identification, various feature extraction and selection methods have been proposed. One of the issues toward instrument identification is that the same spectrum is not always observed even in the same instrument due to the difference of the recording condition. Therefore, it is important to find non-redundant instrument-specific features that maintain information essential for high-quality instrument identification to apply them to various instrumental music analyses. For such a dimensionality reduction method, the authors propose the utilization of linear projection methods: local Fisher discriminant analysis (LFDA) and LFDA combined with principal component analysis (PCA). After experimentally clarifying that raw power spectra are actually good for instrument classification, the authors reduced the feature dimensionality by LFDA or by PCA followed by LFDA (PCA-LFDA). The reduced features achieved reasonably high identification performance that was comparable or higher than those by the power spectra and those achieved by other existing studies. These results demonstrated that our LFDA and PCA-LFDA can successfully extract low-dimensional instrument features that maintain the characteristic information of the instruments.
Thermoelectric properties of low-dimensional clathrates from first principles
Kasinathan, Deepa; Rosner, Helge
2011-03-01
Type-I inorganic clathrates are host-guest structures with the guest atoms trapped in the framework of the host structure. From a thermoelectric point of view, they are interesting because they are semiconductors with adjustable bandgaps. Investigations in the past decade have shown that type-I clathrates X8 Ga 16 Ge 30 (X = Ba, Sr, Eu) may have the unusual property of ``phonon glass-electron crystal'' for good thermoelectric materials. Among the known clathrates, Ba 8 Ga 16 Ge 30 has the highest figure of merit (ZT~1). To enable a more widespread usage of thermoelectric technology power generation and heating/cooling applications, ZT of at least 2-3 is required. Two different research approaches have been proposed for developing next generation thermoelectric materials: one investigating new families of advanced bulk materials, and the other studying low-dimensional materials. In our work, we concentrate on understanding the thermoelectric properties of the nanostructured Ba-based clathrates. We use semi-classical Boltzmann transport equations to calculate the various thermoelectric properties as a function of reduced dimensions. We observe that there exists a delicate balance between the electrical conductivity and the electronic part of the thermal conductivity in reduced dimensions. Insights from these results can directly be used to control particle size in nanostructuring experiments.
Unraveling surface enabled magnetic phenomena in low dimensional systems
Baljozovic, Milos; Girovsky, Jan; Nowakowski, Jan; Ali, Md Ehesan; Rossmann, Harald; Nijs, Thomas; Aeby, Elise; Nowakowska, Sylwia; Siewert, Dorota; Srivastava, Gitika; WäCkerlin, Christian; Dreiser, Jan; Decurtins, Silvio; Liu, Shi-Xia; Oppeneer, Peter M.; Jung, Thomas A.; Ballav, Nirmalya
Molecular spin systems with controllable interactions are of both fundamental and applied importance. These systems help us to better understand the fundamental origins of the interactions involved in low dimensional magnetic systems and to put them in the framework of existing models towards their further development. Following our first observation of exchange induced magnetic ordering in paramagnetic porphyrins adsorbed on ferromagnetic Co surface we showed that magnetic properties of such molecules can be controllably altered upon exposure to chemical and physical stimuli. In our most recent work it was shown that a synthetically programmed co-assembly of Fe and Mn phthalocyanines can also be realized on diamagnetic Au(111) surfaces where it induces long-range 2D ferrimagnetic order, at first glance in conflict with the Mermin-Wagner theory. Here we provide evidence for the first direct observation of such ordering from STM/STS and XMCD data and from DFT +U calculations demonstrating key role of the Au(111) surface states in mediating AFM RKKY coupling of the Kondo underscreened magnetic moments.
Unexpected magnetism in low dimensional systems: the role of symmetry
International Nuclear Information System (INIS)
Munoz, MC; Chico, L; Lopez-Sancho, MP; Beltran, JI; Gallego, S; Cerda, J
2006-01-01
The symmetry underlying the geometric structure of materials determines most of their physical properties. In low dimensional systems the role of symmetry is enhanced and can give rise to new phenomena. Here, we report on unexpected magnetism in carbon nanotubes and O-rich surfaces of ionic oxides, to show how its existence is closely related to the symmetry conditions. First, based on tight-binding models, we demonstrate that chiral carbon nanotubes present spin splitting at the Fermi level in the absence of a magneticfield, whereas achiral tubes preserve spin degeneracy. These remarkably different behaviors of chiral and non-chiral nanotubes are due to the intrinsic symmetry dependence of the spin-orbit interaction. Second, the occurrence of spin-polarization at ZrO 2 , Al 2 O 3 and MgO surfaces is proved by means of abinitio calculations within the density functional theory. Large spin moments develop at O-ended polar terminations, transforming the non-magnetic insulator into a half-metal. The magnetic moments mainly reside in the surface oxygen atoms, and their origin is related to the existence of 2p holes of well-defined spin polarization at the valence band of the ionic oxide. The direct relation between magnetization and local loss of donor charge shows that at the origin of these phenomena is the reduced surface symmetry
Proton tunneling in low dimensional cesium silicate LDS-1
Matsui, Hiroshi; Iwamoto, Kei; Mochizuki, Dai; Osada, Shimon; Asakura, Yusuke; Kuroda, Kazuyuki
2015-07-01
In low dimensional cesium silicate LDS-1 (monoclinic phase of CsHSi2O5), anomalous infrared absorption bands observed at 93, 155, 1210, and 1220 cm-1 are assigned to the vibrational mode of protons, which contribute to the strong hydrogen bonding between terminal oxygen atoms of silicate chain (O-O distance = 2.45 Å). The integrated absorbance (oscillator strength) for those modes is drastically enhanced at low temperatures. The analysis of integrated absorbance employing two different anharmonic double-minimum potentials makes clear that proton tunneling through the potential barrier yields an energy splitting of the ground state. The absorption bands at 93 and 155 cm-1, which correspond to the different vibrational modes of protons, are attributed to the optical transition between the splitting levels (excitation from the ground state (n = 0) to the first excited state (n = 1)). Moreover, the absorption bands at 1210 and 1220 cm-1 are identified as the optical transition from the ground state (n = 0) to the third excited state (n = 3). Weak Coulomb interactions in between the adjacent protons generate two types of vibrational modes: symmetric mode (93 and 1210 cm-1) and asymmetric mode (155 and 1220 cm-1). The broad absorption at 100-600 cm-1 reveals an emergence of collective mode due to the vibration of silicate chain coupled not only with the local oscillation of Cs+ but also with the proton oscillation relevant to the second excited state (n = 2).
Low-Dimensional Network Formation in Molten Sodium Carbonate.
Wilding, Martin C; Wilson, Mark; Alderman, Oliver L G; Benmore, Chris; Weber, J K R; Parise, John B; Tamalonis, Anthony; Skinner, Lawrie
2016-04-15
Molten carbonates are highly inviscid liquids characterized by low melting points and high solubility of rare earth elements and volatile molecules. An understanding of the structure and related properties of these intriguing liquids has been limited to date. We report the results of a study of molten sodium carbonate (Na2CO3) which combines high energy X-ray diffraction, containerless techniques and computer simulation to provide insight into the liquid structure. Total structure factors (F(x)(Q)) are collected on the laser-heated carbonate spheres suspended in flowing gases of varying composition in an aerodynamic levitation furnace. The respective partial structure factor contributions to F(x)(Q) are obtained by performing molecular dynamics simulations treating the carbonate anions as flexible entities. The carbonate liquid structure is found to be heavily temperature-dependent. At low temperatures a low-dimensional carbonate chain network forms, at T = 1100 K for example ~55% of the C atoms form part of a chain. The mean chain lengths decrease as temperature is increased and as the chains become shorter the rotation of the carbonate anions becomes more rapid enhancing the diffusion of Na(+) ions.
International Nuclear Information System (INIS)
Whelan, N.D.
1993-01-01
Random Matrix Theory successfully describes the statistics of the low-lying spectra of some nuclei but not of others. It is currently believed that this theory applies to systems in which the corresponding classical motion is chaotic. This conjecture is tested for collective nuclei by studying the Interacting Boson Model. Quantum and classical measures of chaos are proposed and found to be in agreement throughout the parameter space of the model. For some parameter values the measures indicate the presence of a previously unknown approximate symmetry. A phenomenon called partial dynamical symmetry is explored and shown to lead to a suppression of chaos. A time dependent function calculated from the quantum spectrum is discussed. This function is sensitive to the extent of chaos and provides a robust method of analyzing experimental spectra
He, Temple; Habib, Salman
2013-09-01
Simple dynamical systems--with a small number of degrees of freedom--can behave in a complex manner due to the presence of chaos. Such systems are most often (idealized) limiting cases of more realistic situations. Isolating a small number of dynamical degrees of freedom in a realistically coupled system generically yields reduced equations with terms that can have a stochastic interpretation. In situations where both noise and chaos can potentially exist, it is not immediately obvious how Lyapunov exponents, key to characterizing chaos, should be properly defined. In this paper, we show how to do this in a class of well-defined noise-driven dynamical systems, derived from an underlying Hamiltonian model.
Nonlinear transport behavior of low dimensional electron systems
Zhang, Jingqiao
The nonlinear behavior of low-dimensional electron systems attracts a great deal of attention for its fundamental interest as well as for potentially important applications in nanoelectronics. In response to microwave radiation and dc bias, strongly nonlinear electron transport that gives rise to unusual electron states has been reported in two-dimensional systems of electrons in high magnetic fields. There has also been great interest in the nonlinear response of quantum ballistic constrictions, where the effects of quantum interference, spatial dispersion and electron-electron interactions play crucial roles. In this thesis, experimental results of the research of low dimensional electron gas systems are presented. The first nonlinear phenomena were observed in samples of highly mobile two dimensional electrons in GaAs heavily doped quantum wells at different magnitudes of DC and AC (10 KHz to 20 GHz) excitations. We found that in the DC excitation regime the differential resistance oscillates with the DC current and external magnetic field, similar behavior was observed earlier in AlGaAs/GaAs heterostructures [C.L. Yang et al. ]. At external AC excitations the resistance is found to be also oscillating as a function of the magnetic field. However the form of the oscillations is considerably different from the DC case. We show that at frequencies below 100 KHz the difference is a result of a specific average of the DC differential resistance during the period of the external AC excitations. Secondly, in similar samples, strong suppression of the resistance by the electric field is observed in magnetic fields at which the Landau quantization of electron motion occurs. The phenomenon survives at high temperatures at which the Shubnikov de Haas oscillations are absent. The scale of the electric fields essential for the effect, is found to be proportional to temperature in the low temperature limit. We suggest that the strong reduction of the longitudinal resistance
INTRODUCTION: Physics of Low-dimensional Systems: Nobel Symposium 73
Lundqvist, Stig
1989-01-01
The physics of low-dimensional systems has developed in a remarkable way over the last decade and has accelerated over the last few years, in particular because of the discovery of the new high temperature superconductors. The new developments started more than fifteen years ago with the discovery of the unexpected quasi-one-dimensional character of the TTF-TCNQ. Since then the field of conducting quasi-one-dimensional organic systems have been rapidly growing. Parallel to the experimental work there has been an important theoretical development of great conceptual importance, such as charge density waves, soliton-like excitations, fractional charges, new symmetry properties etc. A new field of fundamental importance was the discovery of the Quantum Hall Effect in 1980. This field is still expanding with new experimental and theoretical discoveries. In 1986, then, came the totally unexpected discovery of high temperature superconductivity which started an explosive development. The three areas just mentioned formed the main themes of the Symposium. They do not in any way exhaust the progress in low-dimensional physics. We should mention the recent important development with both two-dimensional and one-dimensional and even zero-dimensional structures (quantum dots). The physics of mesoscopic systems is another important area where the low dimensionality is a key feature. Because of the small format of this Symposium we could unfortunately not cover these areas. 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 international participants is typically in the range 25-40. These Symposia are arranged through a special Nobel Symposium Committee after proposal from individuals. This Symposium was sponsored by the Nobel Foundation through its Nobel Symposium Fund with grants from The
Chaos and remedial investigations
International Nuclear Information System (INIS)
Galbraith, R.M.
1991-01-01
Current research into the nature of chaos indicates that even for systems that are well known and easily modeled, slight changes in the scale used to measure the input have unpredictable results in the model output. The conduct of a remedial investigation (RI) is dictated by well-established rules of investigation and management, yet small changes in project orientation, regulatory environment, or site conditions have unpredictable consequences to the project. The consequences can lead to either brilliant success or utter failure. The chaotic effect of a change in scale is most often illustrated by an exercise in measuring the length of the coast of Great Britain. If a straight ruler 10-kilometers long is used, the sum of the 10-kilometer increments gives the length of the coast. If the ruler is changed to five kilometers long and the exercise is repeated, the sum of the five-kilometer increments will not be the same as the sum of the 10-kilometer increments. Nor is there a way to predict what the length of the coast will be using any other scale. Several examples from the Fernald Project RI are used to illustrate open-quotes changes in scaleclose quotes in both technical and management situations. Given that there is no way to predict the outcome of scale changes in a RI, technical and project management must be alert to the fact that a scale has changed and the investigation is no longer on the path it was thought to be on. The key to success, therefore, is to develop specific units of measure for a number of activities, in addition to cost and schedule, and track them regularly. An example for tracking a portion of the field investigation is presented. The determination of effective units of measure is perhaps the most difficult aspect of any project. Changes in scale sometimes go unnoticed until suddenly the budget is expended and only a portion of the work is completed. Remedial investigations on large facilities provide new and complex challenges
Directory of Open Access Journals (Sweden)
J. D. Salas
2005-01-01
Full Text Available A review of the literature reveals conflicting results regarding the existence and inherent nature of chaos in hydrological processes such as precipitation and streamflow, i.e. whether they are low dimensional chaotic or stochastic. This issue is examined further in this paper, particularly the effect that certain types of transformations, such as aggregation and sampling, may have on the identification of the dynamics of the underlying system. First, we investigate the dynamics of daily streamflows for two rivers in Florida, one with strong surface and groundwater storage contributions and the other with a lesser basin storage contribution. Based on estimates of the delay time, the delay time window, and the correlation integral, our results suggest that the river with the stronger basin storage contribution departs significantly from the behavior of a chaotic system, while the departure is less significant for the river with the smaller basin storage contribution. We pose the hypothesis that the chaotic behavior depicted on continuous precipitation fields or small time-step precipitation series becomes less identifiable as the aggregation (or sampling time step increases. Similarly, because streamflows result from a complex transformation of precipitation that involves accumulating and routing excess rainfall throughout the basin and adding surface and groundwater flows, the end result may be that streamflows at the outlet of the basin depart from low dimensional chaotic behavior. We also investigate the effect of aggregation and sampling using series derived from the Lorenz equations and show that, as the aggregation and sampling scales increase, the chaotic behavior deteriorates and eventually ceases to show evidence of low dimensional determinism.
Chaos Modelling with Computers
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 5. Chaos Modelling with Computers Unpredicatable Behaviour of Deterministic Systems. Balakrishnan Ramasamy T S K V Iyer. General Article Volume 1 Issue 5 May 1996 pp 29-39 ...
Neural chaos and schizophrenia
Czech Academy of Sciences Publication Activity Database
Bob, P.; Chládek, Jan; Šusta, M.; Glaslová, K.; Jagla, F.; Kukleta, M.
2007-01-01
Roč. 26, č. 4 (2007), s. 298-305 ISSN 0231-5882 Institutional research plan: CEZ:AV0Z20650511 Keywords : EDA * Lyapunov exponent * schizophrenia * chaos Subject RIV: FL - Psychiatry, Sexuology Impact factor: 1.286, year: 2007
International Nuclear Information System (INIS)
Chirikov, B.V.
1990-01-01
Classification of chaotic patterns in classical Hamiltonian systems is given as a series of levels with increasing disorder. Hamiltonian dynamics is presented, including the renormalization chaos, based upon the fairly simple resonant theory. First estimates for the critical structure and related statistical anomalies in arbitrary dimensions are discussed. 49 refs
Directory of Open Access Journals (Sweden)
Tamás Meszéna
2017-04-01
Full Text Available We are faced with chaotic processes in many segments of our life: meteorology, environmental pollution, financial and economic processes, sociology, mechanics, electronics, biology, chemistry. The spreading of high-performance computers and the development of simulation methods made the examination of these processes easily available. Regular, periodic motions (pendulum, harmonic oscillatory motion, bouncing ball, as taught at secondary level, become chaotic even due minor changes. If it is true that the most considerable achievements of twentieth century physics were the theory of relativity, quantum mechanics and chaos theory, then it is presumably time to think about, examine and test how and to what extent chaos can be presented to the students. Here I would like to introduce a 12 lesson long facultative curriculum framework on chaos designed for students aged seventeen. The investigation of chaos phenomenon in this work is based on a freeware, “Dynamics Solver”. This software, with some assistance from the teacher, is suitable for classroom use at secondary level.
Directory of Open Access Journals (Sweden)
Kratochvíl C.
2007-10-01
Full Text Available The purpose of this article is to provide an elementary introduction to the subject of chaos in the electromechanical drive systems. In this article, we explore chaotic solutions of maps and continuous time systems. These solutions are also bounded like equilibrium, periodic and quasiperiodic solutions.
DEFF Research Database (Denmark)
Lykke, Marianne; Lund, Haakon; Skov, Mette
2016-01-01
CHAOS (Cultural Heritage Archive Open System) provides streaming access to more than 500,000 broadcasts by the Danish Broadcast Corporation from 1931 and onwards. The archive is part of the LARM project with the purpose of enabling researchers to search, annotate, and interact with recordings...
DEFF Research Database (Denmark)
Lykke, Marianne; Skov, Mette; Lund, Haakon
CHAOS (Cultural Heritage Archive Open System) provides streaming access to more than 500.000 broad-casts by the Danish Broadcast Corporation from 1931 and onwards. The archive is part of the LARM project with the purpose of enabling researchers to search, annotate, and interact with recordings...
Jesse A. Logan; Fred P. Hain
1990-01-01
Recent advances in applied mathematical analysis have uncovered a fascinating and unexpected dynamical richness that underlies behavior of even the simplest non-linear mathematical models. Due to the complexity of solutions to these non-linear equations, a new mathematical term, chaos, has been coined to describe the resulting dynamics. This term captures the notion...
No evidence of chaos but some evidence of dependence in the US stock market
International Nuclear Information System (INIS)
Serletis, Apostolos; Shintani, Mototsugu
2003-01-01
This paper uses recent advances in the field of applied econometrics and tools from dynamical systems theory to test for random walks and chaos in the US stock market, using daily observations on the Dow Jones Industrial Average (from January 3, 1928 to October 18, 2000 - a total of 18,490 observations). In doing so, we follow the recent contribution by Whang and Linton [J Econometr 91 (1999) 1] and construct the standard error for the Nychka et al. [J Roy Statist Soc B 54 (1992) 399] dominant Lyapunov exponent, thereby providing a statistical test of chaos. We find statistically significant evidence against low-dimensional chaos and point to the use of stochastic models and statistical inference in the modeling of asset markets
No evidence of chaos but some evidence of dependence in the US stock market
Energy Technology Data Exchange (ETDEWEB)
Serletis, Apostolos E-mail: serletis@ucalgary.ca; Shintani, Mototsugu E-mail: mototsugu.shintani@vanderbilt.edu
2003-07-01
This paper uses recent advances in the field of applied econometrics and tools from dynamical systems theory to test for random walks and chaos in the US stock market, using daily observations on the Dow Jones Industrial Average (from January 3, 1928 to October 18, 2000 - a total of 18,490 observations). In doing so, we follow the recent contribution by Whang and Linton [J Econometr 91 (1999) 1] and construct the standard error for the Nychka et al. [J Roy Statist Soc B 54 (1992) 399] dominant Lyapunov exponent, thereby providing a statistical test of chaos. We find statistically significant evidence against low-dimensional chaos and point to the use of stochastic models and statistical inference in the modeling of asset markets.
Energy–pressure relation for low-dimensional gases
Directory of Open Access Journals (Sweden)
Francesco Mancarella
2014-10-01
Full Text Available A particularly simple relation of proportionality between internal energy and pressure holds for scale-invariant thermodynamic systems (with Hamiltonians homogeneous functions of the coordinates, including classical and quantum – Bose and Fermi – ideal gases. One can quantify the deviation from such a relation by introducing the internal energy shift as the difference between the internal energy of the system and the corresponding value for scale-invariant (including ideal gases. After discussing some general thermodynamic properties associated with the scale-invariance, we provide criteria for which the internal energy shift density of an imperfect (classical or quantum gas is a bounded function of temperature. We then study the internal energy shift and deviations from the energy–pressure proportionality in low-dimensional models of gases interpolating between the ideal Bose and the ideal Fermi gases, focusing on the Lieb–Liniger model in 1d and on the anyonic gas in 2d. In 1d the internal energy shift is determined from the thermodynamic Bethe ansatz integral equations and an explicit relation for it is given at high temperature. Our results show that the internal energy shift is positive, it vanishes in the two limits of zero and infinite coupling (respectively the ideal Bose and the Tonks–Girardeau gas and it has a maximum at a finite, temperature-depending, value of the coupling. Remarkably, at fixed coupling the energy shift density saturates to a finite value for infinite temperature. In 2d we consider systems of Abelian anyons and non-Abelian Chern–Simons particles: as it can be seen also directly from a study of the virial coefficients, in the usually considered hard-core limit the internal energy shift vanishes and the energy is just proportional to the pressure, with the proportionality constant being simply the area of the system. Soft-core boundary conditions at coincident points for the two-body wavefunction introduce
Energy–pressure relation for low-dimensional gases
International Nuclear Information System (INIS)
Mancarella, Francesco; Mussardo, Giuseppe; Trombettoni, Andrea
2014-01-01
A particularly simple relation of proportionality between internal energy and pressure holds for scale-invariant thermodynamic systems (with Hamiltonians homogeneous functions of the coordinates), including classical and quantum – Bose and Fermi – ideal gases. One can quantify the deviation from such a relation by introducing the internal energy shift as the difference between the internal energy of the system and the corresponding value for scale-invariant (including ideal) gases. After discussing some general thermodynamic properties associated with the scale-invariance, we provide criteria for which the internal energy shift density of an imperfect (classical or quantum) gas is a bounded function of temperature. We then study the internal energy shift and deviations from the energy–pressure proportionality in low-dimensional models of gases interpolating between the ideal Bose and the ideal Fermi gases, focusing on the Lieb–Liniger model in 1d and on the anyonic gas in 2d. In 1d the internal energy shift is determined from the thermodynamic Bethe ansatz integral equations and an explicit relation for it is given at high temperature. Our results show that the internal energy shift is positive, it vanishes in the two limits of zero and infinite coupling (respectively the ideal Bose and the Tonks–Girardeau gas) and it has a maximum at a finite, temperature-depending, value of the coupling. Remarkably, at fixed coupling the energy shift density saturates to a finite value for infinite temperature. In 2d we consider systems of Abelian anyons and non-Abelian Chern–Simons particles: as it can be seen also directly from a study of the virial coefficients, in the usually considered hard-core limit the internal energy shift vanishes and the energy is just proportional to the pressure, with the proportionality constant being simply the area of the system. Soft-core boundary conditions at coincident points for the two-body wavefunction introduce a length scale
Chaos in neurons and its application: perspective of chaos engineering.
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.
Chaos in oil prices? Evidence from futures markets
International Nuclear Information System (INIS)
Adrangi, B.; Chatrath, A.; Dhanda, K.K.; Raffiee, K.
2001-01-01
We test for the presence of low-dimensional chaotic structure in crude oil, heating oil, and unleaded gasoline futures prices from the early 1980s. Evidence on chaos will have important implications for regulators and short-term trading strategies. While we find strong evidence of non-linear dependencies, the evidence is not consistent with chaos. Our test results indicate that ARCH-type processes, with controls for seasonal variation in prices, generally explain the non-linearities in the data. We also demonstrate that employing seasonally adjusted price series contributes to obtaining robust results via the existing tests for chaotic structure. Maximum likelihood methodologies, that are robust to the non-linear dynamics, lend support for Samuelson's hypothesis on contract-maturity effects in futures price-changes. However, the tests for chaos are not found to be sensitive to the maturity effects in the futures contracts. The results are robust to controls for the oil shocks of 1986 and 1991
Stability and electronic properties of low-dimensional nanostructures
Guan, Jie
As the devices used in daily life become smaller and more concentrated, traditional three-dimensional (3D) bulk materials have reached their limit in size. Low-dimensional nanomaterials have been attracting more attention in research and getting widely applied in many industrial fields because of their atomic-level size, unique advanced properties, and varied nanostructures. In this thesis, I have studied the stability and mechanical and electronic properties of zero-dimensional (0D) structures including carbon fullerenes, nanotori, metallofullerenes and phosphorus fullerenes, one-dimensional (1D) structures including carbon nanotubes and phosphorus nanotubes, as well as two-dimensional (2D) structures including layered transition metal dichalcogenides (TMDs), phosphorene and phosphorus carbide (PC). I first briefly introduce the scientific background and the motivation of all the work in this thesis. Then the computational techniques, mainly density functional theory (DFT), are reviewed in Chapter 2. In Chapter 3, I investigate the stability and electronic structure of endohedral rare-earth metallofullerene La C60 and the trifluoromethylized La C60(CF3)n with n ≤ 5. Odd n is preferred due to the closed-shell electronic configuration or large HOMO-LUMO gap, which is also meaningful for the separation of C 60-based metallofullerenes. Mechanical and electronic properties of layered materials including TMDs and black phosphorus are studied in Chapter 4 and 5. In Chapter 4, a metallic NbSe2/semiconducting WSe2 bilayer is investigated and besides a rigid band shift associated with charge transfer, the presence of NbSe2 does not modify the electronic structure of WSe2. Structural similarity and small lattice mismatch results in the heterojunction being capable of efficiently transferring charge acrossthe interface. In Chapter 5, I investigate the dependence of stability and electronic band structure on the in-layer strain in bulk black phosphorus. In Chapters 6, 7 and
Energy Technology Data Exchange (ETDEWEB)
Tél, Tamás [Institute for Theoretical Physics, Eötvös University, and MTA-ELTE Theoretical Physics Research Group, Pázmány P. s. 1/A, Budapest H-1117 (Hungary)
2015-09-15
We intend to show that transient chaos is a very appealing, but still not widely appreciated, subfield of nonlinear dynamics. Besides flashing its basic properties and giving a brief overview of the many applications, a few recent transient-chaos-related subjects are introduced in some detail. These include the dynamics of decision making, dispersion, and sedimentation of volcanic ash, doubly transient chaos of undriven autonomous mechanical systems, and a dynamical systems approach to energy absorption or explosion.
Tél, Tamás
2015-09-01
We intend to show that transient chaos is a very appealing, but still not widely appreciated, subfield of nonlinear dynamics. Besides flashing its basic properties and giving a brief overview of the many applications, a few recent transient-chaos-related subjects are introduced in some detail. These include the dynamics of decision making, dispersion, and sedimentation of volcanic ash, doubly transient chaos of undriven autonomous mechanical systems, and a dynamical systems approach to energy absorption or explosion.
International Nuclear Information System (INIS)
Bick, Christian; Kolodziejski, Christoph; Timme, Marc
2014-01-01
Predictive feedback control is an easy-to-implement method to stabilize unknown unstable periodic orbits in chaotic dynamical systems. Predictive feedback control is severely limited because asymptotic convergence speed decreases with stronger instabilities which in turn are typical for larger target periods, rendering it harder to effectively stabilize periodic orbits of large period. Here, we study stalled chaos control, where the application of control is stalled to make use of the chaotic, uncontrolled dynamics, and introduce an adaptation paradigm to overcome this limitation and speed up convergence. This modified control scheme is not only capable of stabilizing more periodic orbits than the original predictive feedback control but also speeds up convergence for typical chaotic maps, as illustrated in both theory and application. The proposed adaptation scheme provides a way to tune parameters online, yielding a broadly applicable, fast chaos control that converges reliably, even for periodic orbits of large period
Schuster, H G
2008-01-01
This long-awaited revised second edition of the standard reference on the subject has been considerably expanded to include such recent developments as novel control schemes, control of chaotic space-time patterns, control of noisy nonlinear systems, and communication with chaos, as well as promising new directions in research. The contributions from leading international scientists active in the field provide a comprehensive overview of our current level of knowledge on chaos control and its applications in physics, chemistry, biology, medicine, and engineering. In addition, they show the overlap with the traditional field of control theory in the engineering community.An interdisciplinary approach of interest to scientists and engineers working in a number of areas
Energy Technology Data Exchange (ETDEWEB)
Hosur, Pavan; Qi, Xiao-Liang [Department of Physics, Stanford University,476 Lomita Mall, Stanford, California 94305 (United States); Roberts, Daniel A. [Center for Theoretical Physics and Department of Physics, Massachusetts Institute of Technology,77 Massachusetts Ave, Cambridge, Massachusetts 02139 (United States); Yoshida, Beni [Perimeter Institute for Theoretical Physics,31 Caroline Street North, Waterloo, Ontario N2L 2Y5 (Canada); Walter Burke Institute for Theoretical Physics, California Institute of Technology,1200 E California Blvd, Pasadena CA 91125 (United States)
2016-02-01
We study chaos and scrambling in unitary channels by considering their entanglement properties as states. Using out-of-time-order correlation functions to diagnose chaos, we characterize the ability of a channel to process quantum information. We show that the generic decay of such correlators implies that any input subsystem must have near vanishing mutual information with almost all partitions of the output. Additionally, we propose the negativity of the tripartite information of the channel as a general diagnostic of scrambling. This measures the delocalization of information and is closely related to the decay of out-of-time-order correlators. We back up our results with numerics in two non-integrable models and analytic results in a perfect tensor network model of chaotic time evolution. These results show that the butterfly effect in quantum systems implies the information-theoretic definition of scrambling.
International Nuclear Information System (INIS)
Loskutov, Alexander
2010-01-01
This review introduces most of the concepts used in the study of chaotic phenomena in nonlinear systems and has as its objective to summarize the current understanding of results from the theory of chaotic dynamical systems and to describe the original ideas underlying the study of deterministic chaos. The presentation relies on informal analysis, with abstract mathematical ideas visualized geometrically or by examples from physics. Hyperbolic dynamics, homoclinic trajectories and tangencies, wild hyperbolic sets, and different types of attractors which appear in dynamical systems are considered. The key aspects of ergodic theory are discussed, and the basic statistical properties of chaotic dynamical systems are described. The fundamental difference between stochastic dynamics and deterministic chaos is explained. The review concludes with an investigation of the possibility of studying complex systems on the basis of the analysis of registered signals, i.e. the generated time series. (reviews of topical problems)
Bick, Christian; Kolodziejski, Christoph; Timme, Marc
2014-09-01
Predictive feedback control is an easy-to-implement method to stabilize unknown unstable periodic orbits in chaotic dynamical systems. Predictive feedback control is severely limited because asymptotic convergence speed decreases with stronger instabilities which in turn are typical for larger target periods, rendering it harder to effectively stabilize periodic orbits of large period. Here, we study stalled chaos control, where the application of control is stalled to make use of the chaotic, uncontrolled dynamics, and introduce an adaptation paradigm to overcome this limitation and speed up convergence. This modified control scheme is not only capable of stabilizing more periodic orbits than the original predictive feedback control but also speeds up convergence for typical chaotic maps, as illustrated in both theory and application. The proposed adaptation scheme provides a way to tune parameters online, yielding a broadly applicable, fast chaos control that converges reliably, even for periodic orbits of large period.
Chaos detection and predictability
Gottwald, Georg; Laskar, Jacques
2016-01-01
Distinguishing chaoticity from regularity in deterministic dynamical systems and specifying the subspace of the phase space in which instabilities are expected to occur is of utmost importance in as disparate areas as astronomy, particle physics and climate dynamics. To address these issues there exists a plethora of methods for chaos detection and predictability. The most commonly employed technique for investigating chaotic dynamics, i.e. the computation of Lyapunov exponents, however, may suffer a number of problems and drawbacks, for example when applied to noisy experimental data. In the last two decades, several novel methods have been developed for the fast and reliable determination of the regular or chaotic nature of orbits, aimed at overcoming the shortcomings of more traditional techniques. This set of lecture notes and tutorial reviews serves as an introduction to and overview of modern chaos detection and predictability techniques for graduate students and non-specialists. The book cover...
Energy Technology Data Exchange (ETDEWEB)
Bick, Christian [Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen (Germany); Bernstein Center for Computational Neuroscience (BCCN), 37077 Göttingen (Germany); Institute for Mathematics, Georg–August–Universität Göttingen, 37073 Göttingen (Germany); Kolodziejski, Christoph [Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen (Germany); III. Physical Institute—Biophysics, Georg–August–Universität Göttingen, 37077 Göttingen (Germany); Timme, Marc [Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen (Germany); Institute for Nonlinear Dynamics, Georg–August–Universität Göttingen, 37077 Göttingen (Germany)
2014-09-01
Predictive feedback control is an easy-to-implement method to stabilize unknown unstable periodic orbits in chaotic dynamical systems. Predictive feedback control is severely limited because asymptotic convergence speed decreases with stronger instabilities which in turn are typical for larger target periods, rendering it harder to effectively stabilize periodic orbits of large period. Here, we study stalled chaos control, where the application of control is stalled to make use of the chaotic, uncontrolled dynamics, and introduce an adaptation paradigm to overcome this limitation and speed up convergence. This modified control scheme is not only capable of stabilizing more periodic orbits than the original predictive feedback control but also speeds up convergence for typical chaotic maps, as illustrated in both theory and application. The proposed adaptation scheme provides a way to tune parameters online, yielding a broadly applicable, fast chaos control that converges reliably, even for periodic orbits of large period.
Noise tolerant spatiotemporal chaos computing.
Kia, Behnam; Kia, Sarvenaz; Lindner, John F; Sinha, Sudeshna; Ditto, William L
2014-12-01
We introduce and design a noise tolerant chaos computing system based on a coupled map lattice (CML) and the noise reduction capabilities inherent in coupled dynamical systems. The resulting spatiotemporal chaos computing system is more robust to noise than a single map chaos computing system. In this CML based approach to computing, under the coupled dynamics, the local noise from different nodes of the lattice diffuses across the lattice, and it attenuates each other's effects, resulting in a system with less noise content and a more robust chaos computing architecture.
Czech Academy of Sciences Publication Activity Database
Beran, Zdeněk; Čelikovský, Sergej
2013-01-01
Roč. 23, č. 5 (2013), 1350084-1-1350084-9 ISSN 0218-1274 R&D Projects: GA ČR GA13-20433S Institutional support: RVO:67985556 Keywords : Hyperspace * chaos * shadowing * Bernoulli shift Subject RIV: BC - Control Systems Theory Impact factor: 1.017, year: 2013 http://library.utia.cas.cz/separaty/2013/TR/beran-0392926.pdf
2005-01-01
8 September 2005 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows outcrops of light-toned, sedimentary rock among darker-toned mesas in Aram Chaos. Dark, windblown megaripples -- large ripples -- are also present at this location. Location near: 3.0oN, 21.6oW Image width: width: 3 km (1.9 mi) Illumination from: lower left Season: Northern Autumn
Earnshow, R; Jones, H
1991-01-01
This volume is based upon the presentations made at an international conference in London on the subject of 'Fractals and Chaos'. The objective of the conference was to bring together some of the leading practitioners and exponents in the overlapping fields of fractal geometry and chaos theory, with a view to exploring some of the relationships between the two domains. Based on this initial conference and subsequent exchanges between the editors and the authors, revised and updated papers were produced. These papers are contained in the present volume. We thank all those who contributed to this effort by way of planning and organisation, and also all those who helped in the production of this volume. In particular, we wish to express our appreciation to Gerhard Rossbach, Computer Science Editor, Craig Van Dyck, Production Director, and Nancy A. Rogers, who did the typesetting. A. J. Crilly R. A. Earnshaw H. Jones 1 March 1990 Introduction Fractals and Chaos The word 'fractal' was coined by Benoit Mandelbrot i...
Ruette, Sylvie
2017-01-01
The aim of this book is to survey the relations between the various kinds of chaos and related notions for continuous interval maps from a topological point of view. The papers on this topic are numerous and widely scattered in the literature; some of them are little known, difficult to find, or originally published in Russian, Ukrainian, or Chinese. Dynamical systems given by the iteration of a continuous map on an interval have been broadly studied because they are simple but nevertheless exhibit complex behaviors. They also allow numerical simulations, which enabled the discovery of some chaotic phenomena. Moreover, the "most interesting" part of some higher-dimensional systems can be of lower dimension, which allows, in some cases, boiling it down to systems in dimension one. Some of the more recent developments such as distributional chaos, the relation between entropy and Li-Yorke chaos, sequence entropy, and maps with infinitely many branches are presented in book form for the first time. The author gi...
Kalantari, Bahman
Polynomiography is the algorithmic visualization of iterative systems for computing roots of a complex polynomial. It is well known that iterations of a rational function in the complex plane result in chaotic behavior near its Julia set. In one scheme of computing polynomiography for a given polynomial p(z), we select an individual member from the Basic Family, an infinite fundamental family of rational iteration functions that in particular include Newton's. Polynomiography is an excellent means for observing, understanding, and comparing chaotic behavior for variety of iterative systems. Other iterative schemes in polynomiography are possible and result in chaotic behavior of different kinds. In another scheme, the Basic Family is collectively applied to p(z) and the iterates for any seed in the Voronoi cell of a root converge to that root. Polynomiography reveals chaotic behavior of another kind near the boundary of the Voronoi diagram of the roots. We also describe a novel Newton-Ellipsoid iterative system with its own chaos and exhibit images demonstrating polynomiographies of chaotic behavior of different kinds. Finally, we consider chaos for the more general case of polynomiography of complex analytic functions. On the one hand polynomiography is a powerful medium capable of demonstrating chaos in different forms, it is educationally instructive to students and researchers, also it gives rise to numerous research problems. On the other hand, it is a medium resulting in images with enormous aesthetic appeal to general audiences.
International Nuclear Information System (INIS)
Muñoz, L; Fernández-Ramírez, C; Relaño, A; Retamosa, J
2012-01-01
In the last decade quantum chaos has become a well established discipline with outreach to different fields, from condensed-matter to nuclear physics. The most important signature of quantum chaos is the statistical analysis of the energy spectrum, which distinguishes between systems with integrable and chaotic classical analogues. In recent years, spectral statistical techniques inherited from quantum chaos have been applied successfully to the baryon spectrum revealing its likely chaotic behaviour even at the lowest energies. However, the theoretical spectra present a behaviour closer to the statistics of integrable systems which makes theory and experiment statistically incompatible. The usual statement of missing resonances in the experimental spectrum when compared to the theoretical ones cannot account for the discrepancies. In this communication we report an improved analysis of the baryon spectrum, taking into account the low statistics and the error bars associated with each resonance. Our findings give a major support to the previous conclusions. Besides, analogue analyses are performed in the experimental meson spectrum, with comparison to theoretical models.
Universal signatures of quantum chaos
International Nuclear Information System (INIS)
Aurich, R.; Bolte, J.; Steiner, F.
1994-02-01
We discuss fingerprints of classical chaos in spectra of the corresponding bound quantum systems. A novel quantity to measure quantum chaos in spectra is proposed and a conjecture about its universal statistical behaviour is put forward. Numerical as well as theoretical evidence is provided in favour of the conjecture. (orig.)
Chaos Theory and Post Modernism
Snell, Joel
2009-01-01
Chaos theory is often associated with post modernism. However, one may make the point that both terms are misunderstood. The point of this article is to define both terms and indicate their relationship. Description: Chaos theory is associated with a definition of a theory dealing with variables (butterflies) that are not directly related to a…
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 Criminology: A critical analysis
McCarthy, Adrienne L.
There has been a push since the early 1980's for a paradigm shift in criminology from a Newtonian-based ontology to one of quantum physics. Primarily this effort has taken the form of integrating Chaos Theory into Criminology into what this thesis calls 'Chaos Criminology'. However, with the melding of any two fields, terms and concepts need to be translated properly, which has yet to be done. In addition to proving a translation between fields, this thesis also uses a set of criteria to evaluate the effectiveness of the current use of Chaos Theory in Criminology. While the results of the theory evaluation reveal that the current Chaos Criminology work is severely lacking and in need of development, there is some promise in the development of Marx's dialectical materialism with Chaos Theory.
[Shedding light on chaos theory].
Chou, Shieu-Ming
2004-06-01
Gleick (1987) said that only three twentieth century scientific theories would be important enough to continue be of use in the twenty-first century: The Theory of Relativity, Quantum Theory, and Chaos Theory. Chaos Theory has become a craze which is being used to forge a new scientific system. It has also been extensively applied in a variety of professions. The purpose of this article is to introduce chaos theory and its nursing applications. Chaos is a sign of regular order. This is to say that chaos theory emphasizes the intrinsic potential for regular order within disordered phenomena. It is to be hoped that this article will inspire more nursing scientists to apply this concept to clinical, research, or administrative fields in our profession.
Experimental investigation of new low-dimensional spin systems in vanadium oxides
International Nuclear Information System (INIS)
Kaul, E.E.
2005-01-01
In this dissertation we reported our experimental investigation of the magnetic properties of nine low-dimensional vanadium compounds. Two of these materials are completely new (Pb 2 V 5 O 12 and Pb 2 VO(PO 4 ) 2 ) and were found during our search for new low-dimensional vanadium oxides. Among the other seven vanadium compounds studied, three were physically investigated for the first time (Sr 2 VO(PO 4 ) 2 , BaZnVO(PO 4 ) 2 and SrZnVO(PO 4 ) 2 ). Two had hitherto only preliminary, and wrongly interpreted, susceptibility measurements reported in the literature (Sr 2 V 3 O 9 and Ba 2 V 3 O 9 ) while the remaining two (Li 2 VOSiO 4 and Li 2 VOGeO 4 ) were previously investigated in some detail but the interpretation of the data was controversial. We investigated the magnetic properties of these materials by means of magnetic susceptibility and specific heat (C p (T)) measurements (as well as single crystal ESR measurements in the case of Sr 2 V 3 O 9 ). We synthesized the samples necessary for our physical studies. That required a search of the optimal synthesis conditions for obtaining pure, high quality, polycrystalline samples. Single crystals of Sr 2 V 3 O 9 and Pb 2 VO(PO 4 ) 2 were also successfully grown. Pb 2 VO(PO 4 ) 2 , BaZnVO(PO 4 ) 2 , SrZnVO(PO 4 ) 2 , Li 2 VOSiO 4 and Li 2 VOGeO 4 were found to be experimental examples of frustrated square-lattice systems which are described by theJ 1 -J 2 model. We found that Li 2 VOSiO 4 and Li 2 VOGeO 4 posses a weakly frustrated antiferromagnetic square lattice while Pb 2 VO(PO 4 ) 2 , BaZnVO(PO 4 ) 2 and SrZnVO(PO 4 ) 2 form a more strongly frustrated ferromagnetic square lattice. Pb 2 V 5 O 12 is structurally and compositionally related to the two dimensional A 2+ V 4+ n O 2n+1 vanadates. Its structure consists of layers formed by edge- and corner-shared square VO 5 pyramids. The basic structural units are plaquettes consisting of six corner-shared pyramids pointing in the same direction, which form a spin
Workshop on low-dimensional quantum field theory and its applications
International Nuclear Information System (INIS)
Yamamoto, Hisashi
1990-02-01
The workshop on 'Low-Dimensional Quantum Field Theory and its Applications' was held at INS on December 18 - 20, 1989 with about seventy participants. Some pedagogical reviews and the latest results were delivered on the recent topics related to both solid-state and particle physics. Among them are quantum Hall effect, high T c superconductivity and related topics in low-dimensional quantum field theory. Many active discussions were made on these issues. (J.P.N.)
Fabrication, Characterization, Properties, and Applications of Low-Dimensional BiFeO3 Nanostructures
Directory of Open Access Journals (Sweden)
Heng Wu
2014-01-01
Full Text Available Low-dimensional BiFeO3 nanostructures (e.g., nanocrystals, nanowires, nanotubes, and nanoislands have received considerable attention due to their novel size-dependent properties and outstanding multiferroic properties at room temperature. In recent years, much progress has been made both in fabrications and (microstructural, electrical, and magnetic in characterizations of BiFeO3 low-dimensional nanostructures. An overview of the state of art in BiFeO3 low-dimensional nanostructures is presented. First, we review the fabrications of high-quality BiFeO3 low-dimensional nanostructures via a variety of techniques, and then the structural characterizations and physical properties of the BiFeO3 low-dimensional nanostructures are summarized. Their potential applications in the next-generation magnetoelectric random access memories and photovoltaic devices are also discussed. Finally, we conclude this review by providing our perspectives to the future researches of BiFeO3 low-dimensional nanostructures and some key problems are also outlined.
International Nuclear Information System (INIS)
Lin, Kevin K; Young, Lai-Sang
2008-01-01
Guided by a geometric understanding developed in earlier works of Wang and Young, we carry out numerical studies of shear-induced chaos in several parallel but different situations. The settings considered include periodic kicking of limit cycles, random kicks at Poisson times and continuous-time driving by white noise. The forcing of a quasi-periodic model describing two coupled oscillators is also investigated. In all cases, positive Lyapunov exponents are found in suitable parameter ranges when the forcing is suitably directed
Lin, Kevin K.; Young, Lai-Sang
2008-05-01
Guided by a geometric understanding developed in earlier works of Wang and Young, we carry out numerical studies of shear-induced chaos in several parallel but different situations. The settings considered include periodic kicking of limit cycles, random kicks at Poisson times and continuous-time driving by white noise. The forcing of a quasi-periodic model describing two coupled oscillators is also investigated. In all cases, positive Lyapunov exponents are found in suitable parameter ranges when the forcing is suitably directed.
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
Correlations between chaos in a perturbed sine-Gordon equation and a truncated model system
International Nuclear Information System (INIS)
Bishop, A.R.; Flesch, R.; Forests, M.G.; Overman, E.A.
1990-01-01
The purpose of this paper is to present a first step toward providing coordinates and associated dynamics for low-dimensional attractors in nearly integrable partial differential equations (pdes), in particular, where the truncated system reflects salient geometric properties of the pde. This is achieved by correlating: (1) numerical results on the bifurcations to temporal chaos with spatial coherence of the damped, periodically forced sine-Gordon equation with periodic boundary conditions; (2) an interpretation of the spatial and temporal bifurcation structures of this perturbed integrable system with regard to the exact structure of the sine-Gordon phase space; (3) a model dynamical systems problem, which is itself a perturbed integrable Hamiltonian system, derived from the perturbed sine-Gordon equation by a finite mode Fourier truncation in the nonlinear Schroedinger limit; and (4) the bifurcations to chaos in the truncated phase space. In particular, a potential source of chaos in both the pde and the model ordinary differential equation systems is focused on: the existence of homoclinic orbits in the unperturbed integrable phase space and their continuation in the perturbed problem. The evidence presented here supports the thesis that the chaotic attractors of the weakly perturbed periodic sine-Gordon system consists of low-dimensional metastable attacking states together with intermediate states that are O(1) unstable and correspond to homoclinic states in the integrable phase space. It is surmised that the chaotic dynamics on these attractors is due to the perturbation of these homocline integrable configurations
Quantum chaos: entropy signatures
International Nuclear Information System (INIS)
Miller, P.A.; Sarkar, S.; Zarum, R.
1998-01-01
A definition of quantum chaos is given in terms of entropy production rates for a quantum system coupled weakly to a reservoir. This allows the treatment of classical and quantum chaos on the same footing. In the quantum theory the entropy considered is the von Neumann entropy and in classical systems it is the Gibbs entropy. The rate of change of the coarse-grained Gibbs entropy of the classical system with time is given by the Kolmogorov-Sinai (KS) entropy. The relation between KS entropy and the rate of change of von Neumann entropy is investigated for the kicked rotator. For a system which is classically chaotic there is a linear relationship between these two entropies. Moreover it is possible to construct contour plots for the local KS entropy and compare it with the corresponding plots for the rate of change of von Neumann entropy. The quantitative and qualitative similarities of these plots are discussed for the standard map (kicked rotor) and the generalised cat maps. (author)
Sartori, Massimo; Gizzi, Leonardo; Lloyd, David G; Farina, Dario
2013-01-01
Human locomotion has been described as being generated by an impulsive (burst-like) excitation of groups of musculotendon units, with timing dependent on the biomechanical goal of the task. Despite this view being supported by many experimental observations on specific locomotion tasks, it is still unknown if the same impulsive controller (i.e., a low-dimensional set of time-delayed excitastion primitives) can be used as input drive for large musculoskeletal models across different human locomotion tasks. For this purpose, we extracted, with non-negative matrix factorization, five non-negative factors from a large sample of muscle electromyograms in two healthy subjects during four motor tasks. These included walking, running, sidestepping, and crossover cutting maneuvers. The extracted non-negative factors were then averaged and parameterized to obtain task-generic Gaussian-shaped impulsive excitation curves or primitives. These were used to drive a subject-specific musculoskeletal model of the human lower extremity. Results showed that the same set of five impulsive excitation primitives could be used to predict the dynamics of 34 musculotendon units and the resulting hip, knee and ankle joint moments (i.e., NRMSE = 0.18 ± 0.08, and R (2) = 0.73 ± 0.22 across all tasks and subjects) without substantial loss of accuracy with respect to using experimental electromyograms (i.e., NRMSE = 0.16 ± 0.07, and R (2) = 0.78 ± 0.18 across all tasks and subjects). Results support the hypothesis that biomechanically different motor tasks might share similar neuromuscular control strategies. This might have implications in neurorehabilitation technologies such as human-machine interfaces for the torque-driven, proportional control of powered prostheses and orthoses. In this, device control commands (i.e., predicted joint torque) could be derived without direct experimental data but relying on simple parameterized Gaussian-shaped curves, thus decreasing the input drive
Quantum mechanical suppression of chaos
International Nuclear Information System (INIS)
Bluemel, R.; Smilansky, U.
1990-01-01
The relation between determinism and predictability is the central issue in the study of 'deterministic chaos'. Much knowledge has been accumulated in the past 10 years about the chaotic dynamics of macroscopic (classical) systems. The implications of chaos in the microscopic quantum world is examined, in other words, how to reconcile the correspondence principle with the inherent uncertainties which reflect the wave nature of quantum dynamics. Recent atomic physics experiments demonstrate clearly that chaos is relevant to the microscopic world. In particular, such experiments emphasise the urgent need to clarify the genuine quantum mechanism which imposes severe limitations on quantum dynamics, and renders it so very different from its classical counterpart. (author)
Engineering Low Dimensional Materials with van der Waals Interaction
Jin, Chenhao
Two-dimensional van der Waals materials grow into a hot and big field in condensed matter physics in the past decade. One particularly intriguing thing is the possibility to stack different layers together as one wish, like playing a Lego game, which can create artificial structures that do not exist in nature. These new structures can enable rich new physics from interlayer interaction: The interaction is strong, because in low-dimension materials electrons are exposed to the interface and are susceptible to other layers; and the screening of interaction is less prominent. The consequence is rich, not only from the extensive list of two-dimensional materials available nowadays, but also from the freedom of interlayer configuration, such as displacement and twist angle, which creates a gigantic parameter space to play with. On the other hand, however, the huge parameter space sometimes can make it challenging to describe consistently with a single picture. For example, the large periodicity or even incommensurability in van der Waals systems creates difficulty in using periodic boundary condition. Worse still, the huge superlattice unit cell and overwhelming computational efforts involved to some extent prevent the establishment of a simple physical picture to understand the evolution of system properties in the parameter space of interlayer configuration. In the first part of the dissertation, I will focus on classification of the huge parameter space into subspaces, and introduce suitable theoretical approaches for each subspace. For each approach, I will discuss its validity, limitation, general solution, as well as a specific example of application demonstrating how one can obtain the most important effects of interlayer interaction with little computation efforts. Combining all the approaches introduced will provide an analytic solution to cover majority of the parameter space, which will be very helpful in understanding the intuitive physical picture behind
Careers Education: Evolving, Adapting and Building Resilience through Chaos
Loader, Trent
2011-01-01
Career educators' ultimate goal, given the new career management paradigm, should be to ensure that students are career resilient when they leave their studies (from whatever year level). This article outlines the chaos theory of careers and resilience. It then goes on to describe a four-lesson unit of careers education work that attempts to…
Recent development of chaos theory in topological dynamics
Li, Jian; Ye, Xiangdong
2015-01-01
We give a summary on the recent development of chaos theory in topological dynamics, focusing on Li-Yorke chaos, Devaney chaos, distributional chaos, positive topological entropy, weakly mixing sets and so on, and their relationships.
Low-Dimensional Organic-Inorganic Halide Perovskite: Structure, Properties, and Applications.
Misra, Ravi K; Cohen, Bat-El; Iagher, Lior; Etgar, Lioz
2017-10-09
Three-dimensional (3 D) perovskite has attracted a lot of attention owing to its success in photovoltaic (PV) solar cells. However, one of its major crucial issues lies in its stability, which has limited its commercialization. An important property of organic-inorganic perovskite is the possibility of forming a layered material by using long organic cations that do not fit into the octahedral cage. These long organic cations act as a "barrier" that "caps" 3 D perovskite to form the layered material. Controlling the number of perovskite layers could provide a confined structure with chemical and physical properties that are different from those of 3 D perovskite. This opens up a whole new batch of interesting materials with huge potential for optoelectronic applications. This Minireview presents the synthesis, properties, and structural orientation of low-dimensional perovskite. It also discusses the progress of low-dimensional perovskite in PV solar cells, which, to date, have performance comparable to that of 3 D perovskite but with enhanced stability. Finally, the use of low-dimensional perovskite in light-emitting diodes (LEDs) and photodetectors is discussed. The low-dimensional perovskites are promising candidates for LED devices, mainly because of their high radiative recombination as a result of the confined low-dimensional quantum well. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Ancient and Current Chaos Theories
Directory of Open Access Journals (Sweden)
Güngör Gündüz
2006-07-01
Full Text Available Chaos theories developed in the last three decades have made very important contributions to our understanding of dynamical systems and natural phenomena. The meaning of chaos in the current theories and in the past is somewhat different from each other. In this work, the properties of dynamical systems and the evolution of chaotic systems were discussed in terms of the views of ancient philosophers. The meaning of chaos in Anaximenes’ philosophy and its role in the Ancient natural philosophy has been discussed in relation to other natural philosophers such as of Anaximander, Parmenides, Heraclitus, Empedocles, Leucippus (i.e. atomists and Aristotle. In addition, the fundamental concepts of statistical mechanics and the current chaos theories were discussed in relation to the views in Ancient natural philosophy. The roots of the scientific concepts such as randomness, autocatalysis, nonlinear growth, information, pattern, etc. in the Ancient natural philosophy were investigated.
Quantum Instantons and Quantum Chaos
Jirari, H.; Kröger, H.; Luo, X. Q.; Moriarty, K. J. M.; Rubin, S. G.
1999-01-01
Based on a closed form expression for the path integral of quantum transition amplitudes, we suggest rigorous definitions of both, quantum instantons and quantum chaos. As an example we compute the quantum instanton of the double well potential.
Cryptography with chaos and shadowing
International Nuclear Information System (INIS)
Smaoui, Nejib; Kanso, Ali
2009-01-01
In this paper, we present a novel approach to encrypt a message (a text composed by some alphabets) using chaos and shadowing. First, we generate a numerical chaotic orbit based on the logistic map, and use the shadowing algorithm of Smaoui and Kostelich [Smaoui N, Kostelich E. Using chaos to shadow the quadratic map for all time. Int J Comput Math 1998;70:117-29] to show that there exists a finite number of true orbits that shadow the numerical orbit. Then, the finite number of maps generated is used in Baptista's algorithm [Baptista MS. Cryptography with chaos. Phys Lett A 1998;240:50-4] to encrypt each character of the message. It is shown that the use of chaos and shadowing in the encryption process enhances the security level.
Chaos and complexity by design
Energy Technology Data Exchange (ETDEWEB)
Roberts, Daniel A. [Center for Theoretical Physics and Department of Physics,Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States); School of Natural Sciences, Institute for Advanced Study,Princeton, NJ 08540 (United States); Yoshida, Beni [Perimeter Institute for Theoretical Physics,Waterloo, Ontario N2L 2Y5 (Canada)
2017-04-20
We study the relationship between quantum chaos and pseudorandomness by developing probes of unitary design. A natural probe of randomness is the “frame potential,” which is minimized by unitary k-designs and measures the 2-norm distance between the Haar random unitary ensemble and another ensemble. A natural probe of quantum chaos is out-of-time-order (OTO) four-point correlation functions. We show that the norm squared of a generalization of out-of-time-order 2k-point correlators is proportional to the kth frame potential, providing a quantitative connection between chaos and pseudorandomness. Additionally, we prove that these 2k-point correlators for Pauli operators completely determine the k-fold channel of an ensemble of unitary operators. Finally, we use a counting argument to obtain a lower bound on the quantum circuit complexity in terms of the frame potential. This provides a direct link between chaos, complexity, and randomness.
Chaos and complexity by design
International Nuclear Information System (INIS)
Roberts, Daniel A.; Yoshida, Beni
2017-01-01
We study the relationship between quantum chaos and pseudorandomness by developing probes of unitary design. A natural probe of randomness is the “frame potential,” which is minimized by unitary k-designs and measures the 2-norm distance between the Haar random unitary ensemble and another ensemble. A natural probe of quantum chaos is out-of-time-order (OTO) four-point correlation functions. We show that the norm squared of a generalization of out-of-time-order 2k-point correlators is proportional to the kth frame potential, providing a quantitative connection between chaos and pseudorandomness. Additionally, we prove that these 2k-point correlators for Pauli operators completely determine the k-fold channel of an ensemble of unitary operators. Finally, we use a counting argument to obtain a lower bound on the quantum circuit complexity in terms of the frame potential. This provides a direct link between chaos, complexity, and randomness.
Experimental Induction of Genome Chaos.
Ye, Christine J; Liu, Guo; Heng, Henry H
2018-01-01
Genome chaos, or karyotype chaos, represents a powerful survival strategy for somatic cells under high levels of stress/selection. Since the genome context, not the gene content, encodes the genomic blueprint of the cell, stress-induced rapid and massive reorganization of genome topology functions as a very important mechanism for genome (karyotype) evolution. In recent years, the phenomenon of genome chaos has been confirmed by various sequencing efforts, and many different terms have been coined to describe different subtypes of the chaotic genome including "chromothripsis," "chromoplexy," and "structural mutations." To advance this exciting field, we need an effective experimental system to induce and characterize the karyotype reorganization process. In this chapter, an experimental protocol to induce chaotic genomes is described, following a brief discussion of the mechanism and implication of genome chaos in cancer evolution.
Encounters with chaos and fractals
Gulick, Denny
2012-01-01
Periodic Points Iterates of Functions Fixed Points Periodic Points Families of Functions The Quadratic Family Bifurcations Period-3 Points The Schwarzian Derivative One-Dimensional Chaos Chaos Transitivity and Strong Chaos Conjugacy Cantor Sets Two-Dimensional Chaos Review of Matrices Dynamics of Linear FunctionsNonlinear Maps The Hénon Map The Horseshoe Map Systems of Differential Equations Review of Systems of Differential Equations Almost Linearity The Pendulum The Lorenz System Introduction to Fractals Self-Similarity The Sierpiński Gasket and Other "Monsters"Space-Filling Curves Similarity and Capacity DimensionsLyapunov Dimension Calculating Fractal Dimensions of Objects Creating Fractals Sets Metric Spaces The Hausdorff Metric Contractions and Affine Functions Iterated Function SystemsAlgorithms for Drawing Fractals Complex Fractals: Julia Sets and the Mandelbrot Set Complex Numbers and Functions Julia Sets The Mandelbrot Set Computer Programs Answers to Selected Exercises References Index.
Cryptography with chaos and shadowing
Energy Technology Data Exchange (ETDEWEB)
Smaoui, Nejib [Department of Mathematics and Computer Science, Kuwait University, P.O. Box 5969, Safat 13060 (Kuwait)], E-mail: nsmaoui64@yahoo.com; Kanso, Ali [Department of Mathematics and Computer Science, Kuwait University, P.O. Box 5969, Safat 13060 (Kuwait)], E-mail: akanso@hotmail.com
2009-11-30
In this paper, we present a novel approach to encrypt a message (a text composed by some alphabets) using chaos and shadowing. First, we generate a numerical chaotic orbit based on the logistic map, and use the shadowing algorithm of Smaoui and Kostelich [Smaoui N, Kostelich E. Using chaos to shadow the quadratic map for all time. Int J Comput Math 1998;70:117-29] to show that there exists a finite number of true orbits that shadow the numerical orbit. Then, the finite number of maps generated is used in Baptista's algorithm [Baptista MS. Cryptography with chaos. Phys Lett A 1998;240:50-4] to encrypt each character of the message. It is shown that the use of chaos and shadowing in the encryption process enhances the security level.
Optical digital chaos cryptography
Arenas-Pingarrón, Álvaro; González-Marcos, Ana P.; Rivas-Moscoso, José M.; Martín-Pereda, José A.
2007-10-01
In this work we present a new way to mask the data in a one-user communication system when direct sequence - code division multiple access (DS-CDMA) techniques are used. The code is generated by a digital chaotic generator, originally proposed by us and previously reported for a chaos cryptographic system. It is demonstrated that if the user's data signal is encoded with a bipolar phase-shift keying (BPSK) technique, usual in DS-CDMA, it can be easily recovered from a time-frequency domain representation. To avoid this situation, a new system is presented in which a previous dispersive stage is applied to the data signal. A time-frequency domain analysis is performed, and the devices required at the transmitter and receiver end, both user-independent, are presented for the optical domain.
DEFF Research Database (Denmark)
Lindberg, Erik
1996-01-01
Can we believe in the results of our circuit simulators ? Is it possible to distinguish between results due to numerical chaos and resultsdue to the eventual chaotic nature of our modelsof physical systems ?. Three experiments with SPICE are presented: (1) A "stable" active RCcircuit with poles...... in the right half plane. (2) "Chaotic" steady state behaviour of a non-chaotic dc power supply. (3) Analysis of a Colpitts oscillator with chaotic behaviour. In order to obtain reliable results from the SPICE simulators the users of these programs need insight not only in the use of the programs but also...... in the models of the circuits to be analyzed. If trimmed properly SPICE normally gives the correct result....
Ruelle, David
1991-01-01
Comment expliquer le hasard ? Peut-on rendre raison de l'irraisonnable ? Ce livre, où il est question des jeux de dés, des loteries, des billards, des attracteurs étranges, de l'astrologie et des oracles, du temps qu'il fera, du libre arbitre, de la mécanique quantique, de l'écoulement des fluides, du théorème de Gödel et des limites de l'entendement humain, expose les fondements et les conséquences de la théorie du chaos. David Ruelle est membre de l'Académie des sciences et professeur de physique théorique à l'Institut des hautes études scientifiques de Bures-sur-Yvette.
An Image Encryption Scheme Based on Hyperchaotic Rabinovich and Exponential Chaos Maps
Directory of Open Access Journals (Sweden)
Xiaojun Tong
2015-01-01
Full Text Available This paper proposes a new four-dimensional hyperchaotic map based on the Rabinovich system to realize chaotic encryption in higher dimension and improve the security. The chaotic sequences generated by Runge-Kutta method are combined with the chaotic sequences generated by an exponential chaos map to generate key sequences. The key sequences are used for image encryption. The security test results indicate that the new hyperchaotic system has high security and complexity. The comparison between the new hyperchaotic system and the several low-dimensional chaotic systems shows that the proposed system performs more efficiently.
Low-dimensional modeling of a driven cavity flow with two free parameters
DEFF Research Database (Denmark)
Jørgensen, Bo Hoffmann; Sørensen, Jens Nørkær; Brøns, Morten
2003-01-01
. By carrying out such a procedure one obtains a low-dimensional model consisting of a reduced set of Ordinary Differential Equations (ODEs) which models the original equations. A technique called Sequential Proper Orthogonal Decomposition (SPOD) is developed to perform decompositions suitable for low...... parameters to appear in the inhomogeneous boundary conditions without the addition of any constraints. This is necessary because both the driving lid and the rotating rod are controlled simultaneously. Apparently, the results reported for this model are the first to be obtained for a low-dimensional model...
A New Generation of Luminescent Materials Based on Low-Dimensional Perovskites
Pan, Jun
2017-06-02
Low-dimensional perovskites with high luminescence properties are promising materials for optoelectronic applications. In this article, properties of two emerging types of low-dimensional perovskites are discussed, including perovskite quantum dots CsPbX3 (X = Cl, Br or I) and zero-dimensional perovskite Cs4PbBr6. Moreover, their application for light down conversion in LCD backlighting systems and in visible light communication are also presented. With their superior optical properties, we believe that further development of these materials will potentially open more prospective applications, especially for optoelectronics devices.
Low-dimensionality and predictability of solar wind and global magnetosphere during magnetic storms
Zivkovic, Tatjana; Rypdal, Kristoffer
2011-01-01
This article is part of Tatjana Živkovics' doctoral thesis. Available in Munin at http://hdl.handle.net/10037/3231 The storm index SYM-H, the solar wind velocity v, and interplanetary magnetic field Bz show no signatures of low-dimensional dynamics in quiet periods, but tests for determinism in the time series indicate that SYM-H exhibits a significant low-dimensional component during storm time, suggesting that self-organization takes place during magnetic storms. Even though our analysis...
Effective method for construction of low-dimensional models for heat transfer process
Energy Technology Data Exchange (ETDEWEB)
Blinov, D.G.; Prokopov, V.G.; Sherenkovskii, Y.V.; Fialko, N.M.; Yurchuk, V.L. [National Academy of Sciences of Ukraine, Kiev (Ukraine). Inst. of Engineering Thermophysics
2004-12-01
A low-dimensional model based on the method of proper orthogonal decomposition (POD) and the method of polyargumental systems (MPS) for thermal conductivity problems with strongly localized source of heat has been presented. The key aspect of these methods is that they enable to avoid weak points of other projection methods, which consists in a priori choice of basis functions. It enables us to use the MPS method and the POD method as convenient means to construct low-dimensional models of heat and mass transfer problems. (Author)
Anokhina, Ekaterina V.
Low-dimensional and open-framework materials containing transition metals have a wide range of applications in redox catalysis, solid-state batteries, and electronic and magnetic devices. This dissertation reports on research carried out with the goal to develop a strategy for the preparation of low-dimensional and open-framework materials using octahedral metal clusters as building blocks. Our approach takes its roots from crystal engineering principles where the desired framework topologies are achieved through building block design. The key idea of this work is to induce directional bonding preferences in the cluster units using a combination of ligands with a large difference in charge density. This investigation led to the preparation and characterization of a new family of niobium oxychloride cluster compounds with original structure types exhibiting 1ow-dimensional or open-framework character. Most of these materials have framework topologies unprecedented in compounds containing octahedral clusters. Comparative analysis of their structural features indicates that the novel cluster connectivity patterns in these systems are the result of complex interplay between the effects of anisotropic ligand arrangement in the cluster unit and optimization of ligand-counterion electrostatic interactions. The important role played by these factors sets niobium oxychloride systems apart from cluster compounds with one ligand type or statistical ligand distribution where the main structure-determining factor is the total number of ligands. These results provide a blueprint for expanding the ligand combination strategy to other transition metal cluster systems and for the future rational design of cluster-based materials.
Chaos synchronization in autonomous chaotic system via hybrid feedback control
International Nuclear Information System (INIS)
Yang Lixin; Chu Yandong; Zhang Jiangang; Li Xianfeng; Chang Yingxiang
2009-01-01
This paper presents the synchronization of chaos by designing united controller. First, this method is implemented in synchronization of a simple system, then we realize the synchronization of Lue hyperchaotic system, we also take tracking control to realize the synchronization of Lue hyperchaotic system. Comparing with results, we can find that hybrid feedback control approach is more effective than tracking control for hyperchaotic system. Numerical simulations show the united synchronization method works well.
ICTP Summer Course on Low-Dimensional Quantum Field Theories for Condensed Matter Physicists
Morandi, G; Lu, Y
1995-01-01
This volume contains a set of pedagogical reviews covering the most recent applications of low-dimensional quantum field theory in condensed matter physics, written by experts who have made major contributions to this rapidly developing field of research. The main purpose is to introduce active young researchers to new ideas and new techniques which are not covered by the standard textbooks.
Near-Integrability of Low-Dimensional Periodic Klein-Gordon Lattices
Directory of Open Access Journals (Sweden)
Ognyan Christov
2018-01-01
Full Text Available The low-dimensional periodic Klein-Gordon lattices are studied for integrability. We prove that the periodic lattice with two particles and certain nonlinear potential is nonintegrable. However, in the cases of up to six particles, we prove that their Birkhoff-Gustavson normal forms are integrable, which allows us to apply KAM theory in most cases.
DEFF Research Database (Denmark)
Hvam, Jørn Märcher; Langbein, Wolfgang; Borri, Paola
1999-01-01
Coherent optical spectroscopy in the form of nonlinear transient four-wave mixing (TFWM) and linear resonant Rayleigh scattering (RRS) has been applied to investigate the exciton dynamics of low-dimensional semiconductor heterostructures. The dephasing times of excitons are determined from...
Statistical mechanics of low-dimensional Ginzburg-Landau fields. Some new results
International Nuclear Information System (INIS)
Barsan, V.
1987-08-01
The Ginzburg-Landau theory for low-dimensional systems is approached using the transfer matrix method. Analitical formulae for the thermodynamical quantities of interest are obtained in the one-dimensional case. An exact expression for the free energy of of a planar array of linear chains is deduced. A good agrement with numerical and experimental data is found.(authors)
2012 Symposium on Chaos, Complexity and Leadership
Erçetin, Şefika
2014-01-01
These proceedings from the 2012 symposium on "Chaos, complexity and leadership" reflect current research results from all branches of Chaos, Complex Systems and their applications in Management. Included are the diverse results in the fields of applied nonlinear methods, modeling of data and simulations, as well as theoretical achievements of Chaos and Complex Systems. Also highlighted are Leadership and Management applications of Chaos and Complexity Theory.
Quantum chaos: Statistical relaxation in discrete spectrum
International Nuclear Information System (INIS)
Chirikov, B.V.
1991-01-01
The controversial phenomenon of quantum chaos is discussed using the quantized standard map, or the kicked rotator, as a simple model. The relation to the classical dynamical chaos is tracked down on the basis of the correspondence principle. Various mechanisms of the quantum suppression of classical chaos are considered with an application to the excitation and ionization of Rydberg atoms in a microwave field. Several definitions of the quantum chaos are discussed. (author). 27 refs
Decoherence, determinism and chaos
International Nuclear Information System (INIS)
Noyes, H.P.
1994-01-01
The author claims by now to have made his case that modern work on fractals and chaos theory has already removed the presumption that classical physics is 'deterministic'. Further, he claims that in so far as classical relativistic field theory (i.e. electromagnetism and gravitation) are scale invariant, they are self-consistent only if the idea of 'test-particle' is introduced from outside the theory. Einstein spent the last years of his life trying to use singularities in the metric as 'particles' or to get them out of the non-linearities in a grand unified theory -- in vain. So classical physics in this sense cannot be the fundamental theory. However, the author claims to have shown that if he introduces a 'scale invariance bounded from below' by measurement accuracy, then Tanimura's generalization of the Feynman proof as reconstructed by Dyson allows him to make a consistent classical theory for decoherent sources sinks. Restoring coherence to classical physics via relativistic action-at-a distance is left as a task for the future. Relativistic quantum mechanics, properly reconstructed from a finite and discrete basis, emerges in much better shape. The concept of 'particles has to be replaced by NO-YES particulate events, and particle-antiparticle pair creation and annihilation properly formulated
Quasiperiodic transition to chaos in a plasma
International Nuclear Information System (INIS)
Weixing, D.; Huang Wei; Wang Xiaodong; Yu, C.X.
1993-01-01
The quasiperiodic transition to chaos in an undriven discharge plasma has been investigated. Results from the power spectrum and Lyapunov exponents quantitatively confirm the transition to chaos through quasiperiodicity. A low-dimension strange attractor has been found for this kind of plasma chaos
Further discussion on chaos in duopoly games
International Nuclear Information System (INIS)
Lu, Tianxiu; Zhu, Peiyong
2013-01-01
In this paper, we study Li–Yorke chaos, distributional chaos in a sequence, Li–Yorke sensitivity, sensitivity and distributional chaos of two-dimensional dynamical system of the form Φ(x, y) = (f(y), g(x))
Puzzles in studies of quantum chaos
International Nuclear Information System (INIS)
Xu Gongou
1994-01-01
Puzzles in studies of quantum chaos are discussed. From the view of global properties of quantum states, it is clarified that quantum chaos originates from the break-down of invariant properties of quantum canonical transformations. There exist precise correspondences between quantum and classical chaos
Towards chaos criterion in quantum field theory
Kuvshinov, V. I.; Kuzmin, A. V.
2002-01-01
Chaos criterion for quantum field theory is proposed. Its correspondence with classical chaos criterion in semi-classical regime is shown. It is demonstrated for real scalar field that proposed chaos criterion can be used to investigate stability of classical solutions of field equations.
Quantum chaos: statistical relaxation in discrete spectrum
International Nuclear Information System (INIS)
Chirikov, B.V.
1990-01-01
The controversial phenomenon of quantum chaos is discussed using the quantized standard map, or the kicked rotator, as a simple model. The relation to the classical dynamical chaos is tracked down on the basis of the correspondence principle. Several definitions of the quantum chaos are discussed. 27 refs
Hastily Formed Networks-Chaos to Recovery
2015-09-01
NETWORKS— CHAOS TO RECOVERY by Mark Arezzi September 2015 Thesis Co-Advisors: Douglas J. MacKinnon Brian Steckler THIS PAGE......systems to self-organize, adapt, and exert control over the chaos . Defining the role of communications requires an understanding of complexity, chaos
Chaos in the atomic and subatomic world
International Nuclear Information System (INIS)
Nussenzveig, H.M.
1992-01-01
This work discusses the possibility of the existence of chaos in the quantum level. In the macroscopic scale, chaos can be explained by the use of classical mechanics. The problem is to know whether there is any manifestation of chaos in the evolution of a system following the quantum mechanical laws. (A.C.A.S.)
Generation of flat wideband chaos with suppressed time delay signature by using optical time lens.
Jiang, Ning; Wang, Chao; Xue, Chenpeng; Li, Guilan; Lin, Shuqing; Qiu, Kun
2017-06-26
We propose a flat wideband chaos generation scheme that shows excellent time delay signature suppression effect, by injecting the chaotic output of general external cavity semiconductor laser into an optical time lens module composed of a phase modulator and two dispersive units. The numerical results demonstrate that by properly setting the parameters of the driving signal of phase modulator and the accumulated dispersion of dispersive units, the relaxation oscillation in chaos can be eliminated, wideband chaos generation with an efficient bandwidth up to several tens of GHz can be achieved, and the RF spectrum of generated chaotic signal is nearly as flat as uniform distribution. Moreover, the periodicity of chaos induced by the external cavity modes can be simultaneously destructed by the optical time lens module, based on this the time delay signature can be completely suppressed.
International Nuclear Information System (INIS)
Angius, S.; Bisegni, C.; Ciuffetti, P.
2016-01-01
The paper is aimed to present the !CHAOS open source project aimed to develop a prototype of a national private Cloud Computing infrastructure, devoted to accelerator control systems and large experiments of High Energy Physics (HEP). The !CHAOS project has been financed by MIUR (Italian Ministry of Research and Education) and aims to develop a new concept of control system and data acquisition framework by providing, with a high level of abstraction, all the services needed for controlling and managing a large scientific, or non-scientific, infrastructure. A beta version of the !CHAOS infrastructure will be released at the end of December 2015 and will run on private Cloud infrastructures based on OpenStack.
Angius, S.; Bisegni, C.; Ciuffetti, P.; Di Pirro, G.; Foggetta, L. G.; Galletti, F.; Gargana, R.; Gioscio, E.; Maselli, D.; Mazzitelli, G.; Michelotti, A.; Orrù, R.; Pistoni, M.; Spagnoli, F.; Spigone, D.; Stecchi, A.; Tonto, T.; Tota, M. A.; Catani, L.; Di Giulio, C.; Salina, G.; Buzzi, P.; Checcucci, B.; Lubrano, P.; Piccini, M.; Fattibene, E.; Michelotto, M.; Cavallaro, S. R.; Diana, B. F.; Enrico, F.; Pulvirenti, S.
2016-01-01
The paper is aimed to present the !CHAOS open source project aimed to develop a prototype of a national private Cloud Computing infrastructure, devoted to accelerator control systems and large experiments of High Energy Physics (HEP). The !CHAOS project has been financed by MIUR (Italian Ministry of Research and Education) and aims to develop a new concept of control system and data acquisition framework by providing, with a high level of aaabstraction, all the services needed for controlling and managing a large scientific, or non-scientific, infrastructure. A beta version of the !CHAOS infrastructure will be released at the end of December 2015 and will run on private Cloud infrastructures based on OpenStack.
International Nuclear Information System (INIS)
Soloviev, V.G.
1995-01-01
Order and chaos and order-to-chaos transition are treated in terms of nuclear wave functions. A quasiparticle-phonon interaction is responsible for the fragmentation of one- and many-quasiparticle and phonon states and for the mixing of closely spaced states. Complete damping of one-quasiparticle states cannot be considered as a transition to chaos due to large many-quasiparticle or quasiparticle-phonon terms in their wave functions. An experimental investigation of the strength distribution of many-quasiparticle and quasiparticle-phonon states should uncover a new region of a regularity in nuclei at intermediate excitation energy. A chaotic behaviour of nuclear states can be shifted to higher excitation energies. ((orig.))
Energy Technology Data Exchange (ETDEWEB)
Turiaci, Gustavo J. [Physics Department, Princeton University,Princeton NJ 08544 (United States); Verlinde, Herman [Physics Department, Princeton University,Princeton NJ 08544 (United States); Princeton Center for Theoretical Science, Princeton University,Princeton NJ 08544 (United States)
2016-12-21
We make three observations that help clarify the relation between CFT and quantum chaos. We show that any 1+1-D system in which conformal symmetry is non-linearly realized exhibits two main characteristics of chaos: maximal Lyapunov behavior and a spectrum of Ruelle resonances. We use this insight to identify a lattice model for quantum chaos, built from parafermionic spin variables with an equation of motion given by a Y-system. Finally we point to a relation between the spectrum of Ruelle resonances of a CFT and the analytic properties of OPE coefficients between light and heavy operators. In our model, this spectrum agrees with the quasi-normal modes of the BTZ black hole.
Chaos, decoherence and quantum cosmology
International Nuclear Information System (INIS)
Calzetta, Esteban
2012-01-01
In this topical review we discuss the connections between chaos, decoherence and quantum cosmology. We understand chaos as classical chaos in systems with a finite number of degrees of freedom, decoherence as environment induced decoherence and quantum cosmology as the theory of the Wheeler-DeWitt equation or else the consistent history formulation thereof, first in mini super spaces and later through its extension to midi super spaces. The overall conclusion is that consideration of decoherence is necessary (and probably sufficient) to sustain an interpretation of quantum cosmology based on the wavefunction of the Universe adopting a Wentzel-Kramers-Brillouin form for large Universes, but a definitive account of the semiclassical transition in classically chaotic cosmological models is not available in the literature yet. (topical review)
International Nuclear Information System (INIS)
Turiaci, Gustavo J.; Verlinde, Herman
2016-01-01
We make three observations that help clarify the relation between CFT and quantum chaos. We show that any 1+1-D system in which conformal symmetry is non-linearly realized exhibits two main characteristics of chaos: maximal Lyapunov behavior and a spectrum of Ruelle resonances. We use this insight to identify a lattice model for quantum chaos, built from parafermionic spin variables with an equation of motion given by a Y-system. Finally we point to a relation between the spectrum of Ruelle resonances of a CFT and the analytic properties of OPE coefficients between light and heavy operators. In our model, this spectrum agrees with the quasi-normal modes of the BTZ black hole.
Nuclear spectroscopy and quantum chaos
International Nuclear Information System (INIS)
Sakata, Fumihiko; Marumori, Toshio; Hashimoto, Yukio; Yamamoto, Yoshifumi; Tsukuma, Hidehiko; Iwasawa, Kazuo.
1990-05-01
In this paper, a recent development of INS-TSUKUBA joint research project on large-amplitude collective motion is summerized. The classical theory of nuclear collective dynamics formulated within the time-dependent Hartree-Fock theory is recapitulated and decisive role of the level crossing in the single-particle dynamics on the order-to-chaos transition of collective motion is discussed in detail. Extending the basic idea of the classical theory, we discuss a quantum theory of nuclear collective dynamics which allows us to properly define a concept of quantum chaos for each eigenfunction. By using numerical calculation, we illustrate what the quantum chaos for each eigenfunction means and its relation to usual definition based on the random matrix theory. (author)
1989-01-01
Le mouvement brownien ; la mémoire des atomes ; le chaos ; déterminisme et prédictabilité ; déterminisme et chaos ; les phénomènes de physique et les échelles de longueur ; un ordre caché dans la matière désordonnée ; les verres de spin et l'étude des milieux désordonnés ; la convection ; la croissance fractale ; la physique de la matière hétérogène ; la matière ultradivisée.
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.
Quantum Effects in the Thermoelectric Power Factor of Low-Dimensional Semiconductors.
Hung, Nguyen T; Hasdeo, Eddwi H; Nugraha, Ahmad R T; Dresselhaus, Mildred S; Saito, Riichiro
2016-07-15
We theoretically investigate the interplay between the confinement length L and the thermal de Broglie wavelength Λ to optimize the thermoelectric power factor of semiconducting materials. An analytical formula for the power factor is derived based on the one-band model assuming nondegenerate semiconductors to describe quantum effects on the power factor of the low-dimensional semiconductors. The power factor is enhanced for one- and two-dimensional semiconductors when L is smaller than Λ of the semiconductors. In this case, the low-dimensional semiconductors having L smaller than their Λ will give a better thermoelectric performance compared to their bulk counterpart. On the other hand, when L is larger than Λ, bulk semiconductors may give a higher power factor compared to the lower dimensional ones.
Dynamic screening and electron dynamics in low-dimensional metal systems
International Nuclear Information System (INIS)
Silkin, V.M.; Quijada, M.; Vergniory, M.G.; Alducin, M.; Borisov, A.G.; Diez Muino, R.; Juaristi, J.I.; Sanchez-Portal, D.; Chulkov, E.V.; Echenique, P.M.
2007-01-01
Recent advances in the theoretical description of dynamic screening and electron dynamics in metallic media are reviewed. The time-dependent building-up of screening in different situations is addressed. Perturbative and non-perturbative theories are used to study electron dynamics in low-dimensional systems, such as metal clusters, image states, surface states and quantum wells. Modification of the electronic lifetimes due to confinement effects is analyzed as well
Dielectric spectroscopy studies of low-disorder and low-dimensional materials
Tripathi, Pragya
2016-01-01
In this thesis we employ dielectric spectroscopy (in different implementations) to study the dielectric properties of different materials ranging from completely disordered supercooled liquids to low-disorder solids with only ratcheting reorientational motions, to low-dimensional systems such as thin films or needle-like crystals. The probed material properties include the electrical conductivity, the space-charge processes due to sample heterogeneities, molecular dynamics, hydrogen-bond dyna...
Low-dimensional model of resistive interchange convection in magnetized plasma
International Nuclear Information System (INIS)
Bazdenkov, S.; Sato, Tetsuya
1997-09-01
Self-organization and generation of large shear flow component in turbulent resistive interchange convection in magnetized plasma is considered. The effect of plasma density-electrostatic potential coupling via the inertialess electron dynamics along the magnetic field is shown to play significant role in the onset of shear component. The results of large-scale numerical simulation and low-dimensional (reduced) model are presented and compared. (author)
Distributional chaos for linear operators
Czech Academy of Sciences Publication Activity Database
Bernardes Jr., N.C.; Bonilla, A.; Müller, Vladimír; Peris, A.
2013-01-01
Roč. 265, č. 9 (2013), s. 2143-2163 ISSN 0022-1236 R&D Projects: GA ČR GA201/09/0473 Institutional support: RVO:67985840 Keywords : distributional chaos * hypercyclic operators * irregular vectors Subject RIV: BA - General Mathematics Impact factor: 1.152, year: 2013 http://www.sciencedirect.com/science/article/pii/S0022123613002450
Chaos Theory and International Relations
2016-12-01
King Oscar II 12 James E. Glenn, Chaos Theory: The Essentials for Military Applications (Newport, RI...Adolf Hitler in Germany, Alexander’s conquest of the Persian Empire, the arrival of Attila to Europe, the onset of the two Gulf Wars, the Arab Spring
Bright, Jim E. H.; Pryor, Robert G. L.
2011-01-01
The Chaos Theory of Careers (CTC; Pryor & Bright, 2011) construes both individuals and the contexts in which they develop their careers in terms of complex dynamical systems. Such systems perpetually operate under influences of stability and change both internally and in relation to each other. The CTC introduces new concepts to account for…
On the Mechanisms Behind Chaos
DEFF Research Database (Denmark)
Lindberg, Erik
2006-01-01
behind the chaotic behavior, e.g. one group is based on the sudden interrupt of inductive currents, another group is based on the sudden parallel coupling of capacitors with different voltages, and a third group may be based on multiplication of signals. An example of chaos based on disturbance...
Lecar, Myron; Franklin, Fred A.; Holman, Matthew J.; Murray, Norman J.
2001-01-01
The physical basis of chaos in the solar system is now better understood: In all cases investigated so far, chaotic orbits result from overlapping resonances. Perhaps the clearest examples are found in the asteroid belt. Overlapping resonances account for its kirkwood gaps and were used to predict and find evidence for very narrow gaps in the outer belt. Further afield, about one new "short-peroid" comet is discovered each year. They are believed to come from the "Kuiper Belt" (at 40 AU or more) via chaotic orbits produced by mean-motion and secular resonances with Neptune. Finally, the planetary system itself is not immune from chaos. In the inner solar system, overlapping secular resonances have been identified as the possible source of chaos. For example, Mercury in 1012 years, may suffer a close encounter with Venus or plunge into the Sun. In the outer solar system, three-body resonances have been identified as a source of chaos, but on an even longer time scale of 109 times the age of the solar system. On the human time scale, the planets do follow their orbits in a stately procession, and we can predict their trajectories for hundreds of thousands of years. That is because the mavericks, with shorter instability times, have long since been ejected. The solar system is not stable; it is just old!
Derouane, Eric; Hölderich, Wolfgang
1990-01-01
Low dimensionality is a multifarious concept which applies to very diversified materials. Thus, examples of low-dimensional systems are structures with one or several layers, single lines or patterns of lines, and small clusters isolated or dispersed in solid systems. Such low dimensional features can be produced in a wide variety of materials systems with a broad spectrum of scientific and practical interests. These features, in turn, induce specific properties and, particularly, specific transport properties. In the case of zeolites, low dimensionality appears in the network of small-diameter pores of molecular size, extending in one, two or three di mensions, that these solids exhibit as a characteristic feature and which explains the term of "molecular sieves" currently used to name these ma terials. Indeed, a large number of industrial processes for separation of gases and liquids, and for catalysis are based upon the use of this low dimensional feature in zeolites. For instance, zeolites constit...
Detection of Defect-Induced Magnetism in Low-Dimensional ZnO Structures by Magnetophotocurrent.
Lorite, Israel; Kumar, Yogesh; Esquinazi, Pablo; Zandalazini, Carlos; de Heluani, Silvia Perez
2015-09-09
The detection of defect-induced magnetic order in single low-dimensional oxide structures is in general difficult because of the relatively small yield of magnetically ordered regions. In this work, the effect of an external magnetic field on the transient photocurrent measured after light irradiation on different ZnO samples at room temperature is studied. It has been found that a magnetic field produces a change in the relaxation rate of the transient photocurrent only in magnetically ordered ZnO samples. This rate can decrease or increase with field, depending on whether the magnetically ordered region is in the bulk or only at the surface of the ZnO sample. The phenomenon reported here is of importance for the development of magneto-optical low-dimensional oxides devices and provides a new guideline for the detection of magnetic order in low-dimensional magnetic semiconductors. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Hamiltonian Chaos and Fractional Dynamics
International Nuclear Information System (INIS)
Combescure, M
2005-01-01
This book provides an introduction and discussion of the main issues in the current understanding of classical Hamiltonian chaos, and of its fractional space-time structure. It also develops the most complex and open problems in this context, and provides a set of possible applications of these notions to some fundamental questions of dynamics: complexity and entropy of systems, foundation of classical statistical physics on the basis of chaos theory, and so on. Starting with an introduction of the basic principles of the Hamiltonian theory of chaos, the book covers many topics that can be found elsewhere in the literature, but which are collected here for the readers' convenience. In the last three parts, the author develops topics which are not typically included in the standard textbooks; among them are: - the failure of the traditional description of chaotic dynamics in terms of diffusion equations; - he fractional kinematics, its foundation and renormalization group analysis; - 'pseudo-chaos', i.e. kinetics of systems with weak mixing and zero Lyapunov exponents; - directional complexity and entropy. The purpose of this book is to provide researchers and students in physics, mathematics and engineering with an overview of many aspects of chaos and fractality in Hamiltonian dynamical systems. In my opinion it achieves this aim, at least provided researchers and students (mainly those involved in mathematical physics) can complement this reading with comprehensive material from more specialized sources which are provided as references and 'further reading'. Each section contains introductory pedagogical material, often illustrated by figures coming from several numerical simulations which give the feeling of what's going on, and thus is very useful to the reader who is not very familiar with the topics presented. Some problems are included at the end of most sections to help the reader to go deeper into the subject. My one regret is that the book does not
Hermann, Jeffrey T.
1992-01-01
Every college should have a campuswide computer publishing policy. Policy options include (1) centralized publishing; (2) franchise, with a number of units doing their own publishing; or (3) limited, with the publications office producing the basics and assisting other units when feasible. To be successful, the policy must also be enforced. (MSE)
Meaning Finds a Way: Chaos (Theory) and Composition
Kyburz, Bonnie Lenore
2004-01-01
The explanatory power provided by the chaos theory is explored. A dynamic and reciprocal relationship between culture and chaos theory indicates that the progressive cultural work may be formed by the cross-disciplinary resonance of chaos theory.
Chaos, Chaos Control and Synchronization of a Gyrostat System
GE, Z.-M.; LIN, T.-N.
2002-03-01
The dynamic behavior of a gyrostat system subjected to external disturbance is studied in this paper. By applying numerical results, phase diagrams, power spectrum, period-T maps, and Lyapunov exponents are presented to observe periodic and choatic motions. The effect of the parameters changed in the system can be found in the bifurcation and parametric diagrams. For global analysis, the basins of attraction of each attractor of the system are located by employing the modified interpolated cell mapping (MICM) method. Several methods, the delayed feedback control, the addition of constant torque, the addition of periodic force, the addition of periodic impulse torque, injection of dither signal control, adaptive control algorithm (ACA) control and bang-bang control are used to control chaos effectively. Finally, synchronization of chaos in the gyrostat system is studied.
Does chaos assist localization or delocalization?
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.
Advances in chaos theory and intelligent control
Vaidyanathan, Sundarapandian
2016-01-01
The book reports on the latest advances in and applications of chaos theory and intelligent control. Written by eminent scientists and active researchers and using a clear, matter-of-fact style, it covers advanced theories, methods, and applications in a variety of research areas, and explains key concepts in modeling, analysis, and control of chaotic and hyperchaotic systems. Topics include fractional chaotic systems, chaos control, chaos synchronization, memristors, jerk circuits, chaotic systems with hidden attractors, mechanical and biological chaos, and circuit realization of chaotic systems. The book further covers fuzzy logic controllers, evolutionary algorithms, swarm intelligence, and petri nets among other topics. Not only does it provide the readers with chaos fundamentals and intelligent control-based algorithms; it also discusses key applications of chaos as well as multidisciplinary solutions developed via intelligent control. The book is a timely and comprehensive reference guide for graduate s...
Quantum chaos: diffusion photoeffect in hydrogen
Energy Technology Data Exchange (ETDEWEB)
Shepelyanskij, D L
1987-05-01
Ionization process in highly excited hydrogen atom in electromagnetic field is presented in the form of an extraordinary photoeffect, in which ionization at the frequency, being much lower than ionization energy, occurs much quicker than single-photon one. Such a quick ionization is explained by dynamic chaos occurence. Question, related to quantum effect influence on chaotic movement of the electron (quantum chaos) is considered. Electron excitation in the chaos area is described by a diffusional equation.
Discursive Maps at the Edge of Chaos
2017-05-25
Discursive Maps at the Edge of Chaos A Monograph by Major Mathieu Primeau Canadian Army, Royal Canadian Engineer School of Advanced Military...Master’s Thesis 3. DATES COVERED (From - To) JUN 2016 – MAY 2017 4. TITLE AND SUBTITLE Discursive Maps at the Edge of Chaos 5a. CONTRACT NUMBER 5b...meaning of boundaries and polarize conflict towards violence. The edge of chaos is the fine line between disorder and coherence. Discursive maps
Controlling Mackey-Glass chaos
Kiss, Gábor; Röst, Gergely
2017-11-01
The Mackey-Glass equation is the representative example of delay induced chaotic behavior. Here, we propose various control mechanisms so that otherwise erratic solutions are forced to converge to the positive equilibrium or to a periodic orbit oscillating around that equilibrium. We take advantage of some recent results of the delay differential literature, when a sufficiently large domain of the phase space has been shown to be attractive and invariant, where the system is governed by monotone delayed feedback and chaos is not possible due to some Poincaré-Bendixson type results. We systematically investigate what control mechanisms are suitable to drive the system into such a situation and prove that constant perturbation, proportional feedback control, Pyragas control, and state dependent delay control can all be efficient to control Mackey-Glass chaos with properly chosen control parameters.
Energy Technology Data Exchange (ETDEWEB)
Fitzpatrick, A. Liam [Department of Physics, Boston University,590 Commonwealth Avenue, Boston, MA 02215 (United States); Kaplan, Jared [Department of Physics and Astronomy, Johns Hopkins University,3400 N. Charles St, Baltimore, MD 21218 (United States)
2016-05-12
We use results on Virasoro conformal blocks to study chaotic dynamics in CFT{sub 2} at large central charge c. The Lyapunov exponent λ{sub L}, which is a diagnostic for the early onset of chaos, receives 1/c corrections that may be interpreted as λ{sub L}=((2π)/β)(1+(12/c)). However, out of time order correlators receive other equally important 1/c suppressed contributions that do not have such a simple interpretation. We revisit the proof of a bound on λ{sub L} that emerges at large c, focusing on CFT{sub 2} and explaining why our results do not conflict with the analysis leading to the bound. We also comment on relationships between chaos, scattering, causality, and bulk locality.
Spatiotemporal chaos from bursting dynamics
International Nuclear Information System (INIS)
Berenstein, Igal; De Decker, Yannick
2015-01-01
In this paper, we study the emergence of spatiotemporal chaos from mixed-mode oscillations, by using an extended Oregonator model. We show that bursting dynamics consisting of fast/slow mixed mode oscillations along a single attractor can lead to spatiotemporal chaotic dynamics, although the spatially homogeneous solution is itself non-chaotic. This behavior is observed far from the Hopf bifurcation and takes the form of a spatiotemporal intermittency where the system locally alternates between the fast and the slow phases of the mixed mode oscillations. We expect this form of spatiotemporal chaos to be generic for models in which one or several slow variables are coupled to activator-inhibitor type of oscillators
International Nuclear Information System (INIS)
Fitzpatrick, A. Liam; Kaplan, Jared
2016-01-01
We use results on Virasoro conformal blocks to study chaotic dynamics in CFT_2 at large central charge c. The Lyapunov exponent λ_L, which is a diagnostic for the early onset of chaos, receives 1/c corrections that may be interpreted as λ_L=((2π)/β)(1+(12/c)). However, out of time order correlators receive other equally important 1/c suppressed contributions that do not have such a simple interpretation. We revisit the proof of a bound on λ_L that emerges at large c, focusing on CFT_2 and explaining why our results do not conflict with the analysis leading to the bound. We also comment on relationships between chaos, scattering, causality, and bulk locality.
Oestreicher, Christian
2007-01-01
Whether every effect can be precisely linked to a given cause or to a list of causes has been a matter of debate for centuries, particularly during the 17th century, when astronomers became capable of predicting the trajectories of planets. Recent mathematical models applied to physics have included the idea that given phenomena cannot be predicted precisely, although they can be predicted to some extent, in line with the chaos theory. Concepts such as deterministic models, sensitivity to initial conditions, strange attractors, and fractal dimensions are inherent to the development of this theory A few situations involving normal or abnormal endogenous rhythms in biology have been analyzed following the principles of chaos theory. This is particularly the case with cardiac arrhythmias, but less so with biological clocks and circadian rhythms.
Magnetic field induced dynamical chaos.
Ray, Somrita; Baura, Alendu; Bag, Bidhan Chandra
2013-12-01
In this article, we have studied the dynamics of a particle having charge in the presence of a magnetic field. The motion of the particle is confined in the x-y plane under a two dimensional nonlinear potential. We have shown that constant magnetic field induced dynamical chaos is possible even for a force which is derived from a simple potential. For a given strength of the magnetic field, initial position, and velocity of the particle, the dynamics may be regular, but it may become chaotic when the field is time dependent. Chaotic dynamics is very often if the field is time dependent. Origin of chaos has been explored using the Hamiltonian function of the dynamics in terms of action and angle variables. Applicability of the present study has been discussed with a few examples.
Controlling Mackey-Glass chaos.
Kiss, Gábor; Röst, Gergely
2017-11-01
The Mackey-Glass equation is the representative example of delay induced chaotic behavior. Here, we propose various control mechanisms so that otherwise erratic solutions are forced to converge to the positive equilibrium or to a periodic orbit oscillating around that equilibrium. We take advantage of some recent results of the delay differential literature, when a sufficiently large domain of the phase space has been shown to be attractive and invariant, where the system is governed by monotone delayed feedback and chaos is not possible due to some Poincaré-Bendixson type results. We systematically investigate what control mechanisms are suitable to drive the system into such a situation and prove that constant perturbation, proportional feedback control, Pyragas control, and state dependent delay control can all be efficient to control Mackey-Glass chaos with properly chosen control parameters.
Oestreicher, Christian
2007-01-01
Whether every effect can be precisely linked to a given cause or to a list of causes has been a matter of debate for centuries, particularly during the 17th century when astronomers became capable of predicting the trajectories of planets. Recent mathematical models applied to physics have included the idea that given phenomena cannot be predicted precisely although they can be predicted to some extent in line with the chaos theory Concepts such as deterministic models, sensitivity to initial conditions, strange attractors, and fractal dimensions are inherent to the development of this theory, A few situations involving normal or abnormal endogenous rhythms in biology have been analyzed following the principles of chaos theory This is particularly the case with cardiac arrhythmias, but less so with biological clocks and circadian rhythms. PMID:17969865
International Nuclear Information System (INIS)
Kolesov, Andrei Yu; Rozov, Nikolai Kh
2009-01-01
A new definition of a chaotic invariant set is given for a continuous semiflow in a metric space. It generalizes the well-known definition due to Devaney and allows one to take into account a special feature occurring in the non-compact infinite-dimensional case: so-called turbulent chaos. The paper consists of two sections. The first contains several well-known facts from chaotic dynamics, together with new definitions and results. The second presents a concrete example demonstrating that our definition of chaos is meaningful. Namely, an infinite-dimensional system of ordinary differential equations is investigated having an attractor that is chaotic in the sense of the new definition but not in the sense of Devaney or Knudsen. Bibliography: 65 titles.
PHASE CHAOS IN THE DISCRETE KURAMOTO MODEL
DEFF Research Database (Denmark)
Maistrenko, V.; Vasylenko, A.; Maistrenko, Y.
2010-01-01
The paper describes the appearance of a novel, high-dimensional chaotic regime, called phase chaos, in a time-discrete Kuramoto model of globally coupled phase oscillators. This type of chaos is observed at small and intermediate values of the coupling strength. It arises from the nonlinear...... interaction among the oscillators, while the individual oscillators behave periodically when left uncoupled. For the four-dimensional time-discrete Kuramoto model, we outline the region of phase chaos in the parameter plane and determine the regions where phase chaos coexists with different periodic...
The CHAOS-4 geomagnetic field model
DEFF Research Database (Denmark)
Olsen, Nils; Lühr, H.; Finlay, Chris
2014-01-01
We present CHAOS-4, a new version in the CHAOS model series, which aims to describe the Earth's magnetic field with high spatial and temporal resolution. Terms up to spherical degree of at least n = 85 for the lithospheric field, and up to n = 16 for the time-varying core field are robustly...... to the core field, but the high-degree lithospheric field is regularized for n > 85. CHAOS-4 model is derived by merging two submodels: its low-degree part has been derived using similar model parametrization and data sets as used for previous CHAOS models (but of course including more recent data), while its...
The CHAOS-4 Geomagnetic Field Model
DEFF Research Database (Denmark)
Olsen, Nils; Finlay, Chris; Lühr, H.
We present CHAOS-4, a new version in the CHAOS model series, which aims at describing the Earth's magnetic field with high spatial resolution (terms up to spherical degree n=90 for the crustal field, and up to n=16 for the time-varying core field are robustly determined) and high temporal...... between the coordinate systems of the vector magnetometer and of the star sensor providing attitude information). The final CHAOS-4 model is derived by merging two sub-models: its low-degree part has been obtained using similar model parameterization and data sets as used for previous CHAOS models (but...
A quantum harmonic oscillator and strong chaos
International Nuclear Information System (INIS)
Oprocha, Piotr
2006-01-01
It is known that many physical systems which do not exhibit deterministic chaos when treated classically may exhibit such behaviour if treated from the quantum mechanics point of view. In this paper, we will show that an annihilation operator of the unforced quantum harmonic oscillator exhibits distributional chaos as introduced in B Schweizer and J SmItal (1994 Trans. Am. Math. Soc. 344 737-54). Our approach strengthens previous results on chaos in this model and provides a very powerful tool to measure chaos in other (quantum or classical) models
The chaos cookbook a practical programming guide
Pritchard, Joe
2014-01-01
The Chaos Cookbook: A Practical Programming Guide discusses the use of chaos in computer programming. The book is comprised of 11 chapters that tackle various topics relevant to chaos and programming. Chapter 1 reviews the concept of chaos, and Chapter 2 discusses the iterative functions. Chapters 3 and 4 cover differential and Lorenz equations. Chapter 5 talks about strange attractors, while Chapter 6 deals with the fractal link. The book also discusses the Mandelbrot set, and then covers the Julia sets. The other fractal systems and the cellular automata are also explained. The last chapter
Activation of zero-error classical capacity in low-dimensional quantum systems
Park, Jeonghoon; Heo, Jun
2018-06-01
Channel capacities of quantum channels can be nonadditive even if one of two quantum channels has no channel capacity. We call this phenomenon activation of the channel capacity. In this paper, we show that when we use a quantum channel on a qubit system, only a noiseless qubit channel can generate the activation of the zero-error classical capacity. In particular, we show that the zero-error classical capacity of two quantum channels on qubit systems cannot be activated. Furthermore, we present a class of examples showing the activation of the zero-error classical capacity in low-dimensional systems.
Heat transport in low-dimensional materials: A review and perspective
Directory of Open Access Journals (Sweden)
Zhiping Xu
2016-05-01
Full Text Available Heat transport is a key energetic process in materials and devices. The reduced sample size, low dimension of the problem and the rich spectrum of material imperfections introduce fruitful phenomena at nanoscale. In this review, we summarize recent progresses in the understanding of heat transport process in low-dimensional materials, with focus on the roles of defects, disorder, interfaces, and the quantum-mechanical effect. New physics uncovered from computational simulations, experimental studies, and predictable models will be reviewed, followed by a perspective on open challenges.
Gritsev, Vladimir; Demler, Eugene; Lukin, Mikhail; Polkovnikov, Anatoli
2007-11-16
We study the problem of rapid change of the interaction parameter (quench) in a many-body low-dimensional system. It is shown that, measuring the correlation functions after the quench, the information about a spectrum of collective excitations in a system can be obtained. This observation is supported by analysis of several integrable models and we argue that it is valid for nonintegrable models as well. Our conclusions are supplemented by performing exact numerical simulations on finite systems. We propose that measuring the power spectrum in a dynamically split 1D Bose-Einsten condensate into two coupled condensates can be used as an experimental test of our predictions.
How to measure the cooper pair mass using plasmons in low-dimensional superconductor structures
International Nuclear Information System (INIS)
Mishonov, T.M.
1990-06-01
The creation of the Cooper pair mass-spectroscopy is suggested. The plasmons in low-dimensional superconductor structures (layers or wires in dielectric background) are theoretically considered to that purpose. The Cooper pair mass m * can be determined by measurements of the Doppler shift of the plasmon frequency when a direct current is applied through the superconductor. The plasmons with frequency ω lower than the superconducting gap 2 Δ can be detected by the same fare-infrared (FIR) absorption technique and grating couplings used previously for investigation of two-dimension (2D) plasmons in semiconductor microstructures. (author). 17 refs, 2 figs
Low-Dimensional Nanomaterials as Active Layer Components in Thin-Film Photovoltaics
Shastry, Tejas Attreya
Thin-film photovoltaics offer the promise of cost-effective and scalable solar energy conversion, particularly for applications of semi-transparent solar cells where the poor absorption of commercially-available silicon is inadequate. Applications ranging from roof coatings that capture solar energy to semi-transparent windows that harvest the immense amount of incident sunlight on buildings could be realized with efficient and stable thin-film solar cells. However, the lifetime and efficiency of thin-film solar cells continue to trail their inorganic silicon counterparts. Low-dimensional nanomaterials, such as carbon nanotubes and two-dimensional metal dichalcogenides, have recently been explored as materials in thin-film solar cells due to their exceptional optoelectronic properties, solution-processability, and chemical inertness. Thus far, issues with the processing of these materials has held back their implementation in efficient photovoltaics. This dissertation reports processing advances that enable demonstrations of low-dimensional nanomaterials in thin-film solar cells. These low-dimensional photovoltaics show enhanced photovoltaic efficiency and environmental stability in comparison to previous devices, with a focus on semiconducting single-walled carbon nanotubes as an active layer component. The introduction summarizes recent advances in the processing of carbon nanotubes and their implementation through the thin-film photovoltaic architecture, as well as the use of two-dimensional metal dichalcogenides in photovoltaic applications and potential future directions for all-nanomaterial solar cells. The following chapter reports a study of the interaction between carbon nanotubes and surfactants that enables them to be sorted by electronic type via density gradient ultracentrifugation. These insights are utilized to construct of a broad distribution of carbon nanotubes that absorb throughout the solar spectrum. This polychiral distribution is then shown
Characteristics of exciton photoluminescence kinetics in low-dimensional silicon structures
Sachenko, A V; Manojlov, E G; Svechnikov, S V
2001-01-01
The time-resolved visible photoluminescence of porous nanocrystalline silicon films obtained by laser ablation have been measured within the temperature range 90-300 K. A study has been made of the interrelationship between photoluminescence characteristics (intensity, emission spectra, relaxation times, their temperature dependencies and structural and dielectric properties (size and shapes of Si nanocrystals, oxide phase of nanocrystal coating, porosity). A photoluminescence model is proposed that describes photon absorption and emission occurring in quantum-size Si nanocrystals while coupled subsystems of electron-hole pairs and excitons take part in the recombination. Possible excitonic Auger recombination mechanism in low-dimensional silicon structures is considered
Chaos, complexity, and random matrices
Cotler, Jordan; Hunter-Jones, Nicholas; Liu, Junyu; Yoshida, Beni
2017-11-01
Chaos and complexity entail an entropic and computational obstruction to describing a system, and thus are intrinsically difficult to characterize. In this paper, we consider time evolution by Gaussian Unitary Ensemble (GUE) Hamiltonians and analytically compute out-of-time-ordered correlation functions (OTOCs) and frame potentials to quantify scrambling, Haar-randomness, and circuit complexity. While our random matrix analysis gives a qualitatively correct prediction of the late-time behavior of chaotic systems, we find unphysical behavior at early times including an O(1) scrambling time and the apparent breakdown of spatial and temporal locality. The salient feature of GUE Hamiltonians which gives us computational traction is the Haar-invariance of the ensemble, meaning that the ensemble-averaged dynamics look the same in any basis. Motivated by this property of the GUE, we introduce k-invariance as a precise definition of what it means for the dynamics of a quantum system to be described by random matrix theory. We envision that the dynamical onset of approximate k-invariance will be a useful tool for capturing the transition from early-time chaos, as seen by OTOCs, to late-time chaos, as seen by random matrix theory.
Kasimov, Aslan R.
2013-03-08
We propose the following model equation, ut+1/2(u2−uus)x=f(x,us) that predicts chaotic shock waves, similar to those in detonations in chemically reacting mixtures. The equation is given on the half line, x<0, and the shock is located at x=0 for any t≥0. Here, us(t) is the shock state and the source term f is taken to mimic the chemical energy release in detonations. This equation retains the essential physics needed to reproduce many properties of detonations in gaseous reactive mixtures: steady traveling wave solutions, instability of such solutions, and the onset of chaos. Our model is the first (to our knowledge) to describe chaos in shock waves by a scalar first-order partial differential equation. The chaos arises in the equation thanks to an interplay between the nonlinearity of the inviscid Burgers equation and a novel forcing term that is nonlocal in nature and has deep physical roots in reactive Euler equations.
Low-dimensional carbon and MXene-based electrochemical capacitor electrodes.
Yoon, Yeoheung; Lee, Keunsik; Lee, Hyoyoung
2016-04-29
Due to their unique structure and outstanding intrinsic physical properties such as extraordinarily high electrical conductivity, large surface area, and various chemical functionalities, low-dimension-based materials exhibit great potential for application in electrochemical capacitors (ECs). The electrical properties of electrochemical capacitors are determined by the electrode materials. Because energy charge storage is a surface process, the surface properties of the electrode materials greatly influence the electrochemical performance of the cell. Recently, graphene, a single layer of sp(2)-bonded carbon atoms arrayed into two-dimensional carbon nanomaterial, has attracted wide interest as an electrode material for electrochemical capacitor applications due to its unique properties, including a high electrical conductivity and large surface area. Several low-dimensional materials with large surface areas and high conductivity such as onion-like carbons (OLCs), carbide-derived carbons (CDCs), carbon nanotubes (CNTs), graphene, metal hydroxide, transition metal dichalcogenides (TMDs), and most recently MXene, have been developed for electrochemical capacitors. Therefore, it is useful to understand the current issues of low-dimensional materials and their device applications.
Synthesis, Properties, and Applications of Low-Dimensional Carbon-Related Nano materials
International Nuclear Information System (INIS)
Mostofizadeh, A.; Li, Y.; Song, B.; Huang, Y.; Mostofizadeh, A.
2011-01-01
In recent years, many theoretical and experimental studies have been carried out to develop one of the most interesting aspects of the science and nano technology which is called carbon-related nano materials. The goal of this paper is to provide a review of some of the most exciting and important developments in the synthesis, properties, and applications of low-dimensional carbon nano materials. Carbon nano materials are formed in various structural features using several different processing methods. The synthesis techniques used to produce specific kinds of low-dimensional carbon nano materials such as zero-dimensional carbon nano materials (including fullerene, carbon-encapsulated metal nanoparticles, nano diamond, and onion-like carbons), one-dimensional carbon nano materials (including carbon nano fibers and carbon nano tubes), and two-dimensional carbon nano materials (including graphene and carbon nano walls) are discussed in this paper. Subsequently, the paper deals with an overview of the properties of the mainly important products as well as some important applications and the future outlooks of these advanced nano materials.
Directory of Open Access Journals (Sweden)
Chenchen Jiang
2017-01-01
Full Text Available In the past decades, in situ scanning electron microscopy (SEM has become a powerful technique for the experimental study of low-dimensional (1D/2D nanomaterials, since it can provide unprecedented details for individual nanostructures upon mechanical and electrical stimulus and thus uncover the fundamental deformation and failure mechanisms for their device applications. In this overview, we summarized recent developments on in situ SEM-based mechanical and electrical characterization techniques including tensile, compression, bending, and electrical property probing on individual nanostructures, as well as the state-of-the-art electromechanical coupling analysis. In addition, the advantages and disadvantages of in situ SEM tests were also discussed with some possible solutions to address the challenges. Furthermore, critical challenges were also discussed for the development and design of robust in situ SEM characterization platform with higher resolution and wider range of samples. These experimental efforts have offered in-depth understanding on the mechanical and electrical properties of low-dimensional nanomaterial components and given guidelines for their further structural and functional applications.
Synthesis, Properties, and Applications of Low-Dimensional Carbon-Related Nanomaterials
Directory of Open Access Journals (Sweden)
Ali Mostofizadeh
2011-01-01
Full Text Available In recent years, many theoretical and experimental studies have been carried out to develop one of the most interesting aspects of the science and nanotechnology which is called carbon-related nanomaterials. The goal of this paper is to provide a review of some of the most exciting and important developments in the synthesis, properties, and applications of low-dimensional carbon nanomaterials. Carbon nanomaterials are formed in various structural features using several different processing methods. The synthesis techniques used to produce specific kinds of low-dimensional carbon nanomaterials such as zero-dimensional carbon nanomaterials (including fullerene, carbon-encapsulated metal nanoparticles, nanodiamond, and onion-like carbons, one-dimensional carbon nanomaterials (including carbon nanofibers and carbon nanotubes, and two-dimensional carbon nanomaterials (including graphene and carbon nanowalls are discussed in this paper. Subsequently, the paper deals with an overview of the properties of the mainly important products as well as some important applications and the future outlooks of these advanced nanomaterials.
Low-dimensional carbon and MXene-based electrochemical capacitor electrodes
International Nuclear Information System (INIS)
Yoon, Yeoheung; Lee, Hyoyoung; Lee, Keunsik
2016-01-01
Due to their unique structure and outstanding intrinsic physical properties such as extraordinarily high electrical conductivity, large surface area, and various chemical functionalities, low-dimension-based materials exhibit great potential for application in electrochemical capacitors (ECs). The electrical properties of electrochemical capacitors are determined by the electrode materials. Because energy charge storage is a surface process, the surface properties of the electrode materials greatly influence the electrochemical performance of the cell. Recently, graphene, a single layer of sp 2 -bonded carbon atoms arrayed into two-dimensional carbon nanomaterial, has attracted wide interest as an electrode material for electrochemical capacitor applications due to its unique properties, including a high electrical conductivity and large surface area. Several low-dimensional materials with large surface areas and high conductivity such as onion-like carbons (OLCs), carbide-derived carbons (CDCs), carbon nanotubes (CNTs), graphene, metal hydroxide, transition metal dichalcogenides (TMDs), and most recently MXene, have been developed for electrochemical capacitors. Therefore, it is useful to understand the current issues of low-dimensional materials and their device applications. (topical review)
Jiang, Chenchen; Lu, Haojian; Zhang, Hongti; Shen, Yajing; Lu, Yang
2017-01-01
In the past decades, in situ scanning electron microscopy (SEM) has become a powerful technique for the experimental study of low-dimensional (1D/2D) nanomaterials, since it can provide unprecedented details for individual nanostructures upon mechanical and electrical stimulus and thus uncover the fundamental deformation and failure mechanisms for their device applications. In this overview, we summarized recent developments on in situ SEM-based mechanical and electrical characterization techniques including tensile, compression, bending, and electrical property probing on individual nanostructures, as well as the state-of-the-art electromechanical coupling analysis. In addition, the advantages and disadvantages of in situ SEM tests were also discussed with some possible solutions to address the challenges. Furthermore, critical challenges were also discussed for the development and design of robust in situ SEM characterization platform with higher resolution and wider range of samples. These experimental efforts have offered in-depth understanding on the mechanical and electrical properties of low-dimensional nanomaterial components and given guidelines for their further structural and functional applications.
Chaos desynchronization in strongly coupled systems
International Nuclear Information System (INIS)
Wu Ye; Liu Weiqing; Xiao, Jinghua; Zhan Meng
2007-01-01
The dynamics of chaos desynchronization in strongly coupled oscillator systems is studied. We find a new bifurcation from synchronous chaotic state, chaotic short wave bifurcation, i.e. a chaotic desynchronization attractor is new born in the systems due to chaos desynchronization. In comparison with the usual periodic short wave bifurcation, very rich but distinct phenomena are observed
Galloping instability to chaos of cables
Luo, Albert C J
2017-01-01
This book provides students and researchers with a systematic solution for fluid-induced structural vibrations, galloping instability and the chaos of cables. They will also gain a better understanding of stable and unstable periodic motions and chaos in fluid-induced structural vibrations. Further, the results presented here will help engineers effectively design and analyze fluid-induced vibrations.
Path and semimartingale properties of chaos processes
DEFF Research Database (Denmark)
Basse-O'Connor, Andreas; Graversen, Svend-Erik
2010-01-01
The present paper characterizes various properties of chaos processes which in particular include processes where all time variables admit a Wiener chaos expansion of a fixed finite order. The main focus is on the semimartingale property, p-variation and continuity. The general results obtained...
Chaos and fractals. Applications to nuclear engineering
International Nuclear Information System (INIS)
Clausse, A.; Delmastro, D.F.
1990-01-01
This work presents a description of the research lines carried out by the authors on chaos and fractal theories, oriented to the nuclear field. The possibilities that appear in the nuclear security branch where the information deriving from chaos and fractal techniques may help to the development of better criteria and more reliable designs, are of special importance. (Author) [es
Xiao, Hang
In the past several decades, low-dimensional materials (0D materials, 1D materials and 2D materials) have attracted much interest from both the experimental and theoretical points of view. Because of the quantum confinement effect, low-dimensional materials have exhibited a kaleidoscope of fascinating phenomena and unusual physical and chemical properties, shedding light on many novel applications. Despite the enormous success has been achieved in the research of low-dimensional materials, there are three fundamental challenges of research in low-dimensional materials: 1) Develop new computational tools to accurately describe the properties of low-dimensional materials with low computational cost. 2) Predict and synthesize new low-dimensional materials with novel properties. 3) Reveal new phenomenon induced by the interaction between low-dimensional materials and the surrounding environment. In this thesis, atomistic modelling tools have been applied to address these challenges. We first developed ReaxFF parameters for phosphorus and hydrogen to give an accurate description of the chemical and mechanical properties of pristine and defected black phosphorene. ReaxFF for P/H is transferable to a wide range of phosphorus and hydrogen containing systems including bulk black phosphorus, blue phosphorene, edge-hydrogenated phosphorene, phosphorus clusters and phosphorus hydride molecules. The potential parameters were obtained by conducting global optimization with respect to a set of reference data generated by extensive ab initio calculations. We extended ReaxFF by adding a 60° correction term which significantly improved the description of phosphorus clusters. Emphasis was placed on the mechanical response of black phosphorene with different types of defects. Compared to the nonreactive SW potential of phosphorene, ReaxFF for P/H systems provides a significant improvement in describing the mechanical properties of the pristine and defected black phosphorene, as well
4th international interdisciplinary chaos symposium
Banerjee, Santo; Caglar, Suleyman; Ozer, Mehmet; Chaos and complex systems
2013-01-01
Complexity Science and Chaos Theory are fascinating areas of scientific research with wide-ranging applications. The interdisciplinary nature and ubiquity of complexity and chaos are features that provides scientists with a motivation to pursue general theoretical tools and frameworks. Complex systems give rise to emergent behaviors, which in turn produce novel and interesting phenomena in science, engineering, as well as in the socio-economic sciences. The aim of all Symposia on Chaos and Complex Systems (CCS) is to bring together scientists, engineers, economists and social scientists, and to discuss the latest insights and results obtained in the area of corresponding nonlinear-system complex (chaotic) behavior. Especially for the “4th International Interdisciplinary Chaos Symposium on Chaos and Complex Systems,” which took place April 29th to May 2nd, 2012 in Antalya, Turkey, the scope of the symposium had been further enlarged so as to encompass the presentation of work from circuits to econophysic...
Chaos the science of predictable random motion
Kautz, Richard
2011-01-01
Based on only elementary mathematics, this engaging account of chaos theory bridges the gap between introductions for the layman and college-level texts. It develops the science of dynamics in terms of small time steps, describes the phenomenon of chaos through simple examples, and concludes with a close look at a homoclinic tangle, the mathematical monster at the heart of chaos. The presentation is enhanced by many figures, animations of chaotic motion (available on a companion CD), and biographical sketches of the pioneers of dynamics and chaos theory. To ensure accessibility to motivated high school students, care has been taken to explain advanced mathematical concepts simply, including exponentials and logarithms, probability, correlation, frequency analysis, fractals, and transfinite numbers. These tools help to resolve the intriguing paradox of motion that is predictable and yet random, while the final chapter explores the various ways chaos theory has been put to practical use.
Semiconductor Lasers Stability, Instability and Chaos
Ohtsubo, Junji
2013-01-01
This third edition of “Semiconductor Lasers, Stability, Instability and Chaos” was significantly extended. In the previous edition, the dynamics and characteristics of chaos in semiconductor lasers after the introduction of the fundamental theory of laser chaos and chaotic dynamics induced by self-optical feedback and optical injection was discussed. Semiconductor lasers with new device structures, such as vertical-cavity surface-emitting lasers and broad-area semiconductor lasers, are interesting devices from the viewpoint of chaotic dynamics since they essentially involve chaotic dynamics even in their free-running oscillations. These topics are also treated with respect to the new developments in the current edition. Also the control of such instabilities and chaos control are critical issues for applications. Another interesting and important issue of semiconductor laser chaos in this third edition is chaos synchronization between two lasers and the application to optical secure communication. One o...
Scaling of chaos in strongly nonlinear lattices.
Mulansky, Mario
2014-06-01
Although it is now understood that chaos in complex classical systems is the foundation of thermodynamic behavior, the detailed relations between the microscopic properties of the chaotic dynamics and the macroscopic thermodynamic observations still remain mostly in the dark. In this work, we numerically analyze the probability of chaos in strongly nonlinear Hamiltonian systems and find different scaling properties depending on the nonlinear structure of the model. We argue that these different scaling laws of chaos have definite consequences for the macroscopic diffusive behavior, as chaos is the microscopic mechanism of diffusion. This is compared with previous results on chaotic diffusion [M. Mulansky and A. Pikovsky, New J. Phys. 15, 053015 (2013)], and a relation between microscopic chaos and macroscopic diffusion is established.
Chaos and bifurcations in periodic windows observed in plasmas
International Nuclear Information System (INIS)
Qin, J.; Wang, L.; Yuan, D.P.; Gao, P.; Zhang, B.Z.
1989-01-01
We report the experimental observations of deterministic chaos in a steady-state plasma which is not driven by any extra periodic forces. Two routes to chaos have been found, period-doubling and intermittent chaos. The fine structures in chaos such as periodic windows and bifurcations in windows have also been observed
Prediction based chaos control via a new neural network
International Nuclear Information System (INIS)
Shen Liqun; Wang Mao; Liu Wanyu; Sun Guanghui
2008-01-01
In this Letter, a new chaos control scheme based on chaos prediction is proposed. To perform chaos prediction, a new neural network architecture for complex nonlinear approximation is proposed. And the difficulty in building and training the neural network is also reduced. Simulation results of Logistic map and Lorenz system show the effectiveness of the proposed chaos control scheme and the proposed neural network
Homoclinic tubes and chaos in perturbed sine-Gordon equation
International Nuclear Information System (INIS)
Li, Y. Charles
2004-01-01
Sine-Gordon equation under a quasi-periodic perturbation or a chaotic perturbation is studied. Existence of a homoclinic tube is proved. Established are chaos associated with the homoclinic tube, and 'chaos cascade' referring to the embeddings of smaller scale chaos in larger scale chaos
Kasimov, Aslan R; Faria, Luiz M; Rosales, Rodolfo R
2013-03-08
We propose the following model equation, u(t) + 1/2(u(2)-uu(s))x = f(x,u(s)) that predicts chaotic shock waves, similar to those in detonations in chemically reacting mixtures. The equation is given on the half line, xorder partial differential equation. The chaos arises in the equation thanks to an interplay between the nonlinearity of the inviscid Burgers equation and a novel forcing term that is nonlocal in nature and has deep physical roots in reactive Euler equations.
Chaos control in duffing system
International Nuclear Information System (INIS)
Wang Ruiqi; Deng Jin; Jing Zhujun
2006-01-01
Analytical and numerical results concerning the inhibition of chaos in Duffing's equation with two weak forcing excitations are presented. We theoretically give parameter-space regions by using Melnikov's function, where chaotic states can be suppressed. The intervals of initial phase difference between the two excitations for which chaotic dynamics can be eliminated are given. Meanwhile, the influence of the phase difference on Lyapunov exponents for different frequencies is investigated. Numerical simulation results show the consistence with the theoretical analysis and the chaotic motions can be controlled to period-motions by adjusting parameter of suppressing excitation
Deterministic chaos in entangled eigenstates
Schlegel, K. G.; Förster, S.
2008-05-01
We investigate the problem of deterministic chaos in connection with entangled states using the Bohmian formulation of quantum mechanics. We show for a two particle system in a harmonic oscillator potential, that in a case of entanglement and three energy eigen-values the maximum Lyapunov-parameters of a representative ensemble of trajectories for large times develops to a narrow positive distribution, which indicates nearly complete chaotic dynamics. We also present in short results from two time-dependent systems, the anisotropic and the Rabi oscillator.
Deterministic chaos in entangled eigenstates
Energy Technology Data Exchange (ETDEWEB)
Schlegel, K.G. [Fakultaet fuer Physik, Universitaet Bielefeld, Postfach 100131, D-33501 Bielefeld (Germany)], E-mail: guenter.schlegel@arcor.de; Foerster, S. [Fakultaet fuer Physik, Universitaet Bielefeld, Postfach 100131, D-33501 Bielefeld (Germany)
2008-05-12
We investigate the problem of deterministic chaos in connection with entangled states using the Bohmian formulation of quantum mechanics. We show for a two particle system in a harmonic oscillator potential, that in a case of entanglement and three energy eigen-values the maximum Lyapunov-parameters of a representative ensemble of trajectories for large times develops to a narrow positive distribution, which indicates nearly complete chaotic dynamics. We also present in short results from two time-dependent systems, the anisotropic and the Rabi oscillator.
Deterministic chaos in entangled eigenstates
International Nuclear Information System (INIS)
Schlegel, K.G.; Foerster, S.
2008-01-01
We investigate the problem of deterministic chaos in connection with entangled states using the Bohmian formulation of quantum mechanics. We show for a two particle system in a harmonic oscillator potential, that in a case of entanglement and three energy eigen-values the maximum Lyapunov-parameters of a representative ensemble of trajectories for large times develops to a narrow positive distribution, which indicates nearly complete chaotic dynamics. We also present in short results from two time-dependent systems, the anisotropic and the Rabi oscillator
Decoherence, determinism and chaos revisited
Energy Technology Data Exchange (ETDEWEB)
Noyes, H.P.
1994-11-15
We suggest that the derivation of the free space Maxwell Equations for classical electromagnetism, using a discrete ordered calculus developed by L.H. Kauffman and T. Etter, necessarily pushes the discussion of determinism in natural science down to the level of relativistic quantum mechanics and hence renders the mathematical phenomena studied in deterministic chaos research irrelevant to the question of whether the world investigated by physics is deterministic. We believe that this argument reinforces Suppes` contention that the issue of determinism versus indeterminism should be viewed as a Kantian antinomy incapable of investigation using currently available scientific tools.
Decoherence, determinism and chaos revisited
International Nuclear Information System (INIS)
Noyes, H.P.
1994-01-01
We suggest that the derivation of the free space Maxwell Equations for classical electromagnetism, using a discrete ordered calculus developed by L.H. Kauffman and T. Etter, necessarily pushes the discussion of determinism in natural science down to the level of relativistic quantum mechanics and hence renders the mathematical phenomena studied in deterministic chaos research irrelevant to the question of whether the world investigated by physics is deterministic. We believe that this argument reinforces Suppes' contention that the issue of determinism versus indeterminism should be viewed as a Kantian antinomy incapable of investigation using currently available scientific tools
Merxhani, Branko
2012-01-01
Title: Organizimi i Kaosit (The organization of the chaos) Originally Published: In the monthly review Neo-shqiptarisma, Nr. 1, Tirana, 1930 Language: Albanian The excerpts used are from A. Plasari ed., Formula të Neoshqiptarismës. Përmbledhje shkrimesh (Tirana: Apollonia, 1996), pp. 99–102. About the author Branko Merxhani [1894 Istanbul – 1981, Istanbul]: scholar and writer. He was born in Istanbul and educated in Germany. In all likelihood, only his father was Albanian. By the end of the 1...
Hung, Nguyen T.; Nugraha, Ahmad R. T.; Saito, Riichiro
2018-02-01
This paper is a contribution to the Physical Review Applied collection in memory of Mildred S. Dresselhaus. Analytical formulas for thermoelectric figures of merit and power factors are derived based on the one-band model. We find that there is a direct relationship between the optimum figures of merit and the optimum power factors of semiconductors despite of the fact that the two quantities are generally given by different values of chemical potentials. By introducing a dimensionless parameter consisting of the optimum power factor and lattice thermal conductivity (without electronic thermal conductivity), it is possible to unify optimum figures of merit of both bulk and low-dimensional semiconductors into a single universal curve that covers many materials with different dimensionalities.
Jordan-Wigner fermionization and the theory of low-dimensional quantum spin models
International Nuclear Information System (INIS)
Derzhko, O.
2007-01-01
The idea of mapping quantum spin lattice model onto fermionic lattice model goes back to Jordan and Wigner (1928) who transformed s = 1/2 operators which commute at different lattice sites into fermionic operators. Later on the Jordan-Wigner transformation was used for mapping one-dimensional s = 1/2 isotropic XY (XX) model onto an exactly solvable tight-binding model of spinless fermions (Lieb, Schultz and Mattis, 1961). Since that times the Jordan-Wigner transformation is known as a powerful tool in the condensed matter theory especially in the theory of low-dimensional quantum spin systems. The aim of these lectures is to review the applications of the Jordan-Wigner fermionization technique for calculating dynamic properties of low-dimensional quantum spin models. The dynamic quantities (such as dynamic structure factors or dynamic susceptibilities) are observable directly or indirectly in various experiments. The frequency and wave-vector dependence of the dynamic quantities yields valuable information about the magnetic structure of materials. Owing to a tremendous recent progress in synthesizing low-dimensional magnetic materials detailed comparisons of theoretical results with direct experimental observation are becoming possible. The lectures are organized as follows. After a brief introduction of the Jordan-Wigner transformation for one-dimensional spin one half systems and some of its extensions for higher dimensions and higher spin values we focus on the dynamic properties of several low-dimensional quantum spin models. We start from a famous s = 1/2 XX chain. As a first step we recall well-known results for dynamics of the z-spin-component fluctuation operator and then turn to dynamics of the dimer and trimer fluctuation operators. The dynamics of the trimer fluctuations involves both the two fermion (one particle and one hole) and the four-fermion (two particles and two holes) excitations. We discuss some properties of the two-fermion and four
Inelastic light scattering by low-lying excitations of electrons in low-dimensional semiconductors
Energy Technology Data Exchange (ETDEWEB)
Pellegrini, V. [NEST CNR-INFM and Scuola Normale Superiore, Pisa (Italy); Pinczuk, A. [Department of Physics, Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027 (United States); Bell Laboratories, Lucent Technologies, Murray Hill, New Jersey (United States)
2006-11-15
The low-dimensional electron systems that reside in artificial semiconductor heterostructures of great perfection are a contemporary materials base for explorations of collective phenomena. Studies of low-lying elementary excitations by inelastic light scattering offer insights on properties such energetics, interactions and spin magnetization. We review here recent light scattering results obtained from two-dimensional (2D) quantum fluids in semiconductor heterostructures under extreme conditions of low temperature and large magnetic field, where the quantum Hall phases are archetypes of novel behaviors. We also consider recent light scattering experiments that have probed the excitation spectra of few-electron states in semiconductor quantum dots. (copyright 2006 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Salty popcorn in a homogeneous low-dimensional toy model of holographic QCD
International Nuclear Information System (INIS)
Elliot-Ripley, Matthew
2017-01-01
Recently, a homogeneous ansatz has been used to study cold dense nuclear matter in the Sakai–Sugimoto model of holographic QCD. To justify this homogeneous approximation we here investigate a homogeneous ansatz within a low-dimensional toy version of Sakai–Sugimoto to study finite baryon density configurations and compare it to full numerical solutions. We find the ansatz corresponds to enforcing a dyon salt arrangement in which the soliton solutions are split into half-soliton layers. Within this ansatz we find analogues of the proposed baryonic popcorn transitions, in which solutions split into multiple layers in the holographic direction. The homogeneous results are found to qualitatively match the full numerical solutions, lending confidence to the homogeneous approximations of the full Sakai–Sugimoto model. In addition, we find exact compact solutions in the high density, flat space limit which demonstrate the existence of further popcorn transitions to three layers and beyond. (paper)
ABC-model analysis of gain-switched pulse characteristics in low-dimensional semiconductor lasers
Bao, Xumin; Liu, Yuejun; Weng, Guoen; Hu, Xiaobo; Chen, Shaoqiang
2018-01-01
The gain-switching dynamics of low-dimensional semiconductor lasers is simulated numerically by using a two-dimensional rate-equation model. Use is also made of the ABC model, where the carrier recombination rate is described by a function of carrier densities including Shockley - Read - Hall (SRH) recombination coefficient A, spontaneous emission coefficient B and Auger recombination coefficient C. Effects of the ABC parameters on the ultrafast gain-switched pulse characteristics with high-density pulse excitation are analysed. It is found that while the parameter A has almost no obvious effects, the parameters B and C have distinctly different effects: B influences significantly the delay time of the gain-switched pulse, while C affects mainly the pulse intensity.
A Review on the Low-Dimensional and Hybridized Nanostructured Diamond Films
Directory of Open Access Journals (Sweden)
Hongdong Li
2015-01-01
Full Text Available In the last decade, besides the breakthrough of high-rate growth of chemical vapor deposited single-crystal diamonds, numerous nanostructured diamond films have been rapidly developed in the research fields of the diamond-based sciences and industrial applications. The low-dimensional diamonds of two-dimensional atomic-thick nanofilms and nanostructural diamond on the surface of bulk diamond films have been theoretically and experimentally investigated. In addition, the diamond-related hybrid nanostructures of n-type oxide/p-type diamond and n-type nitride/p-type diamond, having high performance physical and chemical properties, are proposed for further applications. In this review, we first briefly introduce the three categories of diamond nanostructures and then outline the current advances in these topics, including their design, fabrication, characterization, and properties. Finally, we address the remaining challenges in the research field and the future activities.
NATO Advanced Research Workshop on Optical Switching in Low-Dimensional Systems
Bányai, L
1989-01-01
This book contains all the papers presented at the NATO workshop on "Optical Switching in Low Dimensional Systems" held in Marbella, Spain from October 6th to 8th, 1988. Optical switching is a basic function for optical data processing, which is of technological interest because of its potential parallelism and its potential speed. Semiconductors which exhibit resonance enhanced optical nonlinearities in the frequency range close to the band edge are the most intensively studied materials for optical bistability and fast gate operation. Modern crystal growth techniques, particularly molecular beam epitaxy, allow the manufacture of semiconductor microstructures such as quantum wells, quantum wires and quantum dots in which the electrons are only free to move in two, one or zero dimensions, of the optically excited electron-hole pairs in these low respectively. The spatial confinement dimensional structures gives rise to an enhancement of the excitonic nonlinearities. Furthermore, the variations of the microstr...
Evolution of structure with Fe layer thickness in low dimensional Fe/Tb multilayered structures
International Nuclear Information System (INIS)
Harris, V.G.; Aylesworth, K.D.; Elam, W.T.; Koon, N.C.; Coehoorn, R.; Hoving, W.
1992-01-01
This paper reports on the atomic structure of a series of low-dimensional Fe/Tb multilayered structures which has been explored using a conversion-electron, extended x-ray absorption fine structure (EXAFS) technique. A structural transition from a close-packed amorphous structure to a body-centered crystalline structure is detected to occur over an Fe layer thickness range of 12.5 Angstrom to 15.0 Angstrom (Tb thickness is held constant at 4.5 Angstrom). Magnetic properties, specifically, magnetization, anisotropy field, and Kerr rotation angle, are measured and found to change significantly in response to this transition. Exploitation of the polarization properties of synchrotron radiation allowed for the description of the atomic structure both perpendicular and parallel to the sample plane
A low-dimensional tool for predicting force decomposition coefficients for varying inflow conditions
Ghommem, Mehdi; Akhtar, Imran; Hajj, M. R.
2013-01-01
We develop a low-dimensional tool to predict the effects of unsteadiness in the inflow on force coefficients acting on a circular cylinder using proper orthogonal decomposition (POD) modes from steady flow simulations. The approach is based on combining POD and linear stochastic estimator (LSE) techniques. We use POD to derive a reduced-order model (ROM) to reconstruct the velocity field. To overcome the difficulty of developing a ROM using Poisson's equation, we relate the pressure field to the velocity field through a mapping function based on LSE. The use of this approach to derive force decomposition coefficients (FDCs) under unsteady mean flow from basis functions of the steady flow is illustrated. For both steady and unsteady cases, the final outcome is a representation of the lift and drag coefficients in terms of velocity and pressure temporal coefficients. Such a representation could serve as the basis for implementing control strategies or conducting uncertainty quantification. Copyright © 2013 Inderscience Enterprises Ltd.
Low-dimensional morphospace of topological motifs in human fMRI brain networks
Directory of Open Access Journals (Sweden)
Sarah E. Morgan
2018-06-01
Full Text Available We present a low-dimensional morphospace of fMRI brain networks, where axes are defined in a data-driven manner based on the network motifs. The morphospace allows us to identify the key variations in healthy fMRI networks in terms of their underlying motifs, and we observe that two principal components (PCs can account for 97% of the motif variability. The first PC of the motif distribution is correlated with efficiency and inversely correlated with transitivity. Hence this axis approximately conforms to the well-known economical small-world trade-off between integration and segregation in brain networks. Finally, we show that the economical clustering generative model proposed by Vértes et al. (2012 can approximately reproduce the motif morphospace of the real fMRI brain networks, in contrast to other generative models. Overall, the motif morphospace provides a powerful way to visualize the relationships between network properties and to investigate generative or constraining factors in the formation of complex human brain functional networks. Motifs have been described as the building blocks of complex networks. Meanwhile, a morphospace allows networks to be placed in a common space and can reveal the relationships between different network properties and elucidate the driving forces behind network topology. We combine the concepts of motifs and morphospaces to create the first motif morphospace of fMRI brain networks. Crucially, the morphospace axes are defined by the motifs, in a data-driven manner. We observe strong correlations between the networks’ positions in morphospace and their global topological properties, suggesting that motif morphospaces are a powerful way to capture the topology of networks in a low-dimensional space and to compare generative models of brain networks. Motif morphospaces could also be used to study other complex networks’ topologies.
Electron-hole liquid in semiconductors and low-dimensional structures
Sibeldin, N. N.
2017-11-01
The condensation of excitons into an electron-hole liquid (EHL) and the main EHL properties in bulk semiconductors and low-dimensional structures are considered. The EHL properties in bulk materials are discussed primarily in qualitative terms based on the experimental results obtained for germanium and silicon. Some of the experiments in which the main EHL thermodynamic parameters (density and binding energy) have been obtained are described and the basic factors that determine these parameters are considered. Topics covered include the effect of external perturbations (uniaxial strain and magnetic field) on EHL stability; phase diagrams for a nonequilibrium exciton-gas-EHL system; information on the size and concentration of electron-hole drops (EHDs) under various experimental conditions; the kinetics of exciton condensation and of recombination in the exciton-gas-EHD system; dynamic EHD properties and the motion of EHDs under the action of external forces; the properties of giant EHDs that form in potential wells produced by applying an inhomogeneous strain to the crystal; and effects associated with the drag of EHDs by nonequilibrium phonons (phonon wind), including the dynamics and formation of an anisotropic spatial structure of the EHD cloud. In discussing EHLs in low-dimensional structures, a number of studies are reviewed on the observation and experimental investigation of phenomena such as spatially indirect (dipolar) electron-hole and exciton (dielectric) liquids in GaAs/AlGaAs structures with double quantum wells (QWs), EHDs containing only a few electron-hole pairs (dropletons), EHLs in type-I silicon QWs, and spatially direct and dipolar EHLs in type-II silicon-germanium heterostructures.
Directory of Open Access Journals (Sweden)
C. Serio
1997-06-01
Full Text Available The time dynamics of geoelectrical precursory time series has been investigated and a method to discriminate chaotic behaviour in geoelectrical precursory time series is proposed. It allows us to detect low-dimensional chaos when the only information about the time series comes from the time series themselves. The short-term predictability of these time series is evaluated using two possible forecasting approaches: global autoregressive approximation and local autoregressive approximation. The first views the data as a realization of a linear stochastic process, whereas the second considers the data points as a realization of a deterministic process, supposedly non-linear. The comparison of the predictive skill of the two techniques is a test to discriminate between low-dimensional chaos and random dynamics. The analyzed time series are geoelectrical measurements recorded by an automatic station located in Tito (Southern Italy in one of the most seismic areas of the Mediterranean region. Our findings are that the global (linear approach is superior to the local one and the physical system governing the phenomena of electrical nature is characterized by a large number of degrees of freedom. Power spectra of the filtered time series follow a P(f = F-a scaling law: they exhibit the typical behaviour of a broad class of fractal stochastic processes and they are a signature of the self-organized systems.
Quantifying chaos for ecological stoichiometry.
Duarte, Jorge; Januário, Cristina; Martins, Nuno; Sardanyés, Josep
2010-09-01
The theory of ecological stoichiometry considers ecological interactions among species with different chemical compositions. Both experimental and theoretical investigations have shown the importance of species composition in the outcome of the population dynamics. A recent study of a theoretical three-species food chain model considering stoichiometry [B. Deng and I. Loladze, Chaos 17, 033108 (2007)] shows that coexistence between two consumers predating on the same prey is possible via chaos. In this work we study the topological and dynamical measures of the chaotic attractors found in such a model under ecological relevant parameters. By using the theory of symbolic dynamics, we first compute the topological entropy associated with unimodal Poincaré return maps obtained by Deng and Loladze from a dimension reduction. With this measure we numerically prove chaotic competitive coexistence, which is characterized by positive topological entropy and positive Lyapunov exponents, achieved when the first predator reduces its maximum growth rate, as happens at increasing δ1. However, for higher values of δ1 the dynamics become again stable due to an asymmetric bubble-like bifurcation scenario. We also show that a decrease in the efficiency of the predator sensitive to prey's quality (increasing parameter ζ) stabilizes the dynamics. Finally, we estimate the fractal dimension of the chaotic attractors for the stoichiometric ecological model.
Invoking the muse: Dada's chaos.
Rosen, Diane
2014-07-01
Dada, a self-proclaimed (anti)art (non)movement, took shape in 1916 among a group of writers and artists who rejected the traditions of a stagnating bourgeoisie. Instead, they adopted means of creative expression that embraced chaos, stoked instability and undermined logic, an outburst that overturned centuries of classical and Romantic aesthetics. Paradoxically, this insistence on disorder foreshadowed a new order in understanding creativity. Nearly one hundred years later, Nonlinear Dynamical Systems theory (NDS) gives renewed currency to Dada's visionary perspective on chance, chaos and creative cognition. This paper explores commonalities between NDS-theory and this early precursor of the nonlinear paradigm, suggesting that their conceptual synergy illuminates what it means to 'be creative' beyond the disciplinary boundaries of either. Key features are discussed within a 5P model of creativity based on Rhodes' 4P framework (Person, Process, Press, Product), to which I add Participant-Viewer for the interactivity of observer-observed. Grounded in my own art practice, several techniques are then put forward as non-methodical methods that invoke creative border zones, those regions where Dada's chance and design are wedded in a dialectical tension of opposites.
Markov transitions and the propagation of chaos
International Nuclear Information System (INIS)
Gottlieb, A.
1998-01-01
The propagation of chaos is a central concept of kinetic theory that serves to relate the equations of Boltzmann and Vlasov to the dynamics of many-particle systems. Propagation of chaos means that molecular chaos, i.e., the stochastic independence of two random particles in a many-particle system, persists in time, as the number of particles tends to infinity. We establish a necessary and sufficient condition for a family of general n-particle Markov processes to propagate chaos. This condition is expressed in terms of the Markov transition functions associated to the n-particle processes, and it amounts to saying that chaos of random initial states propagates if it propagates for pure initial states. Our proof of this result relies on the weak convergence approach to the study of chaos due to Sztitman and Tanaka. We assume that the space in which the particles live is homomorphic to a complete and separable metric space so that we may invoke Prohorov's theorem in our proof. We also show that, if the particles can be in only finitely many states, then molecular chaos implies that the specific entropies in the n-particle distributions converge to the entropy of the limiting single-particle distribution
Using chaos theory: the implications for nursing.
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.
Cheng, Chih-Hao; Chen, Chih-Ying; Chen, Jun-Da; Pan, Da-Kung; Ting, Kai-Ting; Lin, Fan-Yi
2018-04-30
We develop an unprecedented 3D pulsed chaos lidar system for potential intelligent machinery applications. Benefited from the random nature of the chaos, conventional CW chaos lidars already possess excellent anti-jamming and anti-interference capabilities and have no range ambiguity. In our system, we further employ self-homodyning and time gating to generate a pulsed homodyned chaos to boost the energy-utilization efficiency. Compared to the original chaos, we show that the pulsed homodyned chaos improves the detection SNR by more than 20 dB. With a sampling rate of just 1.25 GS/s that has a native sampling spacing of 12 cm, we successfully achieve millimeter-level accuracy and precision in ranging. Compared with two commercial lidars tested side-by-side, namely the pulsed Spectroscan and the random-modulation continuous-wave Lidar-lite, the pulsed chaos lidar that is in compliance with the class-1 eye-safe regulation shows significantly better precision and a much longer detection range up to 100 m. Moreover, by employing a 2-axis MEMS mirror for active laser scanning, we also demonstrate real-time 3D imaging with errors of less than 4 mm in depth.
How to test for partially predictable chaos.
Wernecke, Hendrik; Sándor, Bulcsú; Gros, Claudius
2017-04-24
For a chaotic system pairs of initially close-by trajectories become eventually fully uncorrelated on the attracting set. This process of decorrelation can split into an initial exponential decrease and a subsequent diffusive process on the chaotic attractor causing the final loss of predictability. Both processes can be either of the same or of very different time scales. In the latter case the two trajectories linger within a finite but small distance (with respect to the overall extent of the attractor) for exceedingly long times and remain partially predictable. Standard tests for chaos widely use inter-orbital correlations as an indicator. However, testing partially predictable chaos yields mostly ambiguous results, as this type of chaos is characterized by attractors of fractally broadened braids. For a resolution we introduce a novel 0-1 indicator for chaos based on the cross-distance scaling of pairs of initially close trajectories. This test robustly discriminates chaos, including partially predictable chaos, from laminar flow. Additionally using the finite time cross-correlation of pairs of initially close trajectories, we are able to identify laminar flow as well as strong and partially predictable chaos in a 0-1 manner solely from the properties of pairs of trajectories.
Chaos and its synchronization in two-neuron systems with discrete delays
International Nuclear Information System (INIS)
Zhou Shangbo; Liao Xiaofeng; Yu Juebang; Wong Kwokwo
2004-01-01
It is well known that complex dynamic behaviors exist in time-delayed neural systems. Infinite positive Lyapunov exponents can be found in time-delayed chaotic systems since the dimension of such systems is infinite. However, theoretical and experimental models studied thus far are low dimensional systems with only one positive Lyapunov exponent. Consequently, messages masked by such chaotic systems are shown to be easily extracted in some cases. Therefore, communication system with a higher security level can be design by means of the time-delayed neuron systems. In this paper, we firstly investigate the dynamical behaviors of two-neuron systems with discrete delays. Then, the chaos synchronization in time-delayed neuron system is studied based on the method of designing the coupled system and employing Krasovskii-Lyapunov theory to search the synchronization conditions. Numerical results illustrate the correctness of our theoretical analyses
Some remarks on chaos in topological dynamics
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Huoyung Wang
2011-10-01
Full Text Available Bau-Sen Du introduced a notion of chaos which is stronger than Li-Yorke sensitivity. A TDS (X, f is called chaotic if there is a positive e such that for any x and any nonempty open set V of X there is a point y in V such that the pair (x, y is proximal but not e-asymptotic. In this article, we show that a TDS (T, f is transitive but not mixing if and only if (T, f is Li-Yorke sensitive but not chaotic, where T is a tree. Moreover, we compare such chaos with other notions of chaos.
A-coupled-expanding and distributional chaos
International Nuclear Information System (INIS)
Kim, Cholsan; Ju, Hyonhui; Chen, Minghao; Raith, Peter
2015-01-01
The concept of A-coupled-expanding maps is one of the more natural and useful ideas generalized from the horseshoe map which is commonly known as a criterion of chaos. It is well known that distributional chaos is one of the concepts which reflect strong chaotic behavior. In this paper, we focus on the relationship between A-coupled-expanding and distributional chaos. We prove two theorems which give sufficient conditions for a strictly A-coupled-expanding map to be distributionally chaotic in the senses of two kinds, where A is an m × m irreducible transition matrix
Towards CHAOS-5 - How can Swarm contribute?
DEFF Research Database (Denmark)
Finlay, Chris; Olsen, Nils; Tøffner-Clausen, Lars
2014-01-01
The launch of ESA's satellite trio Swarm in November 2013 opens an exciting new chapter in the observation and monitoring of Earth's magnetic field from space. We report preliminary results from an extension of the CHAOS series of geomagnetic field models to include both scalar and vector field...... observations from the three Swarm satellites, along with the most recent quasi-definitive ground observatory data. The fit of this new update CHAOS field model to the Swarm observations will be presented in detail providing useful insight the initial Swarm data. Enhancements of the CHAOS modelling scheme...
Chaos from simple models to complex systems
Cencini, Massimo; Vulpiani, Angelo
2010-01-01
Chaos: from simple models to complex systems aims to guide science and engineering students through chaos and nonlinear dynamics from classical examples to the most recent fields of research. The first part, intended for undergraduate and graduate students, is a gentle and self-contained introduction to the concepts and main tools for the characterization of deterministic chaotic systems, with emphasis to statistical approaches. The second part can be used as a reference by researchers as it focuses on more advanced topics including the characterization of chaos with tools of information theor
Some open questions in 'wave chaos'
International Nuclear Information System (INIS)
Nonnenmacher, Stéphane
2008-01-01
The subject area referred to as 'wave chaos', 'quantum chaos' or 'quantum chaology' has been investigated mostly by the theoretical physics community in the last 30 years. The questions it raises have more recently also attracted the attention of mathematicians and mathematical physicists, due to connections with number theory, graph theory, Riemannian, hyperbolic or complex geometry, classical dynamical systems, probability, etc. After giving a rough account on 'what is quantum chaos?', I intend to list some pending questions, some of them having been raised a long time ago, some others more recent. The choice of problems (and of references) is of course partial and personal. (open problem)
Nuclear physics, symmetries, and quantum chaos
International Nuclear Information System (INIS)
Bunakov, V.E.
1999-01-01
The reasons why the problem of chaos is of great topical interest in modern physics are briefly summarized, and it is indicated that ambiguities in the concept of quantum chaos present the greatest difficulties in these realms. The theory of random matrices and strength functions are generalized to demonstrate that chaotization of a system is associated with the violation of its symmetries. A criterion of quantum chaoticity is formulated in terms of the spreading width Γ spr . In the classical limit, this criterion reduces to Lyapunov's stability criteria. It is shown that the proposed criterion is applicable to standard problems of the modern theory of dynamical chaos
Semiconductor Lasers Stability, Instability and Chaos
Ohtsubo, Junji
2008-01-01
This monograph describes fascinating recent progress in the field of chaos, stability and instability of semiconductor lasers. Applications and future prospects are discussed in detail. The book emphasizes the various dynamics induced in semiconductor lasers by optical and electronic feedback, optical injection, and injection current modulation. Recent results of both theoretical and experimental investigations are presented. Demonstrating applications of semiconductor laser chaos, control and noise, Semiconductor Lasers describes suppression and chaotic secure communications. For those who are interested in optics but not familiar with nonlinear systems, a brief introduction to chaos analysis is presented.
Quantum chaos in the Heisenberg picture
International Nuclear Information System (INIS)
McKellar, B.H.J.; Lancaster, M.; McCaw, J.
2000-01-01
Full text: We explore the possibility of defining quantum chaos in the algebra of quantum mechanical operators. The simple definition of the Lyapunov exponent in terms of a metric on that algebra has the expected properties for the quantum logistic map, as we confirm for the simple spin 1 system. We then show numerically and analytically that the Hamiltonian evolution of finite spin systems does not lead to chaos in this definition, and investigate alternative definitions of quantum chaos in the algebra of operators
Chaos in body-vortex interactions
DEFF Research Database (Denmark)
Pedersen, Johan Rønby; Aref, Hassan
2010-01-01
of a circle is integrable. As the body is made slightly elliptic, a chaotic region grows from an unstable relative equilibrium of the circle-vortex case. The case of a cylindrical body of any shape moving in fluid otherwise at rest is also integrable. A second transition to chaos arises from the limit between...... rocking and tumbling motion of the body known in this case. In both instances, the chaos may be detected both in the body motion and in the vortex motion. The effect of increasing body mass at a fixed body shape is to damp the chaos....
Chua's circuit a paradigm for chaos
1993-01-01
For uninitiated researchers, engineers, and scientists interested in a quick entry into the subject of chaos, this book offers a timely collection of 55 carefully selected papers covering almost every aspect of this subject. Because Chua's circuit is endowed with virtually every bifurcation phenomena reported in the extensive literature on chaos, and because it is the only chaotic system which can be easily built by a novice, simulated in a personal computer, and tractable mathematically, it has become a paradigm for chaos, and a vehicle for illustrating this ubiquitous phenomenon. Its supreme
International Nuclear Information System (INIS)
Ge Zhengming; Hsu Maoyuan
2008-01-01
In this paper, chaos excited chaos synchronizations of generalized van der Pol systems with integral and fractional order are studied. Synchronizations of two identified autonomous generalized van der Pol chaotic systems are obtained by replacing their corresponding exciting terms by the same function of chaotic states of a third nonautonomous or autonomous generalized van der Pol system. Numerical simulations, such as phase portraits, Poincare maps and state error plots are given. It is found that chaos excited chaos synchronizations exist for the fractional order systems with the total fractional order both less than and more than the number of the states of the integer order generalized van der Pol system
International Nuclear Information System (INIS)
Ruan, Dan; Keall, Paul
2010-01-01
Accurate real-time prediction of respiratory motion is desirable for effective motion management in radiotherapy for lung tumor targets. Recently, nonparametric methods have been developed and their efficacy in predicting one-dimensional respiratory-type motion has been demonstrated. To exploit the correlation among various coordinates of the moving target, it is natural to extend the 1D method to multidimensional processing. However, the amount of learning data required for such extension grows exponentially with the dimensionality of the problem, a phenomenon known as the 'curse of dimensionality'. In this study, we investigate a multidimensional prediction scheme based on kernel density estimation (KDE) in an augmented covariate-response space. To alleviate the 'curse of dimensionality', we explore the intrinsic lower dimensional manifold structure and utilize principal component analysis (PCA) to construct a proper low-dimensional feature space, where kernel density estimation is feasible with the limited training data. Interestingly, the construction of this lower dimensional representation reveals a useful decomposition of the variations in respiratory motion into the contribution from semiperiodic dynamics and that from the random noise, as it is only sensible to perform prediction with respect to the former. The dimension reduction idea proposed in this work is closely related to feature extraction used in machine learning, particularly support vector machines. This work points out a pathway in processing high-dimensional data with limited training instances, and this principle applies well beyond the problem of target-coordinate-based respiratory-based prediction. A natural extension is prediction based on image intensity directly, which we will investigate in the continuation of this work. We used 159 lung target motion traces obtained with a Synchrony respiratory tracking system. Prediction performance of the low-dimensional feature learning
Wang, Shi-Hong; Ye, Wei-Ping; Lü, Hua-Ping; Kuang, Jin-Yu; Li, Jing-Hua; Luo, Yun-Lun; Hu, Gang
2003-07-01
Spatiotemporal chaos of a two-dimensional one-way coupled map lattice is used for chaotic cryptography. The chaotic outputs of many space units are used for encryption simultaneously. This system shows satisfactory cryptographic properties of high security, fast encryption (decryption) speed, and robustness against noise disturbances in communication channel. The overall features of this spatiotemporal-chaos-based cryptosystem are better than chaotic cryptosystems known so far, and also than currently used conventional cryptosystems, such as the Advanced Encryption Standard (AES). The project supported by National Natural Science Foundation of China under Grant No. 10175010 and the Special Funds for Major State Basic Research Projects under Grant No. G2000077304
Leveraging Chaos in Continuous Thrust Trajectory Design
National Aeronautics and Space Administration — A trajectory design tool is sought to leverage chaos and nonlinear dynamics present in multi-body gravitational fields to design ultra-low energy transfer...
A Chaos Theory Perspective on International Migration
Directory of Open Access Journals (Sweden)
Anca Tănasie
2017-12-01
Full Text Available This paper aims at providing a different approach to international migration analysis, beyond classical models previously proposed by specialized literature. Chaos theory is getting more and more applied into macroeconomics once traditional linear models or even previous dynamic analysis become less suitable. Modern science sees chaos as unpredictable evolution, maybe even disorder. Still, chaos has got its own rules and can describe many dynamic phenomena within our world. Thus, we test whether international migration data falls under the rules of chaos and whether recent developments within the “European migration crisis” (the total daily migration inflows towards the coasts of Italy, by sea, from January 2014 to April 2017 could be described as chaotic.
Chaos concepts, control and constructive use
Bolotin, Yurii; Yanovsky, Vladimir
2017-01-01
This book offers a short and concise introduction to the many facets of chaos theory. While the study of chaotic behavior in nonlinear, dynamical systems is a well-established research field with ramifications in all areas of science, there is a lot to be learnt about how chaos can be controlled and, under appropriate conditions, can actually be constructive in the sense of becoming a control parameter for the system under investigation, stochastic resonance being a prime example. The present work stresses the latter aspects and, after recalling the paradigm changes introduced by the concept of chaos, leads the reader skillfully through the basics of chaos control by detailing the relevant algorithms for both Hamiltonian and dissipative systems, among others. The main part of the book is then devoted to the issue of synchronization in chaotic systems, an introduction to stochastic resonance, and a survey of ratchet models. In this second, revised and enlarged edition, two more chapters explore the many interf...
Homoclinic chaos and energy condition violation
International Nuclear Information System (INIS)
Heinzle, J. Mark; Roehr, Niklas; Uggla, Claes
2006-01-01
In this letter we discuss the connection between so-called homoclinic chaos and the violation of energy conditions in locally rotationally symmetric Bianchi type IX models, where the matter is assumed to be nontilted dust and a positive cosmological constant. We show that homoclinic chaos in these models is an artifact of unphysical assumptions: it requires that there exist solutions with positive matter energy density ρ>0 that evolve through the singularity and beyond as solutions with negative matter energy density ρ<0. Homoclinic chaos is absent when it is assumed that the dust particles always retain their positive mass. In addition, we discuss more general models: for solutions that are not locally rotationally symmetric we demonstrate that the construction of extensions through the singularity, which is required for homoclinic chaos, is not possible in general
Coherence and chaos in condensed matter
International Nuclear Information System (INIS)
Bishop, A.R.
1989-01-01
This paper discusses the following topics: nonlinearity in condensed matter; coherence and chaos in spatially extended condensed matter systems; nonlinearity and magnetism; and solitons and conducting polymers. 52 refs., 7 figs
Semiconductor lasers stability, instability and chaos
Ohtsubo, Junji
2017-01-01
This book describes the fascinating recent advances made concerning the chaos, stability and instability of semiconductor lasers, and discusses their applications and future prospects in detail. It emphasizes the dynamics in semiconductor lasers by optical and electronic feedback, optical injection, and injection current modulation. Applications of semiconductor laser chaos, control and noise, and semiconductor lasers are also demonstrated. Semiconductor lasers with new structures, such as vertical-cavity surface-emitting lasers and broad-area semiconductor lasers, are intriguing and promising devices. Current topics include fast physical number generation using chaotic semiconductor lasers for secure communication, development of chaos, quantum-dot semiconductor lasers and quantum-cascade semiconductor lasers, and vertical-cavity surface-emitting lasers. This fourth edition has been significantly expanded to reflect the latest developments. The fundamental theory of laser chaos and the chaotic dynamics in se...
Nuclear physics and ideas of quantum chaos
International Nuclear Information System (INIS)
Zelevinsky, V.G.
2002-01-01
The field nowadays called 'many-body quantum chaos' was started in 1939 with the article by I.I. Gurevich studying the regularities of nuclear spectra. The field has been extensively developed recently, both mathematically and in application to mesoscopic systems and quantum fields. We argue that nuclear physics and the theory of quantum chaos are mutually beneficial. Many ideas of quantum chaos grew up from the factual material of nuclear physics; this enrichment still continues to take place. On the other hand, many phenomena in nuclear structure and reactions, as well as the general problem of statistical physics of finite strongly interacting systems, can be understood much deeper with the help of ideas and methods borrowed from the field of quantum chaos. A brief review of the selected topics related to the recent development is presented
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).
From classical to quantum chaos
International Nuclear Information System (INIS)
Zaslavsky, G.M.
1991-01-01
The analysis is done for the quantum properties of systems that possess dynamical chaos in classical limit. Two main topics are considered: (i) the problem of quantum macroscopical description of the system and the Ehrenfest-Einstein problem of the validity of the classical approximation; and (ii) the problem of levels spacing distribution for the nonintegrable case. For the first topic the method of projecting on the coherent states base is considered and the ln 1/(h/2π) time for the quasiclassical approximation breaking is described. For the second topic the discussion of GOE and non-GOE distributions is done and estimations and simulations for the non-GOE case are reviewed. (author). 44 refs, 2 figs
Distributional chaos for triangular maps
International Nuclear Information System (INIS)
Smital, Jaroslav; Stefankova, Marta
2004-01-01
In this paper we exhibit a triangular map F of the square with the following properties: (i) F is of type 2 ∞ but has positive topological entropy; we recall that similar example was given by Kolyada in 1992, but our argument is much simpler. (ii) F is distributionally chaotic in the wider sense, but not distributionally chaotic in the sense introduced by Schweizer and Smital [Trans. Amer. Math. Soc. 344 (1994) 737]. In other words, there are lower and upper distribution functions PHI xy and PHI xy * generated by F such that PHI xy * ≡1 and PHI xy (0 + ) uv , and PHI uv * such that PHI uv * ≡1 and PHI uv (t)=0 whenever 0 0. We also show that the two notions of distributional chaos used in the paper, for continuous maps of a compact metric space, are invariants of topological conjugacy
Chaos, Fractals and Their Applications
Thompson, J. Michael T.
2016-12-01
This paper gives an up-to-date account of chaos and fractals, in a popular pictorial style for the general scientific reader. A brief historical account covers the development of the subject from Newton’s laws of motion to the astronomy of Poincaré and the weather forecasting of Lorenz. Emphasis is given to the important underlying concepts, embracing the fractal properties of coastlines and the logistics of population dynamics. A wide variety of applications include: NASA’s discovery and use of zero-fuel chaotic “superhighways” between the planets; erratic chaotic solutions generated by Euler’s method in mathematics; atomic force microscopy; spontaneous pattern formation in chemical and biological systems; impact mechanics in offshore engineering and the chatter of cutting tools; controlling chaotic heartbeats. Reference is made to a number of interactive simulations and movies accessible on the web.
International Nuclear Information System (INIS)
Luo Chuanwen; Wang Gang; Wang Chuncheng; Wei Junjie
2009-01-01
The concepts of uniform index and expectation uniform index are two mathematical descriptions of the uniformity and the mean uniformity of a finite set in a polyhedron. The concepts of instantaneous chaometry (ICM) and k step chaometry (k SCM) are introduced in order to apply the method in statistics for studying the nonlinear difference equations. It is found that k step chaometry is an indirect estimation of the expectation uniform index. The simulation illustrate that the expectation uniform index for the Lorenz System is increasing linearly, but increasing nonlinearly for the Chen's System with parameter b. In other words, the orbits for each system become more and more uniform with parameter b increasing. Finally, a conjecture is also brought forward, which implies that chaos can be interpreted by its orbit's mean uniformity described by the expectation uniform index and indirectly estimated by k SCM. The k SCM of the heart rate showes the feeble and old process of the heart.
Quantum chaos on discrete graphs
International Nuclear Information System (INIS)
Smilansky, Uzy
2007-01-01
Adapting a method developed for the study of quantum chaos on quantum (metric) graphs (Kottos and Smilansky 1997 Phys. Rev. Lett. 79 4794, Kottos and Smilansky 1999 Ann. Phys., NY 274 76), spectral ζ functions and trace formulae for discrete Laplacians on graphs are derived. This is achieved by expressing the spectral secular equation in terms of the periodic orbits of the graph and obtaining functions which belong to the class of ζ functions proposed originally by Ihara (1966 J. Mat. Soc. Japan 18 219) and expanded by subsequent authors (Stark and Terras 1996 Adv. Math. 121 124, Kotani and Sunada 2000 J. Math. Sci. Univ. Tokyo 7 7). Finally, a model of 'classical dynamics' on the discrete graph is proposed. It is analogous to the corresponding classical dynamics derived for quantum graphs (Kottos and Smilansky 1997 Phys. Rev. Lett. 79 4794, Kottos and Smilansky 1999 Ann. Phys., NY 274 76). (fast track communication)
Menstruation, perimenopause, and chaos theory.
Derry, Paula S; Derry, Gregory N
2012-01-01
This article argues that menstruation, including the transition to menopause, results from a specific kind of complex system, namely, one that is nonlinear, dynamical, and chaotic. A complexity-based perspective changes how we think about and research menstruation-related health problems and positive health. Chaotic systems are deterministic but not predictable, characterized by sensitivity to initial conditions and strange attractors. Chaos theory provides a coherent framework that qualitatively accounts for puzzling results from perimenopause research. It directs attention to variability within and between women, adaptation, lifespan development, and the need for complex explanations of disease. Whether the menstrual cycle is chaotic can be empirically tested, and a summary of our research on 20- to 40-year-old women is provided.
Bustamante, M D
2003-01-01
In this paper, we consider the general setting for constructing action principles for three-dimensional first-order autonomous equations. We present the results for some integrable and non-integrable cases of the Lotka-Volterra equation, and show Lagrangian descriptions which are valid for systems satisfying Shil'nikov criteria on the existence of strange attractors, though chaotic behaviour has not been verified up to now. The Euler-Lagrange equations we get for these systems usually present 'time reparametrization' invariance, though other kinds of invariance may be found according to the kernel of the associated symplectic 2-form. The formulation of a Hamiltonian structure (Poisson brackets and Hamiltonians) for these systems from the Lagrangian viewpoint leads to a method of finding new constants of the motion starting from known ones, which is applied to some systems found in the literature known to possess a constant of the motion, to find the other and thus showing their integrability. In particular, w...
Energy Technology Data Exchange (ETDEWEB)
Bustamante, Miguel D [Departamento de Fisica, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile (Chile); Hojman, Sergio A [Departamento de Fisica, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile (Chile)
2003-01-10
In this paper, we consider the general setting for constructing action principles for three-dimensional first-order autonomous equations. We present the results for some integrable and non-integrable cases of the Lotka-Volterra equation, and show Lagrangian descriptions which are valid for systems satisfying Shil'nikov criteria on the existence of strange attractors, though chaotic behaviour has not been verified up to now. The Euler-Lagrange equations we get for these systems usually present 'time reparametrization' invariance, though other kinds of invariance may be found according to the kernel of the associated symplectic 2-form. The formulation of a Hamiltonian structure (Poisson brackets and Hamiltonians) for these systems from the Lagrangian viewpoint leads to a method of finding new constants of the motion starting from known ones, which is applied to some systems found in the literature known to possess a constant of the motion, to find the other and thus showing their integrability. In particular, we show that the so-called ABC system is completely integrable if it possesses one constant of the motion.
True quantum chaos? An instructive example
International Nuclear Information System (INIS)
Berry, M.V.
1992-01-01
Any chaotic classical system can be transformed into a quantum system that preserves the chaos, because the classical Liouville equation involving 2Ν phase-space variables q ,p has the form of a 'Schroedinger equation' with 'coordinates' Q=[q,p]. The feature of this quantum system that allows chaos to persist is linarity of the Hamiltonian' in the 2Ν 'momentum' operators conjugate to Q. (orig.)
Scaling properties of localized quantum chaos
International Nuclear Information System (INIS)
Izrailev, F.M.
1991-01-01
Statistical properties of spectra and eigenfunctions are studied for the model of quantum chaos in the presence of dynamical localization. The main attention is paid to the scaling properties of localization length and level spacing distribution in the intermediate region between Poissonian and Wigner-Dyson statistics. It is shown that main features of such localized quantum chaos are well described by the introduced ensemble of band random matrices. 28 refs.; 7 figs
Deterministic chaos in the processor load
International Nuclear Information System (INIS)
Halbiniak, Zbigniew; Jozwiak, Ireneusz J.
2007-01-01
In this article we present the results of research whose purpose was to identify the phenomenon of deterministic chaos in the processor load. We analysed the time series of the processor load during efficiency tests of database software. Our research was done on a Sparc Alpha processor working on the UNIX Sun Solaris 5.7 operating system. The conducted analyses proved the presence of the deterministic chaos phenomenon in the processor load in this particular case
Chaos control of Chen chaotic dynamical system
International Nuclear Information System (INIS)
Yassen, M.T.
2003-01-01
This paper is devoted to study the problem of controlling chaos in Chen chaotic dynamical system. Two different methods of control, feedback and nonfeedback methods are used to suppress chaos to unstable equilibria or unstable periodic orbits (UPO). The Lyapunov direct method and Routh-Hurwitz criteria are used to study the conditions of the asymptotic stability of the steady states of the controlled system. Numerical simulations are presented to show these results
Chaos control using sliding-mode theory
International Nuclear Information System (INIS)
Nazzal, Jamal M.; Natsheh, Ammar N.
2007-01-01
Chaos control means to design a controller that is able to mitigating or eliminating the chaos behavior of nonlinear systems that experiencing such phenomenon. In this paper, a nonlinear Sliding-Mode Controller (SMC) is presented. Two nonlinear chaotic systems are chosen to be our case study in this paper, the well known Chua's circuit and Lorenz system. The study shows the effectiveness of the designed nonlinear Sliding-Mode Controller
Skokos, C.; Bountis, T.; Antonopoulos, C.
2008-12-01
The recently introduced GALI method is used for rapidly detecting chaos, determining the dimensionality of regular motion and predicting slow diffusion in multi-dimensional Hamiltonian systems. We propose an efficient computation of the GALIk indices, which represent volume elements of k randomly chosen deviation vectors from a given orbit, based on the Singular Value Decomposition (SVD) algorithm. We obtain theoretically and verify numerically asymptotic estimates of GALIs long-time behavior in the case of regular orbits lying on low-dimensional tori. The GALIk indices are applied to rapidly detect chaotic oscillations, identify low-dimensional tori of Fermi-Pasta-Ulam (FPU) lattices at low energies and predict weak diffusion away from quasiperiodic motion, long before it is actually observed in the oscillations.
Indian Academy of Sciences (India)
K Krishan1 Manu2 R Ramaswamy2. Department of Physics, Indian Institute of Technology, Kanpur 208 016, India; School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110 067, India. Resonance – Journal of Science Education. Current Issue : Vol. 23, Issue 4 · Current Issue Volume 23 | Issue 4. April 2018.
Photochemical modification of magnetic properties in organic low-dimensional conductors
International Nuclear Information System (INIS)
Naito, Toshio; Kakizaki, Akihiro; Wakeshima, Makoto; Hinatsu, Yukio; Inabe, Tamotsu
2009-01-01
Magnetic properties of organic charge transfer salts Ag(DX) 2 (DX=2,5-dihalogeno-N,N'-dicyanoquinonediimine; X=Cl, Br, I) were modified by UV irradiation from paramagnetism to diamagnetism in an irreversible way. The temperature dependence of susceptibility revealed that such change in magnetic behavior could be continuously controlled by the duration of irradiation. The observation with scanning electron microprobe revealed that the original appearance of samples, e.g. black well-defined needle-shaped shiny single crystals, remained after irradiation irrespective of the irradiation conditions and the duration. Thermochemical analysis and X-ray diffraction study demonstrated that the change in the physical properties were due to (partial) decomposition of Ag(DX) 2 to AgX, which was incorporated in the original Ag(DX) 2 lattices. Because the physical properties of low-dimensional organic conductors are very sensitive to lattice defects, even a small amount of AgX could effectively modify the electronic properties of Ag(DX) 2 without making the original crystalline appearance collapse. - Graphical abstract: By UV irradiation with appropriate masks, a part of single crystal of organic conductors irreversibly turned diamagnetic retaining their original crystalline shapes.
Low-dimensional organization of angular momentum during walking on a narrow beam.
Chiovetto, Enrico; Huber, Meghan E; Sternad, Dagmar; Giese, Martin A
2018-01-08
Walking on a beam is a challenging motor skill that requires the regulation of upright balance and stability. The difficulty in beam walking results from the reduced base of support compared to that afforded by flat ground. One strategy to maintain stability and hence avoid falling off the beam is to rotate the limb segments to control the body's angular momentum. The aim of this study was to examine the coordination of the angular momentum variations during beam walking. We recorded movement kinematics of participants walking on a narrow beam and computed the angular momentum contributions of the body segments with respect to three different axes. Results showed that, despite considerable variability in the movement kinematics, the angular momentum was characterized by a low-dimensional organization based on a small number of segmental coordination patterns. When the angular momentum was computed with respect to the beam axis, the largest fraction of its variation was accounted for by the trunk segment. This simple organization was robust and invariant across all participants. These findings support the hypothesis that control strategies for complex balancing tasks might be easier to understand by investigating angular momentum instead of the segmental kinematics.
Low-Dimensional-Networked Metal Halide Perovskites: The Next Big Thing
Saidaminov, Makhsud I.
2017-03-03
Low-dimensional-networked (low-DN) perovskite derivatives are bulk quantum materials in which charge carriers are localized within ordered metal halide sheets, rods, or clusters that are separated by cationic lattices. After two decades of hibernation, this class of semiconductors reemerged in the past two years, largely catalyzed by the interest in alternative, more stable absorbers to CH3NH3PbI3-type perovskites in photovoltaics. Whether low-DN perovskites will surpass other photovoltaic technologies remains to be seen, but their impressively high photo- and electroluminescence yields have already set new benchmarks in light emission applications. Here we offer our perspective on the most exciting advances in materials design of low-DN perovskites for energy- and optoelectronic-related applications. The next few years will usher in an explosive growth in this tribe of quantum materials, as only a few members have been synthesized, while the potential library of compositions and structures is believed to be much larger and is yet to be discovered.
Using postural synergies to animate a low-dimensional hand avatar in haptic simulation.
Mulatto, Sara; Formaglio, Alessandro; Malvezzi, Monica; Prattichizzo, Domenico
2013-01-01
A technique to animate a realistic hand avatar with 20 DoFs based on the biomechanics of the human hand is presented. The animation does not use any sensor glove or advanced tracker with markers. The proposed approach is based on the knowledge of a set of kinematic constraints on the model of the hand, referred to as postural synergies, which allows to represent the hand posture using a number of variables lower than the number of joints of the hand model. This low-dimensional set of parameters is estimated from direct measurement of the motion of thumb and index finger tracked using two haptic devices. A kinematic inversion algorithm has been developed, which takes synergies into account and estimates the kinematic configuration of the whole hand, i.e., also of the fingers whose end tips are not directly tracked by the two haptic devices. The hand skin is deformable and its deformation is computed using a linear vertex blending technique. The proposed synergy-based animation of the hand avatar involves only algebraic computations and is suitable for real-time implementation as required in haptics.
Directory of Open Access Journals (Sweden)
Weixun Zhou
2017-05-01
Full Text Available Learning powerful feature representations for image retrieval has always been a challenging task in the field of remote sensing. Traditional methods focus on extracting low-level hand-crafted features which are not only time-consuming but also tend to achieve unsatisfactory performance due to the complexity of remote sensing images. In this paper, we investigate how to extract deep feature representations based on convolutional neural networks (CNNs for high-resolution remote sensing image retrieval (HRRSIR. To this end, several effective schemes are proposed to generate powerful feature representations for HRRSIR. In the first scheme, a CNN pre-trained on a different problem is treated as a feature extractor since there are no sufficiently-sized remote sensing datasets to train a CNN from scratch. In the second scheme, we investigate learning features that are specific to our problem by first fine-tuning the pre-trained CNN on a remote sensing dataset and then proposing a novel CNN architecture based on convolutional layers and a three-layer perceptron. The novel CNN has fewer parameters than the pre-trained and fine-tuned CNNs and can learn low dimensional features from limited labelled images. The schemes are evaluated on several challenging, publicly available datasets. The results indicate that the proposed schemes, particularly the novel CNN, achieve state-of-the-art performance.
NATO Advanced Research Workshop on Thin Film Growth Techniques for Low-Dimensional Structures
Parkin, S; Dobson, P; Neave, J; Arrott, A
1987-01-01
This work represents the account of a NATO Advanced Research Workshop on "Thin Film Growth Techniques for Low Dimensional Structures", held at the University of Sussex, Brighton, England from 15-19 Sept. 1986. The objective of the workshop was to review the problems of the growth and characterisation of thin semiconductor and metal layers. Recent advances in deposition techniques have made it possible to design new material which is based on ultra-thin layers and this is now posing challenges for scientists, technologists and engineers in the assessment and utilisation of such new material. Molecular beam epitaxy (MBE) has become well established as a method for growing thin single crystal layers of semiconductors. Until recently, MBE was confined to the growth of III-V compounds and alloys, but now it is being used for group IV semiconductors and II-VI compounds. Examples of such work are given in this volume. MBE has one major advantage over other crystal growth techniques in that the structure of the growi...
Emerging Low-Dimensional Materials for Nonlinear Optics and Ultrafast Photonics.
Liu, Xiaofeng; Guo, Qiangbing; Qiu, Jianrong
2017-04-01
Low-dimensional (LD) materials demonstrate intriguing optical properties, which lead to applications in diverse fields, such as photonics, biomedicine and energy. Due to modulation of electronic structure by the reduced structural dimensionality, LD versions of metal, semiconductor and topological insulators (TIs) at the same time bear distinct nonlinear optical (NLO) properties as compared with their bulk counterparts. Their interaction with short pulse laser excitation exhibits a strong nonlinear character manifested by NLO absorption, giving rise to optical limiting or saturated absorption associated with excited state absorption and Pauli blocking in different materials. In particular, the saturable absorption of these emerging LD materials including two-dimensional semiconductors as well as colloidal TI nanoparticles has recently been utilized for Q-switching and mode-locking ultra-short pulse generation across the visible, near infrared and middle infrared wavelength regions. Beside the large operation bandwidth, these ultrafast photonics applications are especially benefit from the high recovery rate as well as the facile processibility of these LD materials. The prominent NLO response of these LD materials have also provided new avenues for the development of novel NLO and photonics devices for all-optical control as well as optical circuits beyond ultrafast lasers. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Low-dimensional recurrent neural network-based Kalman filter for speech enhancement.
Xia, Youshen; Wang, Jun
2015-07-01
This paper proposes a new recurrent neural network-based Kalman filter for speech enhancement, based on a noise-constrained least squares estimate. The parameters of speech signal modeled as autoregressive process are first estimated by using the proposed recurrent neural network and the speech signal is then recovered from Kalman filtering. The proposed recurrent neural network is globally asymptomatically stable to the noise-constrained estimate. Because the noise-constrained estimate has a robust performance against non-Gaussian noise, the proposed recurrent neural network-based speech enhancement algorithm can minimize the estimation error of Kalman filter parameters in non-Gaussian noise. Furthermore, having a low-dimensional model feature, the proposed neural network-based speech enhancement algorithm has a much faster speed than two existing recurrent neural networks-based speech enhancement algorithms. Simulation results show that the proposed recurrent neural network-based speech enhancement algorithm can produce a good performance with fast computation and noise reduction. Copyright © 2015 Elsevier Ltd. All rights reserved.
Low-Dimensional Organic Tin Bromide Perovskites and Their Photoinduced Structural Transformation.
Zhou, Chenkun; Tian, Yu; Wang, Mingchao; Rose, Alyssa; Besara, Tiglet; Doyle, Nicholas K; Yuan, Zhao; Wang, Jamie C; Clark, Ronald; Hu, Yanyan; Siegrist, Theo; Lin, Shangchao; Ma, Biwu
2017-07-24
Hybrid organic-inorganic metal halide perovskites possess exceptional structural tunability, with three- (3D), two- (2D), one- (1D), and zero-dimensional (0D) structures on the molecular level all possible. While remarkable progress has been realized in perovskite research in recent years, the focus has been mainly on 3D and 2D structures, with 1D and 0D structures significantly underexplored. The synthesis and characterization of a series of low-dimensional organic tin bromide perovskites with 1D and 0D structures is reported. Using the same organic and inorganic components, but at different ratios and reaction conditions, both 1D (C 4 N 2 H 14 )SnBr 4 and 0D (C 4 N 2 H 14 Br) 4 SnBr 6 can be prepared in high yields. Moreover, photoinduced structural transformation from 1D to 0D was investigated experimentally and theoretically in which photodissociation of 1D metal halide chains followed by structural reorganization leads to the formation of a more thermodynamically stable 0D structure. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Low-dimensional and Data Fusion Techniques Applied to a Rectangular Supersonic Multi-stream Jet
Berry, Matthew; Stack, Cory; Magstadt, Andrew; Ali, Mohd; Gaitonde, Datta; Glauser, Mark
2017-11-01
Low-dimensional models of experimental and simulation data for a complex supersonic jet were fused to reconstruct time-dependent proper orthogonal decomposition (POD) coefficients. The jet consists of a multi-stream rectangular single expansion ramp nozzle, containing a core stream operating at Mj , 1 = 1.6 , and bypass stream at Mj , 3 = 1.0 with an underlying deck. POD was applied to schlieren and PIV data to acquire the spatial basis functions. These eigenfunctions were projected onto their corresponding time-dependent large eddy simulation (LES) fields to reconstruct the temporal POD coefficients. This reconstruction was able to resolve spectral peaks that were previously aliased due to the slower sampling rates of the experiments. Additionally, dynamic mode decomposition (DMD) was applied to the experimental and LES datasets, and the spatio-temporal characteristics were compared to POD. The authors would like to acknowledge AFOSR, program manager Dr. Doug Smith, for funding this research, Grant No. FA9550-15-1-0435.
Towards room-temperature superconductivity in low-dimensional C60 nanoarrays: An ab initio study
Erbahar, Dogan; Liu, Dan; Berber, Savas; Tománek, David
2018-04-01
We propose to raise the critical temperature Tc for superconductivity in doped C60 molecular crystals by increasing the electronic density of states at the Fermi level N (EF) and thus the electron-phonon coupling constant in low-dimensional C60 nanoarrays. We consider both electron and hole dopings and present numerical results for N (EF) , which increases with the decreasing bandwidth of the partly filled hu- and t1 u-derived frontier bands with the decreasing coordination number of C60. Whereas a significant increase in N (EF) occurs in two-dimensional (2D) arrays of doped C60 intercalated in-between graphene layers, we propose that the highest-Tc values approaching room temperature may occur in bundles of nanotubes filled by one-dimensional (1D) arrays of externally doped C60 or La @C60 or in diluted three-dimensional (3D) crystals where quasi-1D arrangements of C60 form percolation paths.
A low-dimensional tool for predicting force decomposition coefficients for varying inflow conditions
Ghommem, Mehdi
2013-01-01
We develop a low-dimensional tool to predict the effects of unsteadiness in the inflow on force coefficients acting on a circular cylinder using proper orthogonal decomposition (POD) modes from steady flow simulations. The approach is based on combining POD and linear stochastic estimator (LSE) techniques. We use POD to derive a reduced-order model (ROM) to reconstruct the velocity field. To overcome the difficulty of developing a ROM using Poisson\\'s equation, we relate the pressure field to the velocity field through a mapping function based on LSE. The use of this approach to derive force decomposition coefficients (FDCs) under unsteady mean flow from basis functions of the steady flow is illustrated. For both steady and unsteady cases, the final outcome is a representation of the lift and drag coefficients in terms of velocity and pressure temporal coefficients. Such a representation could serve as the basis for implementing control strategies or conducting uncertainty quantification. Copyright © 2013 Inderscience Enterprises Ltd.
Expressive body movement responses to music are coherent, consistent, and low dimensional.
Amelynck, Denis; Maes, Pieter-Jan; Martens, Jean Pierre; Leman, Marc
2014-12-01
Embodied music cognition stresses the role of the human body as mediator for the encoding and decoding of musical expression. In this paper, we set up a low dimensional functional model that accounts for 70% of the variability in the expressive body movement responses to music. With the functional principal component analysis, we modeled individual body movements as a linear combination of a group average and a number of eigenfunctions. The group average and the eigenfunctions are common to all subjects and make up what we call the commonalities. An individual performance is then characterized by a set of scores (the individualities), one score per eigenfunction. The model is based on experimental data which finds high levels of coherence/consistency between participants when grouped according to musical education. This shows an ontogenetic effect. Participants without formal musical education focus on the torso for the expression of basic musical structure (tempo). Musically trained participants decode additional structural elements in the music and focus on body parts having more degrees of freedom (such as the hands). Our results confirm earlier studies that different body parts move differently along with the music.
Meng, Fanke
Photocatalytic hydrogen generation by water splitting is a promising technique to produce clean and renewable solar fuel. The development of effective semiconductor photocatalysts to obtain efficient photocatalytic activity is the key objective. However, two critical reasons prevent wide applications of semiconductor photocatalysts: low light usage efficiency and high rates of charge recombination. In this dissertation, several low-dimensional semiconductors were synthesized with hydrothermal, hydrolysis, and chemical impregnation methods. The band structures of the low-dimensional semiconductor materials were engineered to overcome the above mentioned two shortcomings. In addition, the correlation between the photocatalytic activity of the low-dimensional semiconductor materials and their band structures were studied. First, we studied the effect of oxygen vacancies on the photocatalytic activity of one-dimensional anatase TiO2 nanobelts. Given that the oxygen vacancy plays a significant role in band structure and photocatalytic performance of semiconductors, oxygen vacancies were introduced into the anatase TiO2 nanobelts during reduction in H2 at high temperature. The oxygen vacancies of the TiO2 nanobelts boosted visible-light-responsive photocatalytic activity but weakened ultraviolet-light-responsive photocatalytic activity. As oxygen vacancies are commonly introduced by dopants, these results give insight into why doping is not always beneficial to the overall photocatalytic performance despite increases in absorption. Second, we improved the photocatalytic performance of two-dimensional lanthanum titanate (La2Ti2 O7) nanosheets, which are widely studied as an efficient photocatalyst due to the unique layered crystal structure. Nitrogen was doped into the La2Ti2O7 nanosheets and then Pt nanoparticles were loaded onto the La2Ti2O7 nanosheets. Doping nitrogen narrowed the band gap of the La2Ti 2O7 nanosheets by introducing a continuum of states by the valence
On low-dimensional models at NMR line shape analysis in nanomaterial systems
Kucherov, M. M.; Falaleev, O. V.
2018-03-01
We present a model of localized spin dynamics at room temperature for the low-dimensional solid-state spin system, which contains small ensembles of magnetic nuclei (N ~ 40). The standard spin Hamiltonian (XXZ model) is the sum of the Zeeman term in a strong external magnetic field and the magnetic dipole interaction secular term. The 19F spins in a single crystal of fluorapatite [Ca5(PO4)3F] have often been used to approximate a one-dimensional spin system. If the constant external field is parallel to the c axis, the 3D 19F system may be treated as a collection of many identical spin chains. When considering the longitudinal part of the secular term, we suggest that transverse component of a spin in a certain site rotates in a constant local magnetic field. This field changes if the spin jumps to another site. On return, this spin continues to rotate in the former field. Then we expand the density matrix in a set of eigenoperators of the Zeeman Hamiltonian. A system of coupled differential equations for the expansion coefficients then solved by straightforward numerical methods, and the fluorine NMR line shapes of fluorapatite for different chain lengths are calculated.
Modular assembly of low-dimensional coordination architectures on metal surfaces
International Nuclear Information System (INIS)
Stepanow, Sebastian; Lin, Nian; Barth, Johannes V
2008-01-01
The engineering of highly organized molecular architectures has attracted strong interest because of its potential for novel materials and functional nanoscopic devices. An important factor in the development, integration, and exploitation of such systems is the capability to prepare them on surfaces or in nanostructured environments. Recent advances in supramolecular design on metal substrates provide atomistic insight into the underlying self-assembly processes, mainly by scanning tunneling microscopy observations. This review summarizes progress in noncovalent synthesis strategies under ultra-high vacuum conditions employing metal ions as coordination centers directing the molecular organization. The realized metallosupramolecular compounds and arrays combine the properties of their constituent metal ions and organic ligands, and present several attractive features: their redox, magnetic and spin-state transitions. The presented exemplary molecular level studies elucidate the arrangement of organic adsorbates on metal surfaces, demonstrating the interplay between intermolecular and molecule-substrate interactions that needs to be controlled for the fabrication of low-dimensional structures. The understanding of metallosupramolecular organization and metal-ligand interactions on solid surfaces is important for the control of structure and concomitant function
Chaos in World Politics: A Reflection
Ferreira, Manuel Alberto Martins; Filipe, José António Candeias Bonito; Coelho, Manuel F. P.; Pedro, Isabel C.
Chaos theory results from natural scientists' findings in the area of non-linear dynamics. The importance of related models has increased in the last decades, by studying the temporal evolution of non-linear systems. In consequence, chaos is one of the concepts that most rapidly have been expanded in what research topics respects. Considering that relationships in non-linear systems are unstable, chaos theory aims to understand and to explain this kind of unpredictable aspects of nature, social life, the uncertainties, the nonlinearities, the disorders and confusion, scientifically it represents a disarray connection, but basically it involves much more than that. The existing close relationship between change and time seems essential to understand what happens in the basics of chaos theory. In fact, this theory got a crucial role in the explanation of many phenomena. The relevance of this kind of theories has been well recognized to explain social phenomena and has permitted new advances in the study of social systems. Chaos theory has also been applied, particularly in the context of politics, in this area. The goal of this chapter is to make a reflection on chaos theory - and dynamical systems such as the theories of complexity - in terms of the interpretation of political issues, considering some kind of events in the political context and also considering the macro-strategic ideas of states positioning in the international stage.
International Nuclear Information System (INIS)
Allen, J. W.
2003-01-01
This report summarizes a 12-year program of various kinds of synchrotron spectroscopies directed at the electronic structures of narrow band and low-dimensional materials that display correlated electron behaviors such as metal-insulator transitions, mixed valence, superconductivity, Kondo moment quenching, heavy Fermions, and non-Fermi liquid properties
Samara, Ziyad; Fiamma, Marie-Noëlle; Bautin, Nathalie; Ranohavimparany, Anja; Le Coz, Patrick; Golmard, Jean-Louis; Darré, Pierre; Zelter, Marc; Poon, Chi-Sang; Similowski, Thomas
2011-01-01
Human ventilation at rest exhibits mathematical chaos-like complexity that can be described as long-term unpredictability mediated (in whole or in part) by some low-dimensional nonlinear deterministic process. Although various physiological and pathological situations can affect respiratory complexity, the underlying mechanisms remain incompletely elucidated. If such chaos-like complexity is an intrinsic property of central respiratory generators, it should appear or increase when these structures mature or are stimulated. To test this hypothesis, we employed the isolated tadpole brainstem model [Rana (Pelophylax) esculenta] and recorded the neural respiratory output (buccal and lung rhythms) of pre- (n = 8) and postmetamorphic tadpoles (n = 8), at physiologic (7.8) and acidic pH (7.4). We analyzed the root mean square of the cranial nerve V or VII neurograms. Development and acidosis had no effect on buccal period. Lung frequency increased with development (P Chaos-like complexity, assessed through the noise limit, increased from pH 7.8 to pH 7.4 (P chaos-like complexity, especially in the postmetamorphic stage and at low pH. According to the ventilatory generators homology theory, this may also be the case in mammals. PMID:21325645
Li-Yorke chaos and synchronous chaos in a globally nonlocal coupled map lattice
International Nuclear Information System (INIS)
Khellat, Farhad; Ghaderi, Akashe; Vasegh, Nastaran
2011-01-01
Highlights: → A globally nonlocal coupled map lattice is introduced. → A sufficient condition for the existence of Li-Yorke chaos is determined. → A sufficient condition for synchronous behaviors is obtained. - Abstract: This paper investigates a globally nonlocal coupled map lattice. A rigorous proof to the existence of chaos in the scene of Li-Yorke in that system is presented in terms of the Marotto theorem. Analytical sufficient conditions under which the system is chaotic, and has synchronous behaviors are determined, respectively. The wider regions associated with chaos and synchronous behaviors are shown by simulations. Spatiotemporal chaos, synchronous chaos and some other synchronous behaviors such as fixed points, 2-cycles and 2 2 -cycles are also shown by simulations for some values of the parameters.
New developments in the theoretical treatment of low dimensional strongly correlated systems.
James, Andrew J A; Konik, Robert M; Lecheminant, Philippe; Robinson, Neil; Tsvelik, Alexei M
2017-10-09
We review two important non-perturbative approaches for extracting the physics of low- dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of confor- mal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symme- tries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one and two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1+1D quantum chro- modynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. We describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics. © 2017 IOP Publishing Ltd.
Low Dimensional Embedding of Climate Data for Radio Astronomical Site Testing in the Colombian Andes
Chaparro Molano, Germán; Ramírez Suárez, Oscar Leonardo; Restrepo Gaitán, Oscar Alberto; Marcial Martínez Mercado, Alexander
2017-10-01
We set out to evaluate the potential of the Colombian Andes for millimeter-wave astronomical observations. Previous studies for astronomical site testing in this region have suggested that nighttime humidity and cloud cover conditions make most sites unsuitable for professional visible-light observations. Millimeter observations can be done during the day, but require that the precipitable water vapor column above a site stays below ˜10 mm. Due to a lack of direct radiometric or radiosonde measurements, we present a method for correlating climate data from weather stations to sites with a low precipitable water vapor column. We use unsupervised learning techniques to low dimensionally embed climate data (precipitation, rain days, relative humidity, and sunshine duration) in order to group together stations with similar long-term climate behavior. The data were taken over a period of 30 years by 2046 weather stations across the Colombian territory. We find six regions with unusually dry, clear-sky conditions, ranging in elevations from 2200 to 3800 masl. We evaluate the suitability of each region using a quality index derived from a Bayesian probabilistic analysis of the station type and elevation distributions. Two of these regions show a high probability of having an exceptionally low precipitable water vapor column. We compared our results with global precipitable water vapor maps and find a plausible geographical correlation with regions with low water vapor columns (˜10 mm) at an accuracy of ˜20 km. Our methods can be applied to similar data sets taken in other countries as a first step toward astronomical site evaluation.
Experimental study on the spin-orbit coupling property in low-dimensional semiconductor structures
International Nuclear Information System (INIS)
Zhao, Hongming
2010-01-01
The spin-orbit coupling and optical properties have been studied in several low-dimensional semiconductor structures. First, the spin dynamics in (001) GaAs/AlGaAs two-dimensional electron gas was investigated by time resolved Kerr rotation technique under a transverse magnetic field. The in-plane spin lifetime is found to be anisotropic. The results show that the electron density in two-dimensional electron gas channel strongly affects the Rashba spin-orbit coupling. Then, a large anisotropy of the magnitude of in-plane conduction electron g factor in asymmetric (001) GaAs/AlGaAs QWs was observed and its tendency of temperature dependence was studied. Second, the experimental study of the in-plane-orientation dependent spin splitting in the C(0001) GaN/AlGaN two-dimensional electron gas at room temperature was reported. The measurement of circular photo-galvanic effect current clearly shows the isotropic in-plane spin splitting in this system for the first time. Third, the first measurement of conduction electron g factor in GaAsN at room temperature was done by using time resolved Kerr rotation technique. It demonstrates that the g factor can be modified drastically by introducing a small amount of nitrogen in GaAs bulk. Finally, the optical characteristic of indirect type II transition in a series of size and shape-controlled linear CdTe/CdSe/CdTe heterostructure nano-rods was studied by steady-state and time resolved photoluminescence. Results show the steady transfer from the direct optical transition (type I) within CdSe to the indirect transition (type II) between CdSe/CdTe as the length of the nano-rods increases. (author)
Low-dimensional analysis, using POD, for two mixing layer-wake interactions
International Nuclear Information System (INIS)
Braud, Caroline; Heitz, Dominique; Arroyo, Georges; Perret, Laurent; Delville, Joeel; Bonnet, Jean-Paul
2004-01-01
The mixing layer-wake interaction is studied experimentally in the framework of two flow configurations. For the first one, the initial conditions of the mixing layer are modified by using a thick trailing edge, a wake effect is therefore superimposed to the mixing layer from its beginning (blunt trailing edge). In the second flow configuration, a canonical mixing layer is perturbed in its asymptotic region by the wake of a cylinder arranged perpendicular to the plane of the mixing layer. These interactions are analyzed mainly by using two-point velocity correlations and the proper orthogonal decomposition (POD). These two flow configurations differ by the degree of complexity they involve: the former is mainly 2D while the latter is highly 3D. The blunt trailing edge configuration is analyzed by using rakes of hot wire probes. This flow configuration is found to be considerably different when compared to a conventional mixing layer. It appears in particular that the scale of the large structures depends only on the trailing edge thickness and does not grow in its downstream evolution. A criterion, based on POD, is proposed in order to separate wake-mixing layer dominant areas of the downstream evolution of the flow. The complex 3D dynamical behaviour resulting from the interaction between the canonical plane mixing layer and the wake of a cylinder is investigated using data arising from particle image velocimetry measurements. An analysis of the velocity correlations shows different length scales in the regions dominated by wake like structures and shear layer type structures. In order to characterize the particular organization in the plane of symmetry, a POD-Galerkin projection of the Navier-Stokes equations is performed in this plane. This leads to a low-dimensional dynamical system that allows the analysis of the relationship between the dominant frequencies to be performed. A reconstruction of the dominant periodic motion suspected from previous studies is
Genome chaos: survival strategy during crisis.
Liu, Guo; Stevens, Joshua B; Horne, Steven D; Abdallah, Batoul Y; Ye, Karen J; Bremer, Steven W; Ye, Christine J; Chen, David J; Heng, Henry H
2014-01-01
Genome chaos, a process of complex, rapid genome re-organization, results in the formation of chaotic genomes, which is followed by the potential to establish stable genomes. It was initially detected through cytogenetic analyses, and recently confirmed by whole-genome sequencing efforts which identified multiple subtypes including "chromothripsis", "chromoplexy", "chromoanasynthesis", and "chromoanagenesis". Although genome chaos occurs commonly in tumors, both the mechanism and detailed aspects of the process are unknown due to the inability of observing its evolution over time in clinical samples. Here, an experimental system to monitor the evolutionary process of genome chaos was developed to elucidate its mechanisms. Genome chaos occurs following exposure to chemotherapeutics with different mechanisms, which act collectively as stressors. Characterization of the karyotype and its dynamic changes prior to, during, and after induction of genome chaos demonstrates that chromosome fragmentation (C-Frag) occurs just prior to chaotic genome formation. Chaotic genomes seem to form by random rejoining of chromosomal fragments, in part through non-homologous end joining (NHEJ). Stress induced genome chaos results in increased karyotypic heterogeneity. Such increased evolutionary potential is demonstrated by the identification of increased transcriptome dynamics associated with high levels of karyotypic variance. In contrast to impacting on a limited number of cancer genes, re-organized genomes lead to new system dynamics essential for cancer evolution. Genome chaos acts as a mechanism of rapid, adaptive, genome-based evolution that plays an essential role in promoting rapid macroevolution of new genome-defined systems during crisis, which may explain some unwanted consequences of cancer treatment.
Particle ratios, quarks, and Chao-Yang statistics
Energy Technology Data Exchange (ETDEWEB)
Chew, C K; Low, G B; Lo, S Y [Nanyang Univ. (Singapore). Dept. of Physics; Phua, K K [Argonne National Lab., IL (USA)
1980-01-01
By introducing quarks into Chao-Yang statistics for 'violent' collisions, particle ratios are obtained which are consistent with the Chao-Yang results. The present method can also be extended to baryon-meson and baryon-antibaryon ratios.
Digital Communication Devices Based on Nonlinear Dynamics and Chaos
National Research Council Canada - National Science Library
Larson, Lawrence
2003-01-01
The final report of the ARO MURI "Digital Communications Based on Chaos and Nonlinear Dynamics" contains research results in the areas of chaos and nonlinear dynamics applied to wireless and optical communications...
International Nuclear Information System (INIS)
D'Arcy, Michael Brendan
2002-01-01
This thesis presents an account of experimental and numerical investigations of two quantum systems whose respective classical analogues are chaotic. These are the δ-kicked rotor, a paradigm in classical chaos theory, and the novel δ-kicked accelerator, created by application of a constant external acceleration or torque to the rotor. The experimental realisation of these systems has been achieved by the exposure of laser-cooled caesium atoms to approximate δ-kicks from a pulsed, high-intensity, vertical standing wave of laser light. Gravity's effect on the atoms can be controlled by appropriate shifting of the profile of the standing wave. Numerical simulations of the systems are based on a diffractive model of the potential's effect. Each system's dynamics are characterised by the final form of the momentum distribution and the dependence of the atoms' mean kinetic energy on the number and time period of the δ-kicks. The phenomena of dynamical localisation and quantum resonances in the δ-kicked rotor, which have no counterparts in the system's classical analogue, are observed and investigated. Similar experiments on the δ-kicked accelerator reveal the striking phenomenon of the quantum accelerator mode, in which a large momentum is transferred to a substantial fraction of the atomic ensemble. This feature, absent in the system's classical analogue, is characterised and an analytic explanation is presented. The effect on each quantum system of decoherence, introduced through spontaneous emission in the atoms, is examined and comparison is made with the results of classical simulations. While having little effect on the classical systems, the level of decoherence used is found to degrade quantum signatures of behaviour. Classical-like behaviour is, to some extent, restored, although significant quantum features remain. Possible applications of the quantum accelerator mode are discussed. These include use as a tool in atom optics and interferometry, a
2nd International Symposium on Chaos, Complexity and Leadership
Banerjee, Santo
2015-01-01
These proceedings from the 2013 symposium on "Chaos, complexity and leadership" reflect current research results from all branches of Chaos, Complex Systems and their applications in Management. Included are the diverse results in the fields of applied nonlinear methods, modeling of data and simulations, as well as theoretical achievements of Chaos and Complex Systems. Also highlighted are Leadership and Management applications of Chaos and Complexity Theory.
Chaos of discrete dynamical systems in complete metric spaces
International Nuclear Information System (INIS)
Shi Yuming; Chen Guanrong
2004-01-01
This paper is concerned with chaos of discrete dynamical systems in complete metric spaces. Discrete dynamical systems governed by continuous maps in general complete metric spaces are first discussed, and two criteria of chaos are then established. As a special case, two corresponding criteria of chaos for discrete dynamical systems in compact subsets of metric spaces are obtained. These results have extended and improved the existing relevant results of chaos in finite-dimensional Euclidean spaces
The three versions of distributional chaos
International Nuclear Information System (INIS)
Balibrea, F.; Smital, J.; Stefankova, M.
2005-01-01
The notion of distributional chaos was introduced by Schweizer and Smital [Trans. Amer. Math. Soc. 344 (1994) 737] for continuous maps of the interval. However, it turns out that, for continuous maps of a compact metric space three mutually nonequivalent versions of distributional chaos, DC1-DC3, can be considered. In this paper we consider the weakest one, DC3. We show that DC3 does not imply chaos in the sense of Li and Yorke. We also show that DC3 is not invariant with respect to topological conjugacy. In other words, there are lower and upper distribution functions Φ xy and Φxy* generated by a continuous map f of a compact metric space (M, ρ) such that Φxy*(t)>Φxy(t) for all t in an interval. However, f on the same space M, but with a metric ρ' generating the same topology as ρ is no more DC3.Recall that, contrary to this, either DC1 or DC2 is topological conjugacy invariant and implies Li and Yorke chaos (cf. [Chaos, Solitons and Fractals 21 (2004) 1125])
Generic superweak chaos induced by Hall effect
Ben-Harush, Moti; Dana, Itzhack
2016-05-01
We introduce and study the "kicked Hall system" (KHS), i.e., charged particles periodically kicked in the presence of uniform magnetic (B ) and electric (E ) fields that are perpendicular to each other and to the kicking direction. We show that for resonant values of B and E and in the weak-chaos regime of sufficiently small nonintegrability parameter κ (the kicking strength), there exists a generic family of periodic kicking potentials for which the Hall effect from B and E significantly suppresses the weak chaos, replacing it by "superweak" chaos (SWC). This means that the system behaves as if the kicking strength were κ2 rather than κ . For E =0 , SWC is known to be a classical fingerprint of quantum antiresonance, but it occurs under much less generic conditions, in particular only for very special kicking potentials. Manifestations of SWC are a decrease in the instability of periodic orbits and a narrowing of the chaotic layers, relative to the ordinary weak-chaos case. Also, for global SWC, taking place on an infinite "stochastic web" in phase space, the chaotic diffusion on the web is much slower than the weak-chaos one. Thus, the Hall effect can be relatively stabilizing for small κ . In some special cases, the effect is shown to cause ballistic motion for almost all parameter values. The generic global SWC on stochastic webs in the KHS appears to be the two-dimensional closest analog to the Arnol'd web in higher dimensional systems.
The Capabilities of Chaos and Complexity
Directory of Open Access Journals (Sweden)
David L. Abel
2009-01-01
Full Text Available To what degree could chaos and complexity have organized a Peptide or RNA World of crude yet necessarily integrated protometabolism? How far could such protolife evolve in the absence of a heritable linear digital symbol system that could mutate, instruct, regulate, optimize and maintain metabolic homeostasis? To address these questions, chaos, complexity, self-ordered states, and organization must all be carefully defined and distinguished. In addition their cause-and-effect relationships and mechanisms of action must be delineated. Are there any formal (non physical, abstract, conceptual, algorithmic components to chaos, complexity, self-ordering and organization, or are they entirely physicodynamic (physical, mass/energy interaction alone? Chaos and complexity can produce some fascinating self-ordered phenomena. But can spontaneous chaos and complexity steer events and processes toward pragmatic benefit, select function over non function, optimize algorithms, integrate circuits, produce computational halting, organize processes into formal systems, control and regulate existing systems toward greater efficiency? The question is pursued of whether there might be some yet-to-be discovered new law of biology that will elucidate the derivation of prescriptive information and control. Ã¢Â€ÂœSystemÃ¢Â€Â will be rigorously defined. Can a low-informational rapid succession of PrigogineÃ¢Â€Â™s dissipative structures self-order into bona fide organization?
International Nuclear Information System (INIS)
Dattani, Justine; Blake, Jack C.H.; Hilker, Frank M.
2011-01-01
Designing intervention methods to control chaotic behavior in dynamical systems remains a challenging problem, in particular for systems that are difficult to access or to measure. We propose a simple, intuitive technique that modifies the values of the state variables directly toward a certain target. The intervention takes into account the difference to the target value, and is a combination of traditional proportional feedback and constant feedback methods. It proves particularly useful when the target corresponds to the equilibrium of the uncontrolled system, and is available or can be estimated from expert knowledge (e.g. in biology and economy). -- Highlights: → We propose a chaos control method that forces the system to a certain target. → The intervention takes into account the difference to the target value. → It can be seen as a combination of proportional and constant feedback methods. → The method is very robust and highly efficient in the long-term. → It is particularly applicable when suitable target values are known or available.
Chaos and unpredictability in evolution.
Doebeli, Michael; Ispolatov, Iaroslav
2014-05-01
The possibility of complicated dynamic behavior driven by nonlinear feedbacks in dynamical systems has revolutionized science in the latter part of the last century. Yet despite examples of complicated frequency dynamics, the possibility of long-term evolutionary chaos is rarely considered. The concept of "survival of the fittest" is central to much evolutionary thinking and embodies a perspective of evolution as a directional optimization process exhibiting simple, predictable dynamics. This perspective is adequate for simple scenarios, when frequency-independent selection acts on scalar phenotypes. However, in most organisms many phenotypic properties combine in complicated ways to determine ecological interactions, and hence frequency-dependent selection. Therefore, it is natural to consider models for evolutionary dynamics generated by frequency-dependent selection acting simultaneously on many different phenotypes. Here we show that complicated, chaotic dynamics of long-term evolutionary trajectories in phenotype space is very common in a large class of such models when the dimension of phenotype space is large, and when there are selective interactions between the phenotypic components. Our results suggest that the perspective of evolution as a process with simple, predictable dynamics covers only a small fragment of long-term evolution. © 2014 The Author(s). Evolution © 2014 The Society for the Study of Evolution.
Chaos for induced hyperspace maps
International Nuclear Information System (INIS)
Banks, John
2005-01-01
For (X,d) be a metric space, f:X->X a continuous map and (K(X),H) the space of non-empty compact subsets of X with the Hausdorff metric, one may study the dynamical properties of the induced map (*)f-bar :K(X)->K(X):A-bar f(A).H. Roman-Flores [A note on in set-valued discrete systems. Chaos, Solitons and Fractals 2003;17:99-104] has shown that if f-bar is topologically transitive then so is f, but that the reverse implication does not hold. This paper shows that the topological transitivity of f-bar is in fact equivalent to weak topological mixing on the part of f. This is proved in the more general context of an induced map on some suitable hyperspace H of X with the Vietoris topology (which agrees with the topology of the Hausdorff metric in the case discussed by Roman-Flores
Deterministic Chaos - Complex Chance out of Simple Necessity ...
Indian Academy of Sciences (India)
This is a very lucid and lively book on deterministic chaos. Chaos is very common in nature. However, the understanding and realisation of its potential applications is very recent. Thus this book is a timely addition to the subject. There are several books on chaos and several more are being added every day. In spite of this ...
Chaos Theory as a Model for Managing Issues and Crises.
Murphy, Priscilla
1996-01-01
Uses chaos theory to model public relations situations in which the salient feature is volatility of public perceptions. Discusses the premises of chaos theory and applies them to issues management, the evolution of interest groups, crises, and rumors. Concludes that chaos theory is useful as an analogy to structure image problems and to raise…
God's Stuff: The Constructive Powers of Chaos for Teaching Religion
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…
Chaos in the fractional order Chen system and its control
International Nuclear Information System (INIS)
Li Chunguang; Chen Guanrong
2004-01-01
In this letter, we study the chaotic behaviors in the fractional order Chen system. We found that chaos exists in the fractional order Chen system with order less than 3. The lowest order we found to have chaos in this system is 2.1. Linear feedback control of chaos in this system is also studied
The Nature (and Nurture) of Children's Perceptions of Family Chaos
Hanscombe, Ken B.; Haworth, Claire M. A.; Davis, Oliver S. P.; Jaffee, Sara R.; Plomin, Robert
2010-01-01
Chaos in the home is a key environment in cognitive and behavioural development. However, we show that children's experience of home chaos is partly genetically mediated. We assessed children's perceptions of household chaos at ages 9 and 12 in 2337 pairs of twins. Using child-specific reports allowed us to use structural equation modelling to…
Quantum theory of the electronic and optical properties of low-dimensional semiconductor systems
Lau, Wayne Heung
This thesis examines the electronic and optical properties of low-dimensional semiconductor systems. A theory is developed to study the electron-hole generation-recombination process of type-II semimetallic semiconductor heterojunctions based on a 3 x 3 k·p matrix Hamiltonian (three-band model) and an 8 x 8 k·p matrix Hamiltonian (eight-band model). A novel electron-hole generation and recombination process, which is called activationless generation-recombination process, is predicted. It is demonstrated that the current through the type-II semimetallic semiconductor heterojunctions is governed by the activationless electron-hole generation-recombination process at the heterointerfaces, and that the current-voltage characteristics are essentially linear. A qualitative agreement between theory and experiments is observed. The numerical results of the eight-band model are compared with those of the threeband model. Based on a lattice gas model, a theory is developed to study the influence of a random potential on the ionization equilibrium conditions for bound electron-hole pairs (excitons) in III--V semiconductor heterostructures. It is demonstrated that ionization equilibrium conditions for bound electron-hole pairs change drastically in the presence of strong disorder. It is predicted that strong disorder promotes dissociation of excitons in III--V semiconductor heterostructures. A theory of polariton (photon dressed by phonon) spontaneous emission in a III--V semiconductor doped with semiconductor quantum dots (QDs) or quantum wells (QWs) is developed. For the first time, superradiant and subradiant polariton spontaneous emission phenomena in a polariton-QD (QW) coupled system are predicted when the resonance energies of the two identical QDs (QWs) lie outside the polaritonic energy gap. It is also predicted that when the resonance energies of the two identical QDs (QWs) lie inside the polaritonic energy gap, spontaneous emission of polariton in the polariton
Savin, Alexander V.; Kosevich, Yuriy A.; Cantarero, Andres
2012-08-01
We present a detailed description of semiquantum molecular dynamics simulation of stochastic dynamics of a system of interacting particles. Within this approach, the dynamics of the system is described with the use of classical Newtonian equations of motion in which the effects of phonon quantum statistics are introduced through random Langevin-like forces with a specific power spectral density (the color noise). The color noise describes the interaction of the molecular system with the thermostat. We apply this technique to the simulation of thermal properties and heat transport in different low-dimensional nanostructures. We describe the determination of temperature in quantum lattice systems, to which the equipartition limit is not applied. We show that one can determine the temperature of such a system from the measured power spectrum and temperature- and relaxation-rate-independent density of vibrational (phonon) states. We simulate the specific heat and heat transport in carbon nanotubes, as well as the heat transport in molecular nanoribbons with perfect (atomically smooth) and rough (porous) edges, and in nanoribbons with strongly anharmonic periodic interatomic potentials. We show that the effects of quantum statistics of phonons are essential for the carbon nanotube in the whole temperature range T<500K, in which the values of the specific heat and thermal conductivity of the nanotube are considerably less than that obtained within the description based on classical statistics of phonons. This conclusion is also applicable to other carbon-based materials and systems with high Debye temperature like graphene, graphene nanoribbons, fullerene, diamond, diamond nanowires, etc. We show that the existence of rough edges and quantum statistics of phonons change drastically the low-temperature thermal conductivity of the nanoribbon in comparison with that of the nanoribbon with perfect edges and classical phonon dynamics and statistics. The semiquantum molecular
Development of plenoptic infrared camera using low dimensional material based photodetectors
Chen, Liangliang
Infrared (IR) sensor has extended imaging from submicron visible spectrum to tens of microns wavelength, which has been widely used for military and civilian application. The conventional bulk semiconductor materials based IR cameras suffer from low frame rate, low resolution, temperature dependent and highly cost, while the unusual Carbon Nanotube (CNT), low dimensional material based nanotechnology has been made much progress in research and industry. The unique properties of CNT lead to investigate CNT based IR photodetectors and imaging system, resolving the sensitivity, speed and cooling difficulties in state of the art IR imagings. The reliability and stability is critical to the transition from nano science to nano engineering especially for infrared sensing. It is not only for the fundamental understanding of CNT photoresponse induced processes, but also for the development of a novel infrared sensitive material with unique optical and electrical features. In the proposed research, the sandwich-structured sensor was fabricated within two polymer layers. The substrate polyimide provided sensor with isolation to background noise, and top parylene packing blocked humid environmental factors. At the same time, the fabrication process was optimized by real time electrical detection dielectrophoresis and multiple annealing to improve fabrication yield and sensor performance. The nanoscale infrared photodetector was characterized by digital microscopy and precise linear stage in order for fully understanding it. Besides, the low noise, high gain readout system was designed together with CNT photodetector to make the nano sensor IR camera available. To explore more of infrared light, we employ compressive sensing algorithm into light field sampling, 3-D camera and compressive video sensing. The redundant of whole light field, including angular images for light field, binocular images for 3-D camera and temporal information of video streams, are extracted and
International Nuclear Information System (INIS)
Ge Zhengming; Chang Chingming; Chen Yensheng
2006-01-01
Anti-control of chaos of single time scale brushless dc motors (BLDCM) and chaos synchronization of different order systems are studied in this paper. By addition of an external nonlinear term, we can obtain anti-control of chaos. Then, by addition of the coupling terms, by the use of Lyapunov stability theorem and by the linearization of the error dynamics, chaos synchronization between a third-order BLDCM and a second-order Duffing system are presented
International Nuclear Information System (INIS)
Li Qianshu; Zhu Rui
2004-01-01
A three-variable model of the Belousov-Zhabotinsky reaction system subject to external sinusoidal perturbations is investigated by means of frequency spectrum analysis. In the period-1 window of the model, the transitions from periodicity to chaos are observed; in the chaotic window, the transitions from chaos to periodicity are found. The former might be understood by the circle map of two coupled oscillators, and the latter is partly explained by the resonance between the main frequency of the chaos and the frequency of the external periodic perturbations
Hyperbolic Chaos A Physicist’s View
Kuznetsov, Sergey P
2012-01-01
"Hyperbolic Chaos: A Physicist’s View” presents recent progress on uniformly hyperbolic attractors in dynamical systems from a physical rather than mathematical perspective (e.g. the Plykin attractor, the Smale – Williams solenoid). The structurally stable attractors manifest strong stochastic properties, but are insensitive to variation of functions and parameters in the dynamical systems. Based on these characteristics of hyperbolic chaos, this monograph shows how to find hyperbolic chaotic attractors in physical systems and how to design a physical systems that possess hyperbolic chaos. This book is designed as a reference work for university professors and researchers in the fields of physics, mechanics, and engineering. Dr. Sergey P. Kuznetsov is a professor at the Department of Nonlinear Processes, Saratov State University, Russia.
Nonlinear dynamics and quantum chaos an introduction
Wimberger, Sandro
2014-01-01
The field of nonlinear dynamics and chaos has grown very much over the last few decades and is becoming more and more relevant in different disciplines. This book presents a clear and concise introduction to the field of nonlinear dynamics and chaos, suitable for graduate students in mathematics, physics, chemistry, engineering, and in natural sciences in general. It provides a thorough and modern introduction to the concepts of Hamiltonian dynamical systems' theory combining in a comprehensive way classical and quantum mechanical description. It covers a wide range of topics usually not found in similar books. Motivations of the respective subjects and a clear presentation eases the understanding. The book is based on lectures on classical and quantum chaos held by the author at Heidelberg University. It contains exercises and worked examples, which makes it ideal for an introductory course for students as well as for researchers starting to work in the field.
Improved particle swarm optimization combined with chaos
International Nuclear Information System (INIS)
Liu Bo; Wang Ling; Jin Yihui; Tang Fang; Huang Dexian
2005-01-01
As a novel optimization technique, chaos has gained much attention and some applications during the past decade. For a given energy or cost function, by following chaotic ergodic orbits, a chaotic dynamic system may eventually reach the global optimum or its good approximation with high probability. To enhance the performance of particle swarm optimization (PSO), which is an evolutionary computation technique through individual improvement plus population cooperation and competition, hybrid particle swarm optimization algorithm is proposed by incorporating chaos. Firstly, adaptive inertia weight factor (AIWF) is introduced in PSO to efficiently balance the exploration and exploitation abilities. Secondly, PSO with AIWF and chaos are hybridized to form a chaotic PSO (CPSO), which reasonably combines the population-based evolutionary searching ability of PSO and chaotic searching behavior. Simulation results and comparisons with the standard PSO and several meta-heuristics show that the CPSO can effectively enhance the searching efficiency and greatly improve the searching quality
Entanglement as a signature of quantum chaos.
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.
Chaos Concepts, Control and Constructive Use
Bolotin, Yurii; Yanovsky, Vladimir
2009-01-01
The study of chaotic behaviour in nonlinear, dynamical systems is now a well established research domain with ramifications into all fields of sciences, spanning a vast range of applications, from celestial mechanics, via climate change, to the functioning of brownian motors in cells. A more recent discovery is that chaos can be controlled and, under appropriate conditions, can actually be constructive in the sense of becoming a control parameter itself for the system under investigation, stochastic resonance being a prime example. The present work is putting emphasis on the latter aspects, and after recalling the paradigm changes introduced by the concept of chaos, leads the reader skillfully through the basics of chaos control by detailing relevant algorithms for both Hamiltonian and dissipative systems amongst others. The main part of the book is then devoted to the issue of synchronization in chaotic systems, an introduction to stochastic resonance and a survey of ratchet models. This short and concise pr...
Polynomial chaos functions and stochastic differential equations
International Nuclear Information System (INIS)
Williams, M.M.R.
2006-01-01
The Karhunen-Loeve procedure and the associated polynomial chaos expansion have been employed to solve a simple first order stochastic differential equation which is typical of transport problems. Because the equation has an analytical solution, it provides a useful test of the efficacy of polynomial chaos. We find that the convergence is very rapid in some cases but that the increased complexity associated with many random variables can lead to very long computational times. The work is illustrated by exact and approximate solutions for the mean, variance and the probability distribution itself. The usefulness of a white noise approximation is also assessed. Extensive numerical results are given which highlight the weaknesses and strengths of polynomial chaos. The general conclusion is that the method is promising but requires further detailed study by application to a practical problem in transport theory
Navigating Through Chaos: Charge Nurses and Patient Safety.
Cathro, Heather
2016-04-01
The aim of this study was to explore actions and the processes charge nurses (CNs) implement to keep patients safe and generate an emerging theory to inform CN job descriptions, orientation, and training to promote patient safety in practice. Healthcare workers must provide a safe environment for patients. CNs are the frontline leaders on most hospital units and can function as gatekeepers for safe patient care. This grounded theory study utilized purposive sampling of CNs on medical-surgical units in a 400-bed metropolitan hospital. Data collection consisted of 11 interviews and 6 observations. The emerging theory was navigating through chaos: CNs balancing multiple roles, maintaining a watchful eye, and working with and leading the healthcare team to keep patients safe. CNs have knowledge of patients, staff, and complex healthcare environments, putting them in opportune positions to influence patient safety.
Bifurcation and chaos in neural excitable system
International Nuclear Information System (INIS)
Jing Zhujun; Yang Jianping; Feng Wei
2006-01-01
In this paper, we investigate the dynamical behaviors of neural excitable system without periodic external current (proposed by Chialvo [Generic excitable dynamics on a two-dimensional map. Chaos, Solitons and Fractals 1995;5(3-4):461-79] and with periodic external current as system's parameters vary. The existence and stability of three fixed points, bifurcation of fixed points, the conditions of existences of fold bifurcation, flip bifurcation and Hopf bifurcation are derived by using bifurcation theory and center manifold theorem. The chaotic existence in the sense of Marotto's definition of chaos is proved. We then give the numerical simulated results (using bifurcation diagrams, computations of Maximum Lyapunov exponent and phase portraits), which not only show the consistence with the analytic results but also display new and interesting dynamical behaviors, including the complete period-doubling and inverse period-doubling bifurcation, symmetry period-doubling bifurcations of period-3 orbit, simultaneous occurrence of two different routes (invariant cycle and period-doubling bifurcations) to chaos for a given bifurcation parameter, sudden disappearance of chaos at one critical point, a great abundance of period windows (period 2 to 10, 12, 19, 20 orbits, and so on) in transient chaotic regions with interior crises, strange chaotic attractors and strange non-chaotic attractor. In particular, the parameter k plays a important role in the system, which can leave the chaotic behavior or the quasi-periodic behavior to period-1 orbit as k varies, and it can be considered as an control strategy of chaos by adjusting the parameter k. Combining the existing results in [Generic excitable dynamics on a two-dimensional map. Chaos, Solitons and Fractals 1995;5(3-4):461-79] with the new results reported in this paper, a more complete description of the system is now obtained
Harnessing quantum transport by transient chaos.
Yang, Rui; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso; Pecora, Louis M
2013-03-01
Chaos has long been recognized to be generally advantageous from the perspective of control. In particular, the infinite number of unstable periodic orbits embedded in a chaotic set and the intrinsically sensitive dependence on initial conditions imply that a chaotic system can be controlled to a desirable state by using small perturbations. Investigation of chaos control, however, was largely limited to nonlinear dynamical systems in the classical realm. In this paper, we show that chaos may be used to modulate or harness quantum mechanical systems. To be concrete, we focus on quantum transport through nanostructures, a problem of considerable interest in nanoscience, where a key feature is conductance fluctuations. We articulate and demonstrate that chaos, more specifically transient chaos, can be effective in modulating the conductance-fluctuation patterns. Experimentally, this can be achieved by applying an external gate voltage in a device of suitable geometry to generate classically inaccessible potential barriers. Adjusting the gate voltage allows the characteristics of the dynamical invariant set responsible for transient chaos to be varied in a desirable manner which, in turn, can induce continuous changes in the statistical characteristics of the quantum conductance-fluctuation pattern. To understand the physical mechanism of our scheme, we develop a theory based on analyzing the spectrum of the generalized non-Hermitian Hamiltonian that includes the effect of leads, or electronic waveguides, as self-energy terms. As the escape rate of the underlying non-attracting chaotic set is increased, the imaginary part of the complex eigenenergy becomes increasingly large so that pointer states are more difficult to form, making smoother the conductance-fluctuation pattern.
Truccolo, Wilson
2016-11-01
This review presents a perspective on capturing collective dynamics in recorded neuronal ensembles based on multivariate point process models, inference of low-dimensional dynamics and coarse graining of spatiotemporal measurements. A general probabilistic framework for continuous time point processes reviewed, with an emphasis on multivariate nonlinear Hawkes processes with exogenous inputs. A point process generalized linear model (PP-GLM) framework for the estimation of discrete time multivariate nonlinear Hawkes processes is described. The approach is illustrated with the modeling of collective dynamics in neocortical neuronal ensembles recorded in human and non-human primates, and prediction of single-neuron spiking. A complementary approach to capture collective dynamics based on low-dimensional dynamics ("order parameters") inferred via latent state-space models with point process observations is presented. The approach is illustrated by inferring and decoding low-dimensional dynamics in primate motor cortex during naturalistic reach and grasp movements. Finally, we briefly review hypothesis tests based on conditional inference and spatiotemporal coarse graining for assessing collective dynamics in recorded neuronal ensembles. Published by Elsevier Ltd.
Chaos synchronization of coupled hyperchaotic system
International Nuclear Information System (INIS)
Yang Lixin; Chu Yandong; Zhang Jiangang; Li Xianfeng
2009-01-01
Chaos synchronization, as an important topic, has become an active research subject in nonlinear science. Over the past two decades, chaos synchronization between nonlinear systems has been extensively studied, and many types of synchronization have been announced. This paper introduces synchronization of coupled hyperchaotic system, based on the Lapunov stability theory, asymptotic stability of the system is guaranteed by means of Lapunov function. The numerical simulation was provided in order to show the effectiveness of this method for the synchronization of the chaotic hyperchaotic Chen system and Rossler system.
Chaos and random matrices in supersymmetric SYK
Hunter-Jones, Nicholas; Liu, Junyu
2018-05-01
We use random matrix theory to explore late-time chaos in supersymmetric quantum mechanical systems. Motivated by the recent study of supersymmetric SYK models and their random matrix classification, we consider the Wishart-Laguerre unitary ensemble and compute the spectral form factors and frame potentials to quantify chaos and randomness. Compared to the Gaussian ensembles, we observe the absence of a dip regime in the form factor and a slower approach to Haar-random dynamics. We find agreement between our random matrix analysis and predictions from the supersymmetric SYK model, and discuss the implications for supersymmetric chaotic systems.
Shape of power spectrum of intermittent chaos
International Nuclear Information System (INIS)
So, B.C.; Mori, H.
1984-01-01
Power spectra of intermittent chaos are calculated analytically. It is found that the power spectrum near onset point consists of a large number of Lorentzian lines with two peaks around frequencies ω = 0 and ω = ω 0 , where ω 0 is a fundamental frequency of a periodic orbit before the onset point, and furthermore the envelope of lines around ω = 0 obeys the power law 1/ + ω +2 , whereas the envelope around ω 0 obeys 1/ + ω-ω 0 +4 . The universality of these power law dependence in a certain class of intermittent chaos are clarified from a phenomenological view point. (author)
Signatures of chaos in the Brillouin zone.
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.
Chaotic dynamics and chaos control in nonlinear laser systems
International Nuclear Information System (INIS)
Fang Jinqing; Yao Weiguang
2001-01-01
Chaotic dynamics and chaos control have become a great challenge in nonlinear laser systems and its advances are reviewed mainly based on the ring cavity laser systems. The principle and stability conditions for time-delay feedback control are analyzed and applied to chaos control in the laser systems. Other advanced methods of chaos control, such as weak spatial perturbation and occasional proportional feedback technique, are discussed. Prospects of chaos control for application (such as improvement of laser power and performance, synchronized chaos secure communication and information processing) are pointed out finally
Chaos and reliability in balanced spiking networks with temporal drive.
Lajoie, Guillaume; Lin, Kevin K; Shea-Brown, Eric
2013-05-01
Biological information processing is often carried out by complex networks of interconnected dynamical units. A basic question about such networks is that of reliability: If the same signal is presented many times with the network in different initial states, will the system entrain to the signal in a repeatable way? Reliability is of particular interest in neuroscience, where large, complex networks of excitatory and inhibitory cells are ubiquitous. These networks are known to autonomously produce strongly chaotic dynamics-an obvious threat to reliability. Here, we show that such chaos persists in the presence of weak and strong stimuli, but that even in the presence of chaos, intermittent periods of highly reliable spiking often coexist with unreliable activity. We elucidate the local dynamical mechanisms involved in this intermittent reliability, and investigate the relationship between this phenomenon and certain time-dependent attractors arising from the dynamics. A conclusion is that chaotic dynamics do not have to be an obstacle to precise spike responses, a fact with implications for signal coding in large networks.
Chaos and routes to chaos in coupled Duffing oscillators with multiple degrees of freedom
International Nuclear Information System (INIS)
Musielak, D.E.; Musielak, Z.E.; Benner, J.W.
2005-01-01
New results are reported on the routes to chaos in increasingly complex Duffing oscillator systems, which are formed by coupling several oscillators, thereby increasing the number of degrees of freedom. Other forms of increasing system complexity through distributed excitation, different forcing function phasing, different excitation frequency ratios, and higher order coupling are also studied. Changes in the quantitative aspects of the chaotic regions and in the routes to chaos of complex Duffing systems are investigated by performing numerical simulations. It is shown that the number of chaotic regions in these systems is significantly reduced when compared to the original Duffing system, and that crisis replaces period doubling as the dominant route to chaos when the number of degrees of freedom is increased. A new discovered phenomenon is that chaos emerges in the symmetrically and asymmetrically coupled Duffing oscillators only after the quasi-periodic torus breaks down through a 3-periodic and 2-periodic window, respectively
Low-dimensional chiral physics. Gross-Neveu universality and magnetic catalysis
Energy Technology Data Exchange (ETDEWEB)
Scherer, Daniel David
2012-09-27
In this thesis, we investigate the 3-dimensional, chirally symmetric Gross-Neveu model with functional renormalization group methods. This low-dimensional quantum field theory describes the continuum limit of the low-energy sector in certain lattice systems. The functional renormalization group allows to study in a nonperturbative way the physical properties of many-body systems and quantum field theories. The starting point is a formally exact flow equation with 1-loop structure for the generating functional of 1-particle irreducible vertices. Within a gradient expansion - tailor-made for extracting the infrared asymptotics of the momentum and frequency dependent vertices of the theory - we study the strong-coupling fixed point of the Gross-Neveu model even beyond the formal limit of infinite flavor number. This fixed point controls a 2nd order quantum phase transition from a massless phase to a phase with massive Dirac fermions. After a first analysis of the purely fermionic theory, a Hubbard-Stratonovich transformation is used to partially bosonize the theory. Within this bosonized description, we find universal critical exponents that are in excellent quantitative agreement with available results from 1/N{sub f}-expansions and Monte Carlo simulations and are expected to improve upon earlier results. The renormalization group flow allows us to gain insights into the global and local structure of the critical manifold within given truncations and better understanding of the relevant directions in the space of couplings, which in general do not coincide with the Gaussian classification. Within the framework of the so-called ''asymptotic safety''-scenario relevant for the construction of proper field theories, the fixed-point theory could be determined exactly in the limit of infinite flavor number. Here, the Gross-Neveu model yields a simple and intuitive example for how to define a nonperturbatively renormalizable quantum field theory. Going
Low-dimensional chiral physics. Gross-Neveu universality and magnetic catalysis
International Nuclear Information System (INIS)
Scherer, Daniel David
2012-01-01
In this thesis, we investigate the 3-dimensional, chirally symmetric Gross-Neveu model with functional renormalization group methods. This low-dimensional quantum field theory describes the continuum limit of the low-energy sector in certain lattice systems. The functional renormalization group allows to study in a nonperturbative way the physical properties of many-body systems and quantum field theories. The starting point is a formally exact flow equation with 1-loop structure for the generating functional of 1-particle irreducible vertices. Within a gradient expansion - tailor-made for extracting the infrared asymptotics of the momentum and frequency dependent vertices of the theory - we study the strong-coupling fixed point of the Gross-Neveu model even beyond the formal limit of infinite flavor number. This fixed point controls a 2nd order quantum phase transition from a massless phase to a phase with massive Dirac fermions. After a first analysis of the purely fermionic theory, a Hubbard-Stratonovich transformation is used to partially bosonize the theory. Within this bosonized description, we find universal critical exponents that are in excellent quantitative agreement with available results from 1/N f -expansions and Monte Carlo simulations and are expected to improve upon earlier results. The renormalization group flow allows us to gain insights into the global and local structure of the critical manifold within given truncations and better understanding of the relevant directions in the space of couplings, which in general do not coincide with the Gaussian classification. Within the framework of the so-called ''asymptotic safety''-scenario relevant for the construction of proper field theories, the fixed-point theory could be determined exactly in the limit of infinite flavor number. Here, the Gross-Neveu model yields a simple and intuitive example for how to define a nonperturbatively renormalizable quantum field theory. Going beyond the determination
Resurvey of order and chaos in spinning compact binaries
International Nuclear Information System (INIS)
Wu Xin; Xie Yi
2008-01-01
This paper is mainly devoted to applying the invariant, fast, Lyapunov indicator to clarify some doubt regarding the apparently conflicting results of chaos in spinning compact binaries at the second-order post-Newtonian approximation of general relativity from previous literatures. It is shown with a number of examples that no single physical parameter or initial condition can be described as responsible for causing chaos, but a complicated combination of all parameters and initial conditions is responsible. In other words, a universal rule for the dependence of chaos on each parameter or initial condition cannot be found in general. Chaos does not depend only on the mass ratio, and the maximal spins do not necessarily bring the strongest effect of chaos. Additionally, chaos does not always become drastic when the initial spin vectors are nearly perpendicular to the orbital plane, and the alignment of spins cannot trigger chaos by itself
Linear Matrix Inequality Based Fuzzy Synchronization for Fractional Order Chaos
Directory of Open Access Journals (Sweden)
Bin Wang
2015-01-01
Full Text Available This paper investigates fuzzy synchronization for fractional order chaos via linear matrix inequality. Based on generalized Takagi-Sugeno fuzzy model, one efficient stability condition for fractional order chaos synchronization or antisynchronization is given. The fractional order stability condition is transformed into a set of linear matrix inequalities and the rigorous proof details are presented. Furthermore, through fractional order linear time-invariant (LTI interval theory, the approach is developed for fractional order chaos synchronization regardless of the system with uncertain parameters. Three typical examples, including synchronization between an integer order three-dimensional (3D chaos and a fractional order 3D chaos, anti-synchronization of two fractional order hyperchaos, and the synchronization between an integer order 3D chaos and a fractional order 4D chaos, are employed to verify the theoretical results.
Torus Destruction and Chaos-Chaos Intermittency in a Commodity Distribution Chain
DEFF Research Database (Denmark)
Sosnovtseva, O.; Mosekilde, Erik
1997-01-01
The destruction of two-dimensional tori T2 and the transitions to chaos are studied in a high-dimensional model describing the decision-making behavior of human subjects in a simulated managerial environment (the beer production-distribution model). Two different routes from quasiperiodicity...... to chaos can be distinguished. Intermittency transitions between chaotic and hyperchaotic attractors are characterized, and transients in which the system "pursues the ghost" of a vanished hyperchaotic attractor are studied....
Chaos, strange attractors, and fractal basin boundaries
International Nuclear Information System (INIS)
Grebogi, C.
1989-01-01
Even simple mathematical models of physical systems are often observed to exhibit rather complex time evolution. Upon observation, one often has the feeling that such complex time evolutions could, for most practical purposes, be best characterized by statistical properties rather than by detailed knowledge of the exact process. In such situations, the time evolution is often labeled chaotic or turbulent. The study of chaotic dynamics has recently undergone explosive growth. Motivation for this comes partly from the fact that chaotic dynamics is being found to be of fundamental importance in many branches of science and engineering. Examples illustrating the wide-ranging applications of chaotic dynamics to scientific and engineering problems are the following: fluid dynamics, biology, ecology, meteorology, optics, electronics, mechanical engineerings, physiology, economics, chemistry, accelerator technology, thermonuclear fusion, celestial mechanics, and oceanography. The common element in all of the above topics is that they involve nonlinearity in some way. Indeed chaos is expected to be common whenever nonlinearity plays a role. Since nonlinearity is inherent in so much of science and engineering, an understanding of chaos is essential. Given the varied nature of applications where chaos is important, it is natural that researchers in a broad range of fields have become interested in and have contributed to recent developments in chaos
Chaos control applied to heart rhythm dynamics
Energy Technology Data Exchange (ETDEWEB)
Borem Ferreira, Bianca, E-mail: biaborem@gmail.com [Universidade Federal do Rio de Janeiro, COPPE, Department of Mechanical Engineering, P.O. Box 68.503, 21.941.972 Rio de Janeiro, RJ (Brazil); Souza de Paula, Aline, E-mail: alinedepaula@unb.br [Universidade de Brasi' lia, Department of Mechanical Engineering, 70.910.900 Brasilia, DF (Brazil); Amorim Savi, Marcelo, E-mail: savi@mecanica.ufrj.br [Universidade Federal do Rio de Janeiro, COPPE, Department of Mechanical Engineering, P.O. Box 68.503, 21.941.972 Rio de Janeiro, RJ (Brazil)
2011-08-15
Highlights: > A natural cardiac pacemaker is modeled by a modified Van der Pol oscillator. > Responses related to normal and chaotic, pathological functioning of the heart are investigated. > Chaos control methods are applied to avoid pathological behaviors of heart dynamics. > Different approaches are treated: stabilization of unstable periodic orbits and chaos suppression. - Abstract: The dynamics of cardiovascular rhythms have been widely studied due to the key aspects of the heart in the physiology of living beings. Cardiac rhythms can be either periodic or chaotic, being respectively related to normal and pathological physiological functioning. In this regard, chaos control methods may be useful to promote the stabilization of unstable periodic orbits using small perturbations. In this article, the extended time-delayed feedback control method is applied to a natural cardiac pacemaker described by a mathematical model. The model consists of a modified Van der Pol equation that reproduces the behavior of this pacemaker. Results show the ability of the chaos control strategy to control the system response performing either the stabilization of unstable periodic orbits or the suppression of chaotic response, avoiding behaviors associated with critical cardiac pathologies.
Synchronization of chaos by nonlinear feedback
International Nuclear Information System (INIS)
Cheng Yanxiang
1995-01-01
The authors point out that synchronization of chaos may also be achieved by a nonlinear feedback without decomposing the original system. They apply the idea to the Lorentz system, and discuss several forms of nonlinear feedbacks by Lyapunov function and numerical method
Chaos synchronization based on contraction principle
International Nuclear Information System (INIS)
Wang Junwei; Zhou Tianshou
2007-01-01
This paper introduces contraction principle. Based on such a principle, a novel scheme is proposed to synchronize coupled systems with global diffusive coupling. A rigorous sufficient condition on chaos synchronization is derived. As an example, coupled Lorenz systems with nearest-neighbor diffusive coupling are investigated, and numerical simulations are given to validate the proposed synchronization approach
Importance of packing in spiral defect chaos
Indian Academy of Sciences (India)
We develop two measures to characterize the geometry of patterns exhibited by the state of spiral defect chaos, a weakly turbulent regime of Rayleigh-Bénard convection. These describe the packing of contiguous stripes within the pattern by quantifying their length and nearest-neighbor distributions. The distributions ...
Characterizing and quantifying quantum chaos with quantum ...
Indian Academy of Sciences (India)
We explore quantum signatures of classical chaos by studying the rate of information gain in quantum tomography. The tomographic record consists of a time series of expectation values of a Hermitian operator evolving under the application of the Floquet operator of a quantum map that possesses (or lacks) time-reversal ...
Quantum Chaos via the Quantum Action
Kröger, H.
2002-01-01
We discuss the concept of the quantum action with the purpose to characterize and quantitatively compute quantum chaos. As an example we consider in quantum mechanics a 2-D Hamiltonian system - harmonic oscillators with anharmonic coupling - which is classically a chaotic system. We compare Poincar\\'e sections obtained from the quantum action with those from the classical action.
Chaos in schizophrenia associations, reality or metaphor?
Czech Academy of Sciences Publication Activity Database
Bob, P.; Šusta, M.; Chládek, Jan; Glaslová, K.; Paluš, Milan
2009-01-01
Roč. 73, č. 3 (2009), s. 179-185 ISSN 0167-8760 Institutional research plan: CEZ:AV0Z20650511; CEZ:AV0Z10300504 Keywords : Chaos * Schizophrenia * Associations * Electrodermal activity * Lyapunov exponent Subject RIV: FH - Neurology Impact factor: 3.045, year: 2009
Chaos synchronization of nonlinear Bloch equations
International Nuclear Information System (INIS)
Park, Ju H.
2006-01-01
In this paper, the problem of chaos synchronization of Bloch equations is considered. A novel nonlinear controller is designed based on the Lyapunov stability theory. The proposed controller ensures that the states of the controlled chaotic slave system asymptotically synchronizes the states of the master system. A numerical example is given to illuminate the design procedure and advantage of the result derived
Melnikov's vector - a 'measure of chaos'
International Nuclear Information System (INIS)
Haidegger, W.
1990-01-01
In this paper a method of global perturbation theory, the method of Melnikov, is introduced as a way of detecting Smale horseshoe chaos near homoclinic and heteroclinic orbits. Special emphasis is put on the point that Melnikov's method is of great practical value, as it yields computable, often even analytically solvable expressions. (Author) 18 refs
Order, chaos and nuclear dynamics: An introduction
International Nuclear Information System (INIS)
Swiatecki, W.J.
1990-08-01
This is an introductory lecture illustrating by simple examples the anticipated effect on collective nuclear dynamics of a transition from order to chaos in the motions of nucleons inside an idealized nucleus. The destruction of order is paralleled by a transition from a rubber-like to a honey-like behaviour of the independent-particle nuclear model. 10 refs., 6 figs
Chaos and fractals an elementary introduction
Feldman, David P
2012-01-01
For students with a background in elementary algebra, this text provides a vivid introduction to the key phenomena and ideas of chaos and fractals, including the butterfly effect, strange attractors, fractal dimensions, Julia sets and the Mandelbrot set, power laws, and cellular automata.
Chaos in Practice: Techniques for Career Counsellors
Pryor, Robert G. L.; Bright, Jim
2005-01-01
The chaos theory of careers emphasises continual change, the centrality and importance of chance events, the potential of minor events to have disproportionately large impacts on subsequent events, and the capacity for dramatic phase shifts in career behaviour. This approach challenges traditional approaches to career counselling, assumptions…
Controlling chaos in discontinuous dynamical systems
International Nuclear Information System (INIS)
Danca, Marius-F.
2004-01-01
In this paper we consider the possibility to implement the technique of changes in the system variables to control the chaos introduced by Gueemez and Matias for continuous dynamical systems to a class of discontinuous dynamical systems. The approach is realized via differential inclusions following the Filippov theory. Three practical examples are considered
[Chaos theory: a fascinating concept for oncologists].
Denis, F; Letellier, C
2012-05-01
The oncologist is confronted daily by questions related to the fact that any patient presents a specific evolution for his cancer: he is challenged by very different, unexpected and often unpredictable outcomes, in some of his patients. The mathematical approach used today to describe this evolution has recourse to statistics and probability laws: such an approach does not ultimately apply to one particular patient, but to a given more or less heterogeneous population. This approach therefore poorly characterizes the dynamics of this disease and does not allow to state whether a patient is cured, to predict if he will relapse and when this could occur, and in what form, nor to predict the response to treatment and, in particular, to radiation therapy. Chaos theory, not well known by oncologists, could allow a better understanding of these issues. Developed to investigate complex systems producing behaviours that cannot be predicted due to a great sensitivity to initial conditions, chaos theory is rich of suitable concepts for a new approach of cancer dynamics. This article is three-fold: to provide a brief introduction to chaos theory, to clarify the main connecting points between chaos and carcinogenesis and to point out few promising research perspectives, especially in radiotherapy. Copyright © 2012 Société française de radiothérapie oncologique (SFRO). Published by Elsevier SAS. All rights reserved.
Chaos in nuclei: Theory and experiment
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.
Transient chaos in weakly coupled Josephson junctions
Energy Technology Data Exchange (ETDEWEB)
Koch, B P; Bruhn, B
1988-01-01
This paper considers periodic excitations and coupling of nonlinear Josephson oscillators. The Melnikov method is used to prove the existence of horseshoes in the dynamics. The coupling of two systems yields a reduction of the chaos threshold in comparison with the corresponding threshold of a single system. For some selected parameter values the theoretical predictions are checked by numerical methods.
Quantum chaos of the 2-level atom
Energy Technology Data Exchange (ETDEWEB)
Graham, R; Hoehnerbach, M [Essen Univ. (Germany, F.R.). Fachbereich Physik
1984-01-01
Recent work on the two-level atom coupled to a single mode of the electromagnetic field is reviewed from the point of view of 'quantum chaos', defined as the quantum behavior of a dynamical system which is non-integrable in the classical limit. Spectral properties and the dynamics of occupation probabilities including their revivals are obtained without making the rotating wave approximation.
A Framework for Chaos Theory Career Counselling
Pryor, Robert G. L.
2010-01-01
Theory in career development counselling provides a map that counsellors can use to understand and structure the career counselling process. It also provides a means to communicate this understanding and structuring to their clients as part of the counselling intervention. The chaos theory of careers draws attention to the complexity,…
Chaos theory: A fascinating concept for oncologists
International Nuclear Information System (INIS)
Denis, F.; Letellier, C.
2012-01-01
The oncologist is confronted daily by questions related to the fact that any patient presents a specific evolution for his cancer: he is challenged by very different, unexpected and often unpredictable outcomes, in some of his patients. The mathematical approach used today to describe this evolution has recourse to statistics and probability laws: such an approach does not ultimately apply to one particular patient, but to a given more or less heterogeneous population. This approach therefore poorly characterizes the dynamics of this disease and does not allow to state whether a patient is cured, to predict if he will relapse and when this could occur, and in what form, nor to predict the response to treatment and, in particular, to radiation therapy. Chaos theory, not well known by oncologists, could allow a better understanding of these issues. Developed to investigate complex systems producing behaviours that cannot be predicted due to a great sensitivity to initial conditions, chaos theory is rich of suitable concepts for a new approach of cancer dynamics. This article is three-fold: to provide a brief introduction to chaos theory, to clarify the main connecting points between chaos and carcinogenesis and to point out few promising research perspectives, especially in radiotherapy. (authors)
Biologically inspired rate control of chaos.
Olde Scheper, Tjeerd V
2017-10-01
The overall intention of chaotic control is to eliminate chaos and to force the system to become stable in the classical sense. In this paper, I demonstrate a more subtle method that does not eliminate all traces of chaotic behaviour; yet it consistently, and reliably, can provide control as intended. The Rate Control of Chaos (RCC) method is derived from metabolic control processes and has several remarkable properties. RCC can control complex systems continuously, and unsupervised, it can also maintain control across bifurcations, and in the presence of significant systemic noise. Specifically, I show that RCC can control a typical set of chaotic models, including the 3 and 4 dimensional chaotic Lorenz systems, in all modes. Furthermore, it is capable of controlling spatiotemporal chaos without supervision and maintains control of the system across bifurcations. This property of RCC allows a dynamic system to operate in parameter spaces that are difficult to control otherwise. This may be particularly interesting for the control of forced systems or dynamic systems that are chaotically perturbed. These control properties of RCC are applicable to a range of dynamic systems, thereby appearing to have far-reaching effects beyond just controlling chaos. RCC may also point to the existence of a biochemical control function of an enzyme, to stabilise the dynamics of the reaction cascade.
Meeting energy demands: chaos round the corner
Energy Technology Data Exchange (ETDEWEB)
Petrick, A J
1976-02-01
In this interview with Coal Gold and Base Minerals, Dr. Petrick talks about several aspects of his recent report and indicates that it will only be in the next 20 or 30 years that the real energy crisis will appear. He goes on to warn of possible chaos if energy is continually squandered throughout the world.
CHAOS-BASED ADVANCED ENCRYPTION STANDARD
Abdulwahed, Naif B.
2013-01-01
This thesis introduces a new chaos-based Advanced Encryption Standard (AES). The AES is a well-known encryption algorithm that was standardized by U.S National Institute of Standard and Technology (NIST) in 2001. The thesis investigates and explores
Analysis of chaos in plasma turbulence
DEFF Research Database (Denmark)
Pedersen, T.S.; Michelsen, Poul; Juul Rasmussen, J.
1996-01-01
-stationary turbulent state is reached in a finite time, independent of the initial conditions. Different regimes of the turbulent state can be obtained by varying the coupling parameter C, related to the parallel electron dynamics. The turbulence is described by using particle tracking and tools from chaos analysis...
CHAOS-BASED ADVANCED ENCRYPTION STANDARD
Abdulwahed, Naif B.
2013-05-01
This thesis introduces a new chaos-based Advanced Encryption Standard (AES). The AES is a well-known encryption algorithm that was standardized by U.S National Institute of Standard and Technology (NIST) in 2001. The thesis investigates and explores the behavior of the AES algorithm by replacing two of its original modules, namely the S-Box and the Key Schedule, with two other chaos- based modules. Three chaos systems are considered in designing the new modules which are Lorenz system with multiplication nonlinearity, Chen system with sign modules nonlinearity, and 1D multiscroll system with stair case nonlinearity. The three systems are evaluated on their sensitivity to initial conditions and as Pseudo Random Number Generators (PRNG) after applying a post-processing technique to their output then performing NIST SP. 800-22 statistical tests. The thesis presents a hardware implementation of dynamic S-Boxes for AES that are populated using the three chaos systems. Moreover, a full MATLAB package to analyze the chaos generated S-Boxes based on graphical analysis, Walsh-Hadamard spectrum analysis, and image encryption analysis is developed. Although these S-Boxes are dynamic, meaning they are regenerated whenever the encryption key is changed, the analysis results show that such S-Boxes exhibit good properties like the Strict Avalanche Criterion (SAC) and the nonlinearity and in the application of image encryption. Furthermore, the thesis presents a new Lorenz-chaos-based key expansion for the AES. Many researchers have pointed out that there are some defects in the original key expansion of AES and thus have motivated such chaos-based key expansion proposal. The new proposed key schedule is analyzed and assessed in terms of confusion and diffusion by performing the frequency and SAC test respectively. The obtained results show that the new proposed design is more secure than the original AES key schedule and other proposed designs in the literature. The proposed
Chaos: A Very Short Introduction
Energy Technology Data Exchange (ETDEWEB)
Klages, R [School of Mathematical Sciences, Mile End Road, London, E1 4NS (United Kingdom)
2007-07-20
This book is a new volume of a series designed to introduce the curious reader to anything from ancient Egypt and Indian philosophy to conceptual art and cosmology. Very handy in pocket size, Chaos promises an introduction to fundamental concepts of nonlinear science by using mathematics that is 'no more complicated than X=2. Anyone who ever tried to give a popular science account of research knows that this is a more challenging task than writing an ordinary research article. Lenny Smith brilliantly succeeds to explain in words, in pictures and by using intuitive models the essence of mathematical dynamical systems theory and time series analysis as it applies to the modern world. In a more technical part he introduces the basic terms of nonlinear theory by means of simple mappings. He masterly embeds this analysis into the social, historical and cultural context by using numerous examples, from poems and paintings over chess and rabbits to Olbers' paradox, card games and 'phynance'. Fundamental problems of the modelling of nonlinear systems like the weather, sun spots or golf balls falling through an array of nails are discussed from the point of view of mathematics, physics and statistics by touching upon philosophical issues. At variance with Laplace's demon, Smith's 21st century demon makes 'real world' observations only with limited precision. This poses a severe problem to predictions derived from complex chaotic models, where small variations of initial conditions typically yield totally different outcomes. As Smith argues, this difficulty has direct implications on decision-making in everyday modern life. However, it also asks for an inherently probabilistic theory, which somewhat reminds us of what we are used to in the microworld. There is little to criticise in this nice little book except that some figures are of poor quality thus not really reflecting the beauty of fractals and other wonderful objects in this
Chaos: A Very Short Introduction
International Nuclear Information System (INIS)
Klages, R
2007-01-01
This book is a new volume of a series designed to introduce the curious reader to anything from ancient Egypt and Indian philosophy to conceptual art and cosmology. Very handy in pocket size, Chaos promises an introduction to fundamental concepts of nonlinear science by using mathematics that is 'no more complicated than X=2. Anyone who ever tried to give a popular science account of research knows that this is a more challenging task than writing an ordinary research article. Lenny Smith brilliantly succeeds to explain in words, in pictures and by using intuitive models the essence of mathematical dynamical systems theory and time series analysis as it applies to the modern world. In a more technical part he introduces the basic terms of nonlinear theory by means of simple mappings. He masterly embeds this analysis into the social, historical and cultural context by using numerous examples, from poems and paintings over chess and rabbits to Olbers' paradox, card games and 'phynance'. Fundamental problems of the modelling of nonlinear systems like the weather, sun spots or golf balls falling through an array of nails are discussed from the point of view of mathematics, physics and statistics by touching upon philosophical issues. At variance with Laplace's demon, Smith's 21st century demon makes 'real world' observations only with limited precision. This poses a severe problem to predictions derived from complex chaotic models, where small variations of initial conditions typically yield totally different outcomes. As Smith argues, this difficulty has direct implications on decision-making in everyday modern life. However, it also asks for an inherently probabilistic theory, which somewhat reminds us of what we are used to in the microworld. There is little to criticise in this nice little book except that some figures are of poor quality thus not really reflecting the beauty of fractals and other wonderful objects in this field. I feel that occasionally the book
THEORY OF SECULAR CHAOS AND MERCURY'S ORBIT
International Nuclear Information System (INIS)
Lithwick, Yoram; Wu Yanqin
2011-01-01
We study the chaotic orbital evolution of planetary systems, focusing on secular (i.e., orbit-averaged) interactions, which dominate on long timescales. We first focus on the evolution of a test particle that is forced by multiple planets. To linear order in eccentricity and inclination, its orbit precesses with constant frequencies. But nonlinearities modify the frequencies, and can shift them into and out of resonance with either the planets' eigenfrequencies (forming eccentricity or inclination secular resonances), or with linear combinations of those frequencies (forming mixed high-order secular resonances). The overlap of these nonlinear secular resonances drives secular chaos. We calculate the locations and widths of nonlinear secular resonances, display them together on a newly developed map (the 'map of the mean momenta'), and find good agreement between analytical and numerical results. This map also graphically demonstrates how chaos emerges from overlapping secular resonances. We then apply this newfound understanding to Mercury to elucidate the origin of its orbital chaos. We find that since Mercury's two free precession frequencies (in eccentricity and inclination) lie within ∼25% of two other eigenfrequencies in the solar system (those of the Jupiter-dominated eccentricity mode and the Venus-dominated inclination mode), secular resonances involving these four modes overlap and cause Mercury's chaos. We confirm this with N-body integrations by showing that a slew of these resonant angles alternately librate and circulate. Our new analytical understanding allows us to calculate the criterion for Mercury to become chaotic: Jupiter and Venus must have eccentricity and inclination of a few percent. The timescale for Mercury's chaotic diffusion depends sensitively on the forcing. As it is, Mercury appears to be perched on the threshold for chaos, with an instability timescale comparable to the lifetime of the solar system.
EMRS Spring Meeting 2014 Symposium D: Phonons and fluctuations in low dimensional structures
International Nuclear Information System (INIS)
2014-01-01
The E-MRS 2014 Spring meeting, held from 26-30th May 2014 in Lille included the Symposium D entitled ''Phonons and Fluctuations in Low Dimensional Structures'', the first edition of its kind. The symposium was organised in response to the increasing interest in the study of phonons in the context of advances in condensed matter physics, electronics, experimental methods and theory and, in particular, the transfer of energy across atomic interfaces and the propagation of energy in the nm-scale. Steering heat by light or vice versa and examining nano-scale energy conversion (as in thermoelectricity and harvesting e.g. in biological systems) are two aspects that share the underlying science of energy processes across atomic interfaces and energy propagation in the nanoscale and or in confined systems. The nanometer scale defies several of the bulk relationships as confinement of electrons and phonons, locality and non-equilibrium become increasingly important. The propagation of phonons as energy carriers impacts not only heat transfer, but also the very concept and handling of temperature in non-equilibrium and highly localised conditions. Much of the needed progress depends on the materials studied and this symposium targeted the interface material aspects as well as the emerging concepts to advance in this field. The symposium had its origins in a series of meetings and seminars including: (1) the first Phonon Engineering Workshop, funded by Catalan Institute for Research and Advanced Studies (ICREA), the then MICINN, the CNRS, VTT, and several EU projects, held in Saint Feliu de Guixols (Girona, Spain) from 24th to 27th of May 2010 with 65 participants from Europe, the USA and Japan; (2) the first Phonons and Fluctuations workshop, held in Paris on 8th and 9th November 2010, supported by French, Spanish and Finnish national projects and EU projects, attended by about 50 researchers; (3) the second Phonon and Fluctuations workshop, held in Paris
EMRS Spring Meeting 2014 Symposium D: Phonons and fluctuations in low dimensional structures
2014-11-01
The E-MRS 2014 Spring meeting, held from 26-30th May 2014 in Lille included the Symposium D entitled ''Phonons and Fluctuations in Low Dimensional Structures'', the first edition of its kind. The symposium was organised in response to the increasing interest in the study of phonons in the context of advances in condensed matter physics, electronics, experimental methods and theory and, in particular, the transfer of energy across atomic interfaces and the propagation of energy in the nm-scale. Steering heat by light or vice versa and examining nano-scale energy conversion (as in thermoelectricity and harvesting e.g. in biological systems) are two aspects that share the underlying science of energy processes across atomic interfaces and energy propagation in the nanoscale and or in confined systems. The nanometer scale defies several of the bulk relationships as confinement of electrons and phonons, locality and non-equilibrium become increasingly important. The propagation of phonons as energy carriers impacts not only heat transfer, but also the very concept and handling of temperature in non-equilibrium and highly localised conditions. Much of the needed progress depends on the materials studied and this symposium targeted the interface material aspects as well as the emerging concepts to advance in this field. The symposium had its origins in a series of meetings and seminars including: (1) the first Phonon Engineering Workshop, funded by Catalan Institute for Research and Advanced Studies (ICREA), the then MICINN, the CNRS, VTT, and several EU projects, held in Saint Feliu de Guixols (Girona, Spain) from 24th to 27th of May 2010 with 65 participants from Europe, the USA and Japan; (2) the first Phonons and Fluctuations workshop, held in Paris on 8th and 9th November 2010, supported by French, Spanish and Finnish national projects and EU projects, attended by about 50 researchers; (3) the second Phonon and Fluctuations workshop, held in Paris on 8th and 9th
DEFF Research Database (Denmark)
Bechgaard, Klaus; Nielsen, Martin Meedom; Krebs, Frederik C
2000-01-01
The structural characteristics and the relation to the electronic properties of three types of molecular materials are discussed. In TMTSF2X salts a triclinic unit cell it suggested to be important in avoiding a 2k(F) Peierls distortion. In polythiophenes appropriate ordering of microcrystallites...
Llinas’ Phase Reset Mechanism Delays the Onset of Chaos in Shark and Dolphin Wall Turbulence
2014-02-10
the results of the modeling of chaos control by sharks . Skins of great white ,33 Atlantic sharpnose,36 and tiger shark37 dermal denticles (dd), with...13. c: Dermal denticles (diamond-shaped scales) of great white shark ; depending on species, there may be three to six riblets per scale (five to...Denticles of Great White Shark ," Electron Microscope Unit, University of Cape Town, Smithsonian Museum of Natural History, http://ocean.si.edu/ocean
Straus, Christian; Samara, Ziyad; Fiamma, Marie-Noëlle; Bautin, Nathalie; Ranohavimparany, Anja; Le Coz, Patrick; Golmard, Jean-Louis; Darré, Pierre; Zelter, Marc; Poon, Chi-Sang; Similowski, Thomas
2011-05-01
Human ventilation at rest exhibits mathematical chaos-like complexity that can be described as long-term unpredictability mediated (in whole or in part) by some low-dimensional nonlinear deterministic process. Although various physiological and pathological situations can affect respiratory complexity, the underlying mechanisms remain incompletely elucidated. If such chaos-like complexity is an intrinsic property of central respiratory generators, it should appear or increase when these structures mature or are stimulated. To test this hypothesis, we employed the isolated tadpole brainstem model [Rana (Pelophylax) esculenta] and recorded the neural respiratory output (buccal and lung rhythms) of pre- (n = 8) and postmetamorphic tadpoles (n = 8), at physiologic (7.8) and acidic pH (7.4). We analyzed the root mean square of the cranial nerve V or VII neurograms. Development and acidosis had no effect on buccal period. Lung frequency increased with development (P acidosis, but in postmetamorphic tadpoles only (P respiratory central rhythm generator accounts for ventilatory chaos-like complexity, especially in the postmetamorphic stage and at low pH. According to the ventilatory generators homology theory, this may also be the case in mammals.
Phase Chaos and Multistability in the Discrete Kuramoto Model
DEFF Research Database (Denmark)
Maistrenko, V. L.; Vasylenko, A. A.; Maistrenko, Y. L.
2008-01-01
The paper describes the appearance of a novel high-dimensional chaotic regime, called phase chaos, in the discrete Kuramoto model of globally coupled phase oscillators. This type of chaos is observed at small and intermediate values of the coupling strength. It is caused by the nonlinear interact......The paper describes the appearance of a novel high-dimensional chaotic regime, called phase chaos, in the discrete Kuramoto model of globally coupled phase oscillators. This type of chaos is observed at small and intermediate values of the coupling strength. It is caused by the nonlinear...... interaction of the oscillators, while the individual oscillators behave periodically when left uncoupled. For the four-dimensional discrete Kuramoto model, we outline the region of phase chaos in the parameter plane, distinguish the region where the phase chaos coexists with other periodic attractors...
Chaos in electric drive systems analysis control and application
Chau, K T
2011-01-01
In Chaos in Electric Drive Systems: Analysis, Control and Application authors Chau and Wang systematically introduce an emerging technology of electrical engineering that bridges abstract chaos theory and practical electric drives. The authors consolidate all important information in this interdisciplinary technology, including the fundamental concepts, mathematical modeling, theoretical analysis, computer simulation, and hardware implementation. The book provides comprehensive coverage of chaos in electric drive systems with three main parts: analysis, control and application. Corresponding drive systems range from the simplest to the latest types: DC, induction, synchronous reluctance, switched reluctance, and permanent magnet brushless drives.The first book to comprehensively treat chaos in electric drive systemsReviews chaos in various electrical engineering technologies and drive systemsPresents innovative approaches to stabilize and stimulate chaos in typical drivesDiscusses practical application of cha...
REVISITING EVIDENCE OF CHAOS IN X-RAY LIGHT CURVES: THE CASE OF GRS 1915+105
Energy Technology Data Exchange (ETDEWEB)
Mannattil, Manu; Gupta, Himanshu; Chakraborty, Sagar, E-mail: mmanu@iitk.ac.in, E-mail: hiugupta@iitk.ac.in, E-mail: sagarc@iitk.ac.in [Department of Physics, Indian Institute of Technology Kanpur, Uttar Pradesh 208016 (India)
2016-12-20
Nonlinear time series analysis has been widely used to search for signatures of low-dimensional chaos in light curves emanating from astrophysical bodies. A particularly popular example is the microquasar GRS 1915+105, whose irregular but systematic X-ray variability has been well studied using data acquired by the Rossi X-ray Timing Explorer . With a view to building simpler models of X-ray variability, attempts have been made to classify the light curves of GRS 1915+105 as chaotic or stochastic. Contrary to some of the earlier suggestions, after careful analysis, we find no evidence for chaos or determinism in any of the GRS 1915+105 classes. The dearth of long and stationary data sets representing all the different variability classes of GRS 1915+105 makes it a poor candidate for analysis using nonlinear time series techniques. We conclude that either very exhaustive data analysis with sufficiently long and stationary light curves should be performed, keeping all the pitfalls of nonlinear time series analysis in mind, or alternative schemes of classifying the light curves should be adopted. The generic limitations of the techniques that we point out in the context of GRS 1915+105 affect all similar investigations of light curves from other astrophysical sources.
[Turbulence and spatio-temporal chaos
International Nuclear Information System (INIS)
1990-01-01
This report discusses Saffman-Taylor instability; cylinder wake; Levy walk and turbulent channel flow; bubble motion and bubble streams; spinal turbulent and wetting; collective behavior of a coupled map system with a conserved quantity; stability of temporally periodic states; generic nonergodic behavior in continuous systems; characterization of unstable periodic orbits; in low-dimensional chaotic attractors and repellers; and Ginzburg-Landau theory for oil-water-surfactant mixture
Approximate motion integrals and the quantum chaos problem
International Nuclear Information System (INIS)
Bunakov, V.E.; Ivanov, I.B.
2001-01-01
One discusses the problem of occurrence and seek for the motion integrals in the stationary quantum mechanics and its relation to the quantum chaos. One studies decomposition of quantum numbers and derives the criterion of chaos. To seek the motion integrals one applies the convergence method. One derived the approximate integrals in the Hennone-Hales problem. One discusses the problem of compatibility of chaos and integrability [ru
Directory of Open Access Journals (Sweden)
Yuandong Sun
2017-01-01
Full Text Available Silicon is regarded as the next generation anode material for LIBs with its ultra-high theoretical capacity and abundance. Nevertheless, the severe capacity degradation resulting from the huge volume change and accumulative solid-electrolyte interphase (SEI formation hinders the silicon based anode material for further practical applications. Hence, a variety of methods have been applied to enhance electrochemical performances in terms of the electrochemical stability and rate performance of the silicon anodes such as designing nanostructured Si, combining with carbonaceous material, exploring multifunctional polymer binders, and developing artificial SEI layers. Silicon anodes with low-dimensional structures (0D, 1D, and 2D, compared with bulky silicon anodes, are strongly believed to have several advanced characteristics including larger surface area, fast electron transfer, and shortened lithium diffusion pathway as well as better accommodation with volume changes, which leads to improved electrochemical behaviors. In this review, recent progress of silicon anode synthesis methodologies generating low-dimensional structures for lithium ion batteries (LIBs applications is listed and discussed.
Directory of Open Access Journals (Sweden)
Ezequiel M Arneodo
Full Text Available Because of the parallels found with human language production and acquisition, birdsong is an ideal animal model to study general mechanisms underlying complex, learned motor behavior. The rich and diverse vocalizations of songbirds emerge as a result of the interaction between a pattern generator in the brain and a highly nontrivial nonlinear periphery. Much of the complexity of this vocal behavior has been understood by studying the physics of the avian vocal organ, particularly the syrinx. A mathematical model describing the complex periphery as a nonlinear dynamical system leads to the conclusion that nontrivial behavior emerges even when the organ is commanded by simple motor instructions: smooth paths in a low dimensional parameter space. An analysis of the model provides insight into which parameters are responsible for generating a rich variety of diverse vocalizations, and what the physiological meaning of these parameters is. By recording the physiological motor instructions elicited by a spontaneously singing muted bird and computing the model on a Digital Signal Processor in real-time, we produce realistic synthetic vocalizations that replace the bird's own auditory feedback. In this way, we build a bio-prosthetic avian vocal organ driven by a freely behaving bird via its physiologically coded motor commands. Since it is based on a low-dimensional nonlinear mathematical model of the peripheral effector, the emulation of the motor behavior requires light computation, in such a way that our bio-prosthetic device can be implemented on a portable platform.
Nonlinear physics: Catastrophe, chaos and complexity
International Nuclear Information System (INIS)
Arecchi, F.T.
1992-01-01
Currently in the world of physics, there is open debate on the role of the three C's - catastrophe, chaos and complexity. Seen as new ideas or paradigms, incapable of being harmonized within the realm of traditional physics, these terms seem to be creating turmoil in the classical physics establishment whose foundations date back to the early seventeenth century. This paper first defines catastrophe, chaos and complexity and shows how these terms are all connected to nonlinear dynamics and how they have long since been present within scientific treatises. It also evidences the relationship of the three C's with the concept of organization, inappropriately called self-organization, and with recognition and decisional strategies of cognitive systems. Relevant to natural science, the development of these considerations is necessitating the re-examination of the role and capabilities of human knowledge and a return to inter-disciplinary scientific-philosophical debate
Communication with spatial periodic chaos synchronization
International Nuclear Information System (INIS)
Zhou, J.; Huang, H.B.; Qi, G.X.; Yang, P.; Xie, X.
2005-01-01
Based on the spatial periodic chaos synchronization in coupled ring and linear arrays, we proposed a random high-dimensional chaotic encryption scheme. The transmitter can choose hyperchaotic signals randomly from the ring at any different time and simultaneously transmit the information of chaotic oscillators in the ring to receiver through public channel, so that the message can be masked by different hyperchaotic signals in different time intervals during communication, and the receiver can decode the message based on chaos synchronization but the attacker does not know the random hyperchaotic dynamics and cannot decode the message. Furthermore, the high sensitivity to the symmetry of the coupling structure makes the attacker very difficult to obtain any useful message from the channel
An exploration of dynamical systems and chaos
Argyris, John H; Haase, Maria; Friedrich, Rudolf
2015-01-01
This book is conceived as a comprehensive and detailed text-book on non-linear dynamical systems with particular emphasis on the exploration of chaotic phenomena. The self-contained introductory presentation is addressed both to those who wish to study the physics of chaotic systems and non-linear dynamics intensively as well as those who are curious to learn more about the fascinating world of chaotic phenomena. Basic concepts like Poincaré section, iterated mappings, Hamiltonian chaos and KAM theory, strange attractors, fractal dimensions, Lyapunov exponents, bifurcation theory, self-similarity and renormalisation and transitions to chaos are thoroughly explained. To facilitate comprehension, mathematical concepts and tools are introduced in short sub-sections. The text is supported by numerous computer experiments and a multitude of graphical illustrations and colour plates emphasising the geometrical and topological characteristics of the underlying dynamics. This volume is a completely revised and enlar...
Inequivalent topologies of chaos in simple equations
International Nuclear Information System (INIS)
Letellier, Christophe; Roulin, Elise; Roessler, Otto E.
2006-01-01
In the 1970, one of us introduced a few simple sets of ordinary differential equations as examples showing different types of chaos. Most of them are now more or less forgotten with the exception of the so-called Roessler system published in [Roessler OE. An equation for continuous chaos. Phys Lett A 1976;57(5):397-8]. In the present paper, we review most of the original systems and classify them using the tools of modern topological analysis, that is, using the templates and the bounding tori recently introduced by Tsankov and Gilmore in [Tsankov TD, Gilmore R. Strange attractors are classified by bounding tori. Phys Rev Lett 2003;91(13):134104]. Thus, examples of inequivalent topologies of chaotic attractors are provided in modern spirit
Order in nuclei and transition to chaos
International Nuclear Information System (INIS)
Soloviev, V.G.
1995-01-01
Based on the statement that there is order in the large and chaos in the small components of nuclear wave functions, the order-to-chaos transition is treated as a transition from the large to small components of wave functions. Therefore, experimental investigation of fragmentation of the many-quasiparticle and quasiparticle-phonon states plays a decisive role. The mixing of closely-spaced states having the same K π in the doubly even well-deformed nuclei is investigated. The quasiparticle-phonon interaction is responsible for fragmentation of the quasiparticle and phonon states and therefore for their mixing. Experimental investigation of the strength distribution of the many-quasiparticle and quasiparticle-phonon states should discover a new region of regularity in nuclei at intermediate excitation energies. A chaotic behaviour of nuclear states can be shifted to higher excitation energies. (author). 21 refs., 1 fig., 1 tab
Order in nuclei and transition to chaos
International Nuclear Information System (INIS)
Soloviev, V.G.
1995-01-01
Based on the statement that there is order in the large and chaos in the small components of nuclear wave functions, the order-to-chaos transition is treated as a transition from the large to small components of wave functions. Therefore, experimental investigation of fragmentation of the many-quasiparticle and quasiparticle-phonon states a decisive role. The mixing of closely-spaced states having the same K π in the doubly even well-deformed nuclei is investigated. The quasiparticle-phonon interaction is responsible for fragmentation of the quasiparticle and phonon states and therefore for their mixing. Experimental investigation of the strength distribution of the many-quasiparticle and quasiparticle-phonon states should discover a new region of regularity in nuclei at intermediate excitation energies. A chaotic behaviour of nuclear states can be shifted to higher excitation energies. (author). 21 refs., 1 fig., 1 tab
Tuning quantum measurements to control chaos.
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.
Kac-Moody algebras and controlled chaos
International Nuclear Information System (INIS)
Wesley, Daniel H
2007-01-01
Compactification can control chaotic Mixmaster behaviour in gravitational systems with p-form matter: we consider this in light of the connection between supergravity models and Kac-Moody algebras. We show that different compactifications define 'mutations' of the algebras associated with the noncompact theories. We list the algebras obtained in this way, and find novel examples of wall systems determined by Lorentzian (but not hyperbolic) algebras. Cosmological models with a smooth pre-big bang phase require that chaos is absent: we show that compactification alone cannot eliminate chaos in the simplest compactifications of the heterotic string on a Calabi-Yau, or M theory on a manifold of G 2 holonomy. (fast track communication)
Chaos theory perspective for industry clusters development
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.
Polynomial chaos representation of databases on manifolds
Energy Technology Data Exchange (ETDEWEB)
Soize, C., E-mail: christian.soize@univ-paris-est.fr [Université Paris-Est, Laboratoire Modélisation et Simulation Multi-Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-La-Vallée, Cedex 2 (France); Ghanem, R., E-mail: ghanem@usc.edu [University of Southern California, 210 KAP Hall, Los Angeles, CA 90089 (United States)
2017-04-15
Characterizing the polynomial chaos expansion (PCE) of a vector-valued random variable with probability distribution concentrated on a manifold is a relevant problem in data-driven settings. The probability distribution of such random vectors is multimodal in general, leading to potentially very slow convergence of the PCE. In this paper, we build on a recent development for estimating and sampling from probabilities concentrated on a diffusion manifold. The proposed methodology constructs a PCE of the random vector together with an associated generator that samples from the target probability distribution which is estimated from data concentrated in the neighborhood of the manifold. The method is robust and remains efficient for high dimension and large datasets. The resulting polynomial chaos construction on manifolds permits the adaptation of many uncertainty quantification and statistical tools to emerging questions motivated by data-driven queries.
Poincaré chaos and unpredictable functions
Akhmet, Marat; Fen, Mehmet Onur
2017-07-01
The results of this study are continuation of the research of Poincaré chaos initiated in the papers (M. Akhmet and M.O. Fen, Commun Nonlinear Sci Numer Simulat 40 (2016) 1-5; M. Akhmet and M.O. Fen, Turk J Math, doi:10.3906/mat-1603-51, in press). We focus on the construction of an unpredictable function, continuous on the real axis. As auxiliary results, unpredictable orbits for the symbolic dynamics and the logistic map are obtained. By shaping the unpredictable function as well as Poisson function we have performed the first step in the development of the theory of unpredictable solutions for differential and discrete equations. The results are preliminary ones for deep analysis of chaos existence in differential and hybrid systems. Illustrative examples concerning unpredictable solutions of differential equations are provided.
Controllable chaos in hybrid electro-optomechanical systems
Wang, Mei; Lü, Xin-You; Ma, Jin-Yong; Xiong, Hao; Si, Liu-Gang; Wu, Ying
2016-01-01
We investigate the nonlinear dynamics of a hybrid electro-optomechanical system (EOMS) that allows us to realize the controllable opto-mechanical nonlinearity by driving the microwave LC resonator with a tunable electric field. A controllable optical chaos is realized even without changing the optical pumping. The threshold and lifetime of the chaos could be optimized by adjusting the strength, frequency, or phase of the electric field. This study provides a method of manipulating optical chaos with an electric field. It may offer the prospect of exploring the controllable chaos in on-chip optoelectronic devices and its applications in secret communication. PMID:26948505
Controllable chaos in hybrid electro-optomechanical systems.
Wang, Mei; Lü, Xin-You; Ma, Jin-Yong; Xiong, Hao; Si, Liu-Gang; Wu, Ying
2016-03-07
We investigate the nonlinear dynamics of a hybrid electro-optomechanical system (EOMS) that allows us to realize the controllable opto-mechanical nonlinearity by driving the microwave LC resonator with a tunable electric field. A controllable optical chaos is realized even without changing the optical pumping. The threshold and lifetime of the chaos could be optimized by adjusting the strength, frequency, or phase of the electric field. This study provides a method of manipulating optical chaos with an electric field. It may offer the prospect of exploring the controllable chaos in on-chip optoelectronic devices and its applications in secret communication.
Congenital high airway obstruction syndrome (CHAOS) associated with cervical myelomeningocele.
Adin, Mehmet Emin
2017-10-01
Congenital high airway obstruction syndrome (CHAOS) is a rare and potentially fatal entity resulting from complete or near complete developmental airway obstruction. Although most reported cases of CHAOS are sporadic, the condition may also be associated with certain syndromes and a variety of cervical masses. Meningocele and myelomeningocele have not yet been reported in association with CHAOS. We describe the typical constellation of sonographic findings in a case of early diagnosis of CHAOS associated with cervical myelomeningocele. © 2016 Wiley Periodicals, Inc. J Clin Ultrasound 45:507-510, 2017. © 2016 Wiley Periodicals, Inc.
Nonlinear Dynamics In Quantum Physics -- Quantum Chaos and Quantum Instantons
Kröger, H.
2003-01-01
We discuss the recently proposed quantum action - its interpretation, its motivation, its mathematical properties and its use in physics: quantum mechanical tunneling, quantum instantons and quantum chaos.
Robinson's chaos in set-valued discrete systems
International Nuclear Information System (INIS)
Roman-Flores, Heriberto; Chalco-Cano, Y.
2005-01-01
Let (X,d) be a compact metric space and f:X->X a continuous function. If we consider the space (K(X),H) of all non-empty compact subsets of X endowed with the Hausdorff metric induced by d and f-bar :K(X)->K(X), f-bar (A)={f(a)/a-bar A}, then the aim of this work is to show that Robinson's chaos in f-bar implies Robinson's chaos in f. Also, we give an example showing that R-chaos in f does not implies R-chaos in f-bar
Chaos theory in geophysics: past, present and future
International Nuclear Information System (INIS)
Sivakumar, B.
2004-01-01
The past two decades of research on chaos theory in geophysics has brought about a significant shift in the way we view geophysical phenomena. Research on chaos theory in geophysics continues to grow at a much faster pace, with applications to a wide variety of geophysical phenomena and geophysical problems. In spite of our success in understanding geophysical phenomena also from a different (i.e. chaotic) perspective, there still seems to be lingering suspicions on the scope of chaos theory in geophysics. The goal of this paper is to present a comprehensive account of the achievements and status of chaos theory in geophysics, and to disseminate the hope and scope for the future. A systematic review of chaos theory in geophysics, covering a wide spectrum of geophysical phenomena studied (e.g. rainfall, river flow, sediment transport, temperature, pressure, tree ring series, etc.), is presented to narrate our past achievements not only in understanding and predicting geophysical phenomena but also in improving the chaos identification and prediction techniques. The present state of chaos research in geophysics (in terms of geophysical phenomena, problems, and chaos methods) and potential for future improvements (in terms of where, why and possibly how) are also highlighted. Our popular views of nature (i.e. stochastic and deterministic), and of geophysical phenomena in particular, are discussed, and the usefulness of chaos theory as a bridge between such views is also put forth
Chaos synchronization of a new chaotic system via nonlinear control
International Nuclear Information System (INIS)
Zhang Qunjiao; Lu Junan
2008-01-01
This paper investigates chaos synchronization of a new chaotic system [Lue J, Chen G, Cheng D. A new chaotic system and beyond: the generalized Lorenz-like system. Int J Bifurcat Chaos 2004;14:1507-37]. Two kinds of novel nonlinear controllers are designed based on the Lyapunov stability theory. It can be viewed as an improvement to the existing results of reference [Park JH. Chaos synchronization of a chaotic system via nonlinear control. Chaos, Solitons and Fractals 2005;25:579-84] because we use less controllers but realize a global and exponential asymptotical synchronization. Numerical simulations are provided to show the effectiveness and advantage of this method
Chaos and creation in Fernando Pessoa
Directory of Open Access Journals (Sweden)
José Nuno Gil
2016-07-01
Full Text Available Fernando Pessoa's poem "A Múmia" describes a sort of psychotic experience, which shows the condition of the literary creation by itself. The poem springs from – and describes – the experience of psychic and existential chaos: criticism and clinic overlap in the making and analysis of "A Múmia" This critical reading aims at bringing some intelligibility to the creative processes and, in particular, to Pessoa's heteronyms.
Bifurcations and chaos of DNA solitonic dynamics
International Nuclear Information System (INIS)
Gonzalez, J.A.; Martin-Landrove, M.; Carbo, J.R.; Chacon, M.
1994-09-01
We investigated the nonlinear DNA torsional equations proposed by Yakushevich in the presence of damping and external torques. Analytical expressions for some solutions are obtained in the case of the isolated chain. Special attention is paid to the stability of the solutions and the range of soliton interaction in the general case. The bifurcation analysis is performed and prediction of chaos is obtained for some set of parameters. Some biological implications are suggested. (author). 11 refs, 13 figs
Li-Yorke chaos in linear dynamics
Czech Academy of Sciences Publication Activity Database
Bernardes Jr., N.C.; Bonilla, A.; Müller, Vladimír; Peris, A.
2015-01-01
Roč. 35, č. 6 (2015), s. 1723-1745 ISSN 0143-3857 R&D Projects: GA ČR GA201/09/0473; GA AV ČR IAA100190903 Institutional support: RVO:67985840 Keywords : Li-York chaos * Banach space * Fréchet space Subject RIV: BA - General Mathematics Impact factor: 0.983, year: 2015 http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9884748&fileId=S0143385714000200
The chaos theory and the quality assurance
International Nuclear Information System (INIS)
Aguilar, Omar; Domech More, Jesus
1999-01-01
In the present paper we suggest the importance that the new science of chaos offers in the analysis,design and improvement processes in the production of gamma shielding devices as part of the quality assurance system. A brief analysis of the influence of the errors of measures, the interactions between the process and its environment in determining of the basic behaviour of the process and its stability is done.(author)
Coherence and chaos in extended dynamical systems
International Nuclear Information System (INIS)
Bishop, A.R.
1994-01-01
Coherence, chaos, and pattern formation are characteristic elements of the nonequilibrium statistical mechanics controlling mesoscopic order and disorder in many-degree-of-freedom nonlinear dynamical systems. Competing length scales and/or time scales are the underlying microscopic driving forces for many of these aspects of ''complexity.'' We illustrate the basic concepts with some model examples of classical and quantum, ordered and disordered, nonlinear systems
Classical and Quantum Chaos in Atom Optics
Saif, Farhan
2006-01-01
The interaction of an atom with an electromagnetic field is discussed in the presence of a time periodic external modulating force. It is explained that a control on atom by electromagnetic fields helps to design the quantum analog of classical optical systems. In these atom optical systems chaos may appear at the onset of external fields. The classical and quantum chaotic dynamics is discussed, in particular in an atom optics Fermi accelerator. It is found that the quantum dynamics exhibits ...
Wave Chaos and Coupling to EM Structures
2006-07-01
Antonsen, E. Ott and S. Anlage, Aspects of the Scattering and Impedance Properties of Chaotic Microwave Cavities, Acta Physica Polonica A 109, 65...other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a ...currently valid OMB control number. 1. REPORT DATE JUL 2006 2. REPORT TYPE N/ A 3. DATES COVERED - 4. TITLE AND SUBTITLE Wave Chaos and Coupling
Complex motions and chaos in nonlinear systems
Machado, José; Zhang, Jiazhong
2016-01-01
This book brings together 10 chapters on a new stream of research examining complex phenomena in nonlinear systems—including engineering, physics, and social science. Complex Motions and Chaos in Nonlinear Systems provides readers a particular vantage of the nature and nonlinear phenomena in nonlinear dynamics that can develop the corresponding mathematical theory and apply nonlinear design to practical engineering as well as the study of other complex phenomena including those investigated within social science.
Energy Technology Data Exchange (ETDEWEB)
Eminov, P.A., E-mail: peminov@mail.ru [Moscow State University of Instrument Engineering and Computer Sciences, 20 Stromynka Street, Moscow 2107996 (Russian Federation); National Research University Higher School of Economics, 3/12 Bolshoy Trekhsvyatskiy pereulok, Moscow 109028 (Russian Federation)
2013-10-01
Ionization processes for a two dimensional quantum dot subjected to combined electrostatic and alternating electric fields of the same direction are studied using quantum mechanical methods. We derive analytical equations for the ionization probability in dependence on characteristic parameters of the system for both extreme cases of a constant electric field and of a linearly polarized electromagnetic wave. The ionization probabilities for a superposition of dc and low frequency ac electric fields of the same direction are calculated. The impulse distribution of ionization probability for a system bound by short range forces is found for a superposition of constant and alternating fields. The total probability for this process per unit of time is derived within exponential accuracy. For the first time the influence of alternating electric field on electron tunneling probability induced by an electrostatic field is studied taking into account the pre-exponential term.
Effect of smoothing on robust chaos.
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.
Dynamics and chaos control of gyrostat satellite
International Nuclear Information System (INIS)
Aslanov, Vladimir; Yudintsev, Vadim
2012-01-01
Highlights: ► Free dual-spin gyrostat with a small rotor asymmetry is considered. ► Equations in Andoyer-Deprit canonical dimensionless variables are obtained. ► Phase space heteroclinic and homoclinic trajectories are written in closed form. ► Modified Melnikov function is used to construct the control that eliminates chaos. - Abstract: We consider the chaotic motion of the free gyrostat consisting of a platform with a triaxial inertia ellipsoid and a rotor with a small asymmetry with respect to the axis of rotation. Dimensionless equations of motion of the system with perturbations caused by small asymmetries of the rotor are written in Andoyer-Deprit variables. These perturbations lead to separatrix chaos. For gyrostats with different ratios of moments of inertia heteroclinic and homoclinic trajectories are written in closed-form. These trajectories are used for constructing modified Melnikov function, which is used for determine the control that eliminates separatrix chaos. Melnikov function and phase space trajectory are built to show the effectiveness of the control.
Chaos and Structures in Nonlinear Plasmas
Chen, James
In recent decades, the concepts and applications of chaos, complexity, and nonlinear dynamics have profoundly influenced scientific as well as literary thinking. Some aspects of these concepts are used in almost all of the geophysical disciplines. Chaos and Structures in Nonlinear Plasmas, written by two respected plasma physicists, focuses on nonlinear phenomena in laboratory and space plasmas, which are rich in nonlinear and complex collective effects. Chaos is treated only insofar as it relates to some aspects of nonlinear plasma physics.At the outset, the authors note that plasma physics research has made fundamental contributions to modern nonlinear sciences. For example, the Poincare surface of section technique was extensively used in studies of stochastic field lines in magnetically confined plasmas and turbulence. More generally, nonlinearity in plasma waves and wave-wave and wave-particle interactions critically determines the propagation of energy through a plasma medium. The book also makes it clear that the importance of understanding nonlinear waves goes beyond plasma physics, extending to such diverse fields as solid state physics, fluid dynamics, atmospheric physics, and optics. In space physics, non-linear plasma physics is essential for interpreting in situ as well as remote-sensing data.
Dynamical chaos: systems of classical mechanics
International Nuclear Information System (INIS)
Loskutov, A Yu
2007-01-01
This article is a methodological manual for those who are interested in chaotic dynamics. An exposition is given on the foundations of the theory of deterministic chaos that originates in classical mechanics systems. Fundamental results obtained in this area are presented, such as elements of the theory of nonlinear resonance and the Kolmogorov-Arnol'd-Moser theory, the Poincare-Birkhoff fixed-point theorem, and the Mel'nikov method. Particular attention is given to the analysis of the phenomena underlying the self-similarity and nature of chaos: splitting of separatrices and homoclinic and heteroclinic tangles. Important properties of chaotic systems - unpredictability, irreversibility, and decay of temporal correlations - are described. Models of classical statistical mechanics with chaotic properties, which have become popular in recent years - billiards with oscillating boundaries - are considered. It is shown that if a billiard has the property of well-developed chaos, then perturbations of its boundaries result in Fermi acceleration. But in nearly-integrable billiard systems, excitations of the boundaries lead to a new phenomenon in the ensemble of particles, separation of particles in accordance their velocities. If the initial velocity of the particles exceeds a certain critical value characteristic of the given billiard geometry, the particles accelerate; otherwise, they decelerate. (methodological notes)
Detecting chaos in irregularly sampled time series.
Kulp, C W
2013-09-01
Recently, Wiebe and Virgin [Chaos 22, 013136 (2012)] developed an algorithm which detects chaos by analyzing a time series' power spectrum which is computed using the Discrete Fourier Transform (DFT). Their algorithm, like other time series characterization algorithms, requires that the time series be regularly sampled. Real-world data, however, are often irregularly sampled, thus, making the detection of chaotic behavior difficult or impossible with those methods. In this paper, a characterization algorithm is presented, which effectively detects chaos in irregularly sampled time series. The work presented here is a modification of Wiebe and Virgin's algorithm and uses the Lomb-Scargle Periodogram (LSP) to compute a series' power spectrum instead of the DFT. The DFT is not appropriate for irregularly sampled time series. However, the LSP is capable of computing the frequency content of irregularly sampled data. Furthermore, a new method of analyzing the power spectrum is developed, which can be useful for differentiating between chaotic and non-chaotic behavior. The new characterization algorithm is successfully applied to irregularly sampled data generated by a model as well as data consisting of observations of variable stars.
Chaos, dynamical structure and climate variability
Energy Technology Data Exchange (ETDEWEB)
Stewart, H.B. [Brookhaven National Lab., Upton, NY (United States). Dept. of Applied Science
1995-09-01
Deterministic chaos in dynamical systems offers a new paradigm for understanding irregular fluctuations. Techniques for identifying deterministic chaos from observed data, without recourse to mathematical models, are being developed. Powerful methods exist for reconstructing multidimensional phase space from an observed time series of a single scalar variable; these methods are invaluable when only a single scalar record of the dynamics is available. However, in some applications multiple concurrent time series may be available for consideration as phase space coordinates. Here the authors propose some basic analytical tools for such multichannel time series data, and illustrate them by applications to a simple synthetic model of chaos, to a low-order model of atmospheric circulation, and to two high-resolution paleoclimate proxy data series. The atmospheric circulation model, originally proposed by Lorenz, has 27 principal unknowns; they establish that the chaotic attractor can be embedded in a subspace of eight dimensions by exhibiting a specific subset of eight unknowns which pass multichannel tests for false nearest neighbors. They also show that one of the principal unknowns in the 27-variable model--the global mean sea surface temperature--is of no discernible usefulness in making short-term forecasts.
The chaos and order in nuclear molecular dynamics; Chaos i porzadek w jadrowej dynamice molekularnej
Energy Technology Data Exchange (ETDEWEB)
Srokowski, T. [Institute of Nuclear Physics, Cracow (Poland)
1995-12-31
The subject of the presented report is role of chaos in scattering processes in the frame of molecular dynamics. In this model, it is assumed that scattering particles (nuclei) consist of not-interacted components as alpha particles or {sup 12}C, {sup 16}O and {sup 20}Ne clusters. The results show such effects as dynamical in stabilities and fractal structure as well as compound nuclei decay and heavy-ion fusion. The goal of the report is to make the reader more familiar with the chaos model and its application to nuclear phenomena. 157 refs, 40 figs.
An empirical study on identifying critical success factors on chaos management
Directory of Open Access Journals (Sweden)
Naser Azad
2012-08-01
Full Text Available Chaos management is one of the most necessary efforts on managing business units. Many organizations fail to cope with undesirable circumstances, which may happen without any prior notice and as a result, they may face with significant financial losses. In this paper, we present an empirical study to determine critical success factors, which could help handle any possible chaos in organizations. The proposed study of this paper is implemented for a set of travel agencies located in Tehran, Iran. Chronbach alpha is calculated as 0.821, which is well above the minimum desirable level. In addition, we have also performed factor analysis, which yields a KMO value of 0.576 with the level of significance of 0.000. The results indicate that there are six important factors including effective management strategy, internal environmental factors, creative and innovative attitudes, external environmental factors and top level management thoughts.
Application of Chaos Theory to Psychological Models
Blackerby, Rae Fortunato
This dissertation shows that an alternative theoretical approach from physics--chaos theory--offers a viable basis for improved understanding of human beings and their behavior. Chaos theory provides achievable frameworks for potential identification, assessment, and adjustment of human behavior patterns. Most current psychological models fail to address the metaphysical conditions inherent in the human system, thus bringing deep errors to psychological practice and empirical research. Freudian, Jungian and behavioristic perspectives are inadequate psychological models because they assume, either implicitly or explicitly, that the human psychological system is a closed, linear system. On the other hand, Adlerian models that require open systems are likely to be empirically tenable. Logically, models will hold only if the model's assumptions hold. The innovative application of chaotic dynamics to psychological behavior is a promising theoretical development because the application asserts that human systems are open, nonlinear and self-organizing. Chaotic dynamics use nonlinear mathematical relationships among factors that influence human systems. This dissertation explores these mathematical relationships in the context of a sample model of moral behavior using simulated data. Mathematical equations with nonlinear feedback loops describe chaotic systems. Feedback loops govern the equations' value in subsequent calculation iterations. For example, changes in moral behavior are affected by an individual's own self-centeredness, family and community influences, and previous moral behavior choices that feed back to influence future choices. When applying these factors to the chaos equations, the model behaves like other chaotic systems. For example, changes in moral behavior fluctuate in regular patterns, as determined by the values of the individual, family and community factors. In some cases, these fluctuations converge to one value; in other cases, they diverge in
ELS-LEED-study of low-dimensional plasmons in DySi2 layers and nanowires
International Nuclear Information System (INIS)
Rugeramigabo, Eddy Patrick
2007-01-01
Low-dimensional dysprosium silicide metal systems grown on Si have been characterized by means of energy loss spectroscopy of low energy electron diffraction. The several silicide phases depending on the growth conditions have been observed. Moreover collective charge excitations were clearly detected and identified as low-dimensional plasmons which have a different dispersion compared to the well known bulk and surface plasmons. Dy-silicide has been grown on Si(111) by means of molecular beam epitaxy. Due to its small lattice mismatch (-0.3%) to Si(111), Dy-silicide grows in epitaxial high quality crystalline layers. In the submonolayer regime, many silicide phases coexist until the silicide coverage approaches 1ML, and shows the characteristic 1 x 1 diffraction pattern with the stoichiometry DySi 2 . With further increasing of the coverage, the silicide turns to the multilayer phase. The collective electronic excitations in the monolayer structure have been found to have a 2D-character. Accordingly the plasmon dispersion reaches zero in the long-wavelength limit (at vanishing wave number q) and shows a √(q) behaviour until it entered the domain of strong damping. When grown on Si (001) the Dy-silicide formed an array of parallel nanowires, in the direction normal to the dimer row direction and their length was limited by the crossing of another nanowire. A structure dependent energy loss was observed: the energy loss were only sufficiently intense when the 7 x 2 reconstruction has formed. An possibility of creating vast area with only parallel nanowires in one direction was performed on vicinal Si(001) with four degree miscut. At the same coverage where the 7 x 2 reconstruction occurs on flat Si(001), it was surprising that, besides the 7 x 2 periodicity, the diffraction pattern revealed a mixture of phases, with periodicities ranging from the 10 x 2 to that of the 7 x 2, which was observed as the limit of shifting reflex positions. We were able to confirm the
Household chaos and family sleep during infants' first year.
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).
Directory of Open Access Journals (Sweden)
Karishma eChhabria
2016-03-01
Full Text Available The motivation of developing simple minimal models for neuro-glio-vascular system arises from a recent modeling study elucidating the bidirectional information flow within the neuro-glio-vascular system having 89 dynamic equations (Chander and Chakravarthy 2012. While this was one of the first attempts at formulating a comprehensive model for neuro-glia-vascular system, it poses severe restrictions in scaling up to network levels. On the contrary, low dimensional models are convenient devices in simulating large networks that also provide an intuitive understanding of the complex interactions occurring within the neuro-glio-vascular system. The key idea underlying the proposed models is to describe the glio-vascular system as a lumped system which takes neural firing rate as input and returns an ‘energy’ variable (analogous to ATP as output. To this end we present two models: Biophysical neuro-energy (Model #1 with 5 variables, comprising of KATP channel activity governed by neuronal ATP dynamics and the Dynamic threshold (Model #2 with 3 variables depicting the dependence of neural firing threshold on the ATP dynamics. Both the models show different firing regimes such as continuous spiking, phasic and tonic bursting depending on the ATP production coefficient, εp and external current. We then demonstrate that in a network comprising of such energy-dependent neuron units, εp could modulate the Local field potential (LFP frequency and amplitude. Interestingly, low frequency LFP dominates under low εp conditions, which is thought to be reminiscent of seizure-like activity observed in epilepsy. The proposed ‘neuron-energy’ unit may be implemented in building models of neuro-glio-vascular networks to simulate data obtained from multimodal neuroimaging systems such as fNIRS-EEG and fMRI-EEG. Such models could also provide a theoretical basis for devising optimal neurorehabilitation strategies such as non-invasive brain stimulation for
The complexity of translationally invariant low-dimensional spin lattices in 3D
Bausch, Johannes; Piddock, Stephen
2017-11-01
In this theoretical paper, we consider spin systems in three spatial dimensions and consider the computational complexity of estimating the ground state energy, known as the local Hamiltonian problem, for translationally invariant Hamiltonians. We prove that the local Hamiltonian problem for 3D lattices with face-centered cubic unit cells and 4-local translationally invariant interactions between spin-3/2 particles and open boundary conditions is QMAEXP-complete, where QMAEXP is the class of problems which can be verified in exponential time on a quantum computer. We go beyond a mere embedding of past hard 1D history state constructions, for which the local spin dimension is enormous: even state-of-the-art constructions have local dimension 42. We avoid such a large local dimension by combining some different techniques in a novel way. For the verifier circuit which we embed into the ground space of the local Hamiltonian, we utilize a recently developed computational model, called a quantum ring machine, which is especially well suited for translationally invariant history state constructions. This is encoded with a new and particularly simple universal gate set, which consists of a single 2-qubit gate applied only to nearest-neighbour qubits. The Hamiltonian construction involves a classical Wang tiling problem as a binary counter which translates one cube side length into a binary description for the encoded verifier input and a carefully engineered history state construction that implements the ring machine on the cubic lattice faces. These novel techniques allow us to significantly lower the local spin dimension, surpassing the best translationally invariant result to date by two orders of magnitude (in the number of degrees of freedom per coupling). This brings our models on par with the best non-translationally invariant construction.
Natarajan, Sundararajan
2014-12-01
The main objectives of the paper are to (1) present an overview of nonlocal integral elasticity and Aifantis gradient elasticity theory and (2) discuss the application of partition of unity methods to study the response of low-dimensional structures. We present different choices of approximation functions for gradient elasticity, namely Lagrange intepolants, moving least-squares approximants and non-uniform rational B-splines. Next, we employ these approximation functions to study the response of nanobeams based on Euler-Bernoulli and Timoshenko theories as well as to study nanoplates based on first-order shear deformation theory. The response of nanobeams and nanoplates is studied using Eringen's nonlocal elasticity theory. The influence of the nonlocal parameter, the beam and the plate aspect ratio and the boundary conditions on the global response is numerically studied. The influence of a crack on the axial vibration and buckling characteristics of nanobeams is also numerically studied.
International Nuclear Information System (INIS)
Blau, M.; Thompson, G.
1995-01-01
We review localization techniques for functional integrals which have recently been used to perform calculations in and gain insight into the structure of certain topological field theories and low-dimensional gauge theories. These are the functional integral counterparts of the Mathai-Quillen formalism, the Duistermaat-Heckman theorem, and the Weyl integral formula respectively. In each case, we first introduce the necessary mathematical background (Euler classes of vector bundles, equivariant cohomology, topology of Lie groups), and describe the finite dimensional integration formulae. We then discuss some applications to path integrals and give an overview of the relevant literature. The applications we deal with include supersymmetric quantum mechanics, cohomological field theories, phase space path integrals, and two-dimensional Yang-Mills theory. (author). 83 refs
Institute of Scientific and Technical Information of China (English)
Jing Liu; Qi-Wei Chen; Kai Wu
2017-01-01
Bottom-up approach to constructing low-dimensional nanostructures on surfaces with terminal alkynes has drawn great interest because of its potential applications in fabricating advanced functional nanomaterials.The diversity of the achieved products manifests rich chemistry of terminal alkynes and hence careful linking strategies and proper controlling methodologies are required for selective preparations of high-quality target nanoarchitectures.This review summarizes various on-surface linking strategies for terminal alkynes,including non-bonding interactions as well as organometallic and covalent bonds,and presents examples to show effective control of surface assemblies and reactions of terminal alkynes by variations of the precursor structures,substrates and activation modes.Systematic studies of the on-surface linkage of terminal alkynes may help efficient and predictable preparations of surface nanomaterials and further understanding of surface chemistry.
Energy Technology Data Exchange (ETDEWEB)
Moore, Joel; Rabe, Karin; Nayak, Chetan; Troyer, Matthias
2012-05-01
Aspen Center for Physics Project Summary DOE Budget Period: 10/1/2011 to 9/30/2012 Contract # DE-SC0007479 New Paradigms for Low-Dimensional Electronic Materials The 2012 Aspen Winter Conference on Condensed Matter Physics was held at the Aspen Center for Physics from February 5 to 10, 2012. Seventy-four participants from seven countries, and several universities and national labs attended the workshop titled, New Paradigms for Low-Dimensional Electronic Materials. There were 34 formal talks, and a number of informal discussions held during the week. Talks covered a variety of topics related to DOE BES priorities, including, for example, advanced photon techniques (Hasan, Abbamonte, Orenstein, Shen, Ghosh) and predictive theoretical modeling of materials properties (Rappe, Pickett, Balents, Zhang, Vanderbilt); the full conference schedule is provided with this report. The week's events included a public lecture (Quantum Matters given by Chetan Nayak from Microsoft Research) and attended by 234 members of the public, and a physics caf© geared for high schoolers that is a discussion with physicists conducted by Kathryn Moler (Stanford University) and Andrew M. Rappe (University of Pennsylvania) and attended by 67 locals and visitors. While there were no published proceedings, some of the talks are posted online and can be Googled. The workshop was organized by Joel Moore (University of California Berkeley), Chetan Nayak (Microsoft Research), Karin Rabe (Rutgers University), and Matthias Troyer (ETH Zurich). Two organizers who did not attend the conference were Gabriel Aeppli (University College London & London Centre for Nanotechnology) and Andrea Cavalleri (Oxford University & Max Planck Hamburg).
Chaos controlling problems for circuit systems with Josephson junction
International Nuclear Information System (INIS)
Gou, X-F; Wang, X; Xie, J-L
2008-01-01
The complex dynamical characters of the Josephson junction circuit system are studied and the tunnel effect is considered. The dynamical equation of the system is established. The route from periodic motion to chaos is illustrated using bifurcation diagram. An adscititious coupling controller is constructed to control the chaos
Synchronization and suppression of chaos in non-locally coupled ...
Indian Academy of Sciences (India)
Coupled map lattices have been intensively investigated as models to understand many spatiotemporal phenomena observed in extended system, and consequently spatiotemporal chaos. We used the complex order parameter to quantify chaos synchronization for a one-dimensional chain of coupled logistic maps with a ...
Research on a family of n-scroll chaos generators
International Nuclear Information System (INIS)
Zhang, G; Yang, S-Z; He, L-F
2008-01-01
This paper studies a family of n-scroll chaos generators using a modified Chua's circuit. A mathematic model of the generators is established, the relationship between equilibrium points and scrolls is also analyzed, and a general theorem for generation of n-scroll chaos attractors is given. Numerical simulation is illustrated, showing excellent agreement with our theoretical predictions
On the suppression of chaos in quantum and classical physics
International Nuclear Information System (INIS)
Fried, H.M.; Gabellini, Y.
1997-01-01
A brief outline is presented of an example of potential-theory quantum chaos, which is suppressed by the full radiative corrections of quantum field theory. A similar mechanism may be devised and applied to classically chaotic systems, and provides an example in which an explicit diminution of the original chaos becomes apparent. (author)
Applying Chaos Theory to Lesson Planning and Delivery
Cvetek, Slavko
2008-01-01
In this article, some of the ways in which thinking about chaos theory can help teachers and student-teachers to accept uncertainty and randomness as natural conditions in the classroom are considered. Building on some key features of complex systems commonly attributed to chaos theory (e.g. complexity, nonlinearity, sensitivity to initial…
The Chaos Theory of Careers: A User's Guide
Bright, Jim E. H.; Pryor, Robert G. L.
2005-01-01
The purpose of this article is to set out the key elements of the Chaos Theory of Careers. The complexity of influences on career development presents a significant challenge to traditional predictive models of career counseling. Chaos theory can provide a more appropriate description of career behavior, and the theory can be applied with clients…
Switching control of linear systems for generating chaos
International Nuclear Information System (INIS)
Liu Xinzhi; Teo, Kok-Lay; Zhang Hongtao; Chen Guanrong
2006-01-01
In this paper, a new switching method is developed, which can be applied to generating different types of chaos or chaos-like dynamics from two or more linear systems. A numerical simulation is given to illustrate the generated chaotic dynamic behavior of the systems with some variable parameters. Finally, a circuit is built to realize various chaotic dynamical behaviors
Chaos: A Topic for Interdisciplinary Education in Physics
Bae, Saebyok
2009-01-01
Since society and science need interdisciplinary works, the interesting topic of chaos is chosen for interdisciplinary education in physics. The educational programme contains various university-level activities such as computer simulations, chaos experiment and team projects besides ordinary teaching. According to the participants, the programme…
Chaos and the classical limit of quantum systems
Energy Technology Data Exchange (ETDEWEB)
Hogg, T; Huberman, B A [Xerox Palo Alto Research Center, CA (USA)
1984-10-01
The authors discuss the question of whether experiments can be designed to test the existence of quantum chaos. In particular, they show that high energies are not sufficient to guarantee that an initially localized wave packet will behave classically for long times. Computer simulations illustrating these ideas are presented and the question whether experiments can be designed to observe quantum chaos is commented on.
Specifying the Links between Household Chaos and Preschool Children's Development
Martin, Anne; Razza, Rachel A.; Brooks-Gunn, Jeanne
2012-01-01
Household chaos has been linked to poorer cognitive, behavioural, and self-regulatory outcomes in young children, but the mechanisms responsible remain largely unknown. Using a diverse sample of families in Chicago, the present study tests for the independent contributions made by five indicators of household chaos: noise, crowding, family…
Random matrices and chaos in nuclear physics: Nuclear structure
International Nuclear Information System (INIS)
Weidenmueller, H. A.; Mitchell, G. E.
2009-01-01
Evidence for the applicability of random-matrix theory to nuclear spectra is reviewed. In analogy to systems with few degrees of freedom, one speaks of chaos (more accurately, quantum chaos) in nuclei whenever random-matrix predictions are fulfilled. An introduction into the basic concepts of random-matrix theory is followed by a survey over the extant experimental information on spectral fluctuations, including a discussion of the violation of a symmetry or invariance property. Chaos in nuclear models is discussed for the spherical shell model, for the deformed shell model, and for the interacting boson model. Evidence for chaos also comes from random-matrix ensembles patterned after the shell model such as the embedded two-body ensemble, the two-body random ensemble, and the constrained ensembles. All this evidence points to the fact that chaos is a generic property of nuclear spectra, except for the ground-state regions of strongly deformed nuclei.
Replication of chaos in neural networks, economics and physics
Akhmet, Marat
2016-01-01
This book presents detailed descriptions of chaos for continuous-time systems. It is the first-ever book to consider chaos as an input for differential and hybrid equations. Chaotic sets and chaotic functions are used as inputs for systems with attractors: equilibrium points, cycles and tori. The findings strongly suggest that chaos theory can proceed from the theory of differential equations to a higher level than previously thought. The approach selected is conducive to the in-depth analysis of different types of chaos. The appearance of deterministic chaos in neural networks, economics and mechanical systems is discussed theoretically and supported by simulations. As such, the book offers a valuable resource for mathematicians, physicists, engineers and economists studying nonlinear chaotic dynamics.
Strong chaos in one-dimensional quantum system
International Nuclear Information System (INIS)
Yang, C.-D.; Wei, C.-H.
2008-01-01
According to the Poincare-Bendixson theorem, a minimum of three autonomous equations is required to exhibit deterministic chaos. Because a one-dimensional quantum system is described by only two autonomous equations using de Broglie-Bohm's trajectory interpretation, chaos in one-dimensional quantum systems has long been considered impossible. We will prove in this paper that chaos phenomenon does exist in one-dimensional quantum systems, if the domain of quantum motions is extended to complex space by noting that the quantum world is actually characterized by a four-dimensional complex spacetime according to the E (∞) theory. Furthermore, we point out that the interaction between the real and imaginary parts of complex trajectories produces a new chaos phenomenon unique to quantum systems, called strong chaos, which describes the situation that quantum trajectories may emerge and diverge spontaneously without any perturbation in the initial position
Relativistic quantum chaos-An emergent interdisciplinary field.
Lai, Ying-Cheng; Xu, Hong-Ya; Huang, Liang; Grebogi, Celso
2018-05-01
Quantum chaos is referred to as the study of quantum manifestations or fingerprints of classical chaos. A vast majority of the studies were for nonrelativistic quantum systems described by the Schrödinger equation. Recent years have witnessed a rapid development of Dirac materials such as graphene and topological insulators, which are described by the Dirac equation in relativistic quantum mechanics. A new field has thus emerged: relativistic quantum chaos. This Tutorial aims to introduce this field to the scientific community. Topics covered include scarring, chaotic scattering and transport, chaos regularized resonant tunneling, superpersistent currents, and energy level statistics-all in the relativistic quantum regime. As Dirac materials have the potential to revolutionize solid-state electronic and spintronic devices, a good understanding of the interplay between chaos and relativistic quantum mechanics may lead to novel design principles and methodologies to enhance device performance.
A new approach for realizing electronic chaos generators
International Nuclear Information System (INIS)
Elwakeel, A.E.
1997-01-01
A dictionary definition of chaos is a 'formless primordial matter, utter confusion' [1]. The study of chaos is part of a larger program of study of so-called strongly nonlinear systems. No strict definition of chaos yet exists, however, nonrandom complicated motions that exhibit a very rapid growth of errors and that, despite perfect determinism, inhibit any ability to render accurate long-term prediction are usually termed chaotic. In other words, chaos may be referred to as deterministic randomness since it is the phenomenon where deterministic laws, are sometimes extremely simple, show random (or random-like) behaviours while random (or random-like) motions happen to follow strict deterministic laws. The sense of order in chaos can be usually observed in the space of dimensions where time is not a dimension, while the sense of randomness is usually evident when time is incorporated. 10 refs., 29 figs
Elimination of spiral chaos by periodic force for the Aliev-Panfilov model
Sakaguchi, Hidetsugu; Fujimoto, Takefumi
2003-01-01
Spiral chaos appears in the two dimensional Aliev-Panfilov model. The generation mechanism of the spiral chaos is related to the breathing instability of pulse trains. The spiral chaos can be eliminated by applying periodic force uniformly. The elimination of spiral chaos is most effective, when the frequency of the periodic force is close to that of the breathing motion.
Chaos and its Role in Design and Simulation of Railway Vehicles
DEFF Research Database (Denmark)
True, Hans
1996-01-01
First certain important properties of nonlinear problems are discussed. Thenthe concept of chaos is described. It can only appear in nonlinear systemsand it is very common in the real world. Certain characteristic features ofdeterministic chaos and in relation hereto tests for the existence...... of chaos indynamical systems are presented.\\ Next the relevance of chaos for railwaydynamics is discussed and examples of chaotic oscillations in railwaydynamical model are shown, whereby the distinction between a chaoticattractor and transient chaos is introduces. Some causes of chaos in railwaytechnology...... are discussed. Finally the effects of chaos on field tests andnumerical simulations are discussed....
Method of controlling chaos in laser equations
International Nuclear Information System (INIS)
Duong-van, M.
1993-01-01
A method of controlling chaotic to laminar flows in the Lorenz equations using fixed points dictated by minimizing the Lyapunov functional was proposed by Singer, Wang, and Bau [Phys. Rev. Lett. 66, 1123 (1991)]. Using different fixed points, we find that the solutions in a chaotic regime can also be periodic. Since the laser equations are isomorphic to the Lorenz equations we use this method to control chaos when the laser is operated over the pump threshold. Furthermore, by solving the laser equations with an occasional proportional feedback mechanism, we recover the essential laser controlling features experimentally discovered by Roy, Murphy, Jr., Maier, Gills, and Hunt [Phys. Rev. Lett. 68, 1259 (1992)
Chaos of several typical asymmetric systems
International Nuclear Information System (INIS)
Feng Jingjing; Zhang Qichang; Wang Wei
2012-01-01
The threshold for the onset of chaos in asymmetric nonlinear dynamic systems can be determined using an extended Padé method. In this paper, a double-well asymmetric potential system with damping under external periodic excitation is investigated, as well as an asymmetric triple-well potential system under external and parametric excitation. The integrals of Melnikov functions are established to demonstrate that the motion is chaotic. Threshold values are acquired when homoclinic and heteroclinic bifurcations occur. The results of analytical and numerical integration are compared to verify the effectiveness and feasibility of the analytical method.
Method of controlling chaos in laser equations
Duong-van, Minh
1993-01-01
A method of controlling chaotic to laminar flows in the Lorenz equations using fixed points dictated by minimizing the Lyapunov functional was proposed by Singer, Wang, and Bau [Phys. Rev. Lett. 66, 1123 (1991)]. Using different fixed points, we find that the solutions in a chaotic regime can also be periodic. Since the laser equations are isomorphic to the Lorenz equations we use this method to control chaos when the laser is operated over the pump threshold. Furthermore, by solving the laser equations with an occasional proportional feedback mechanism, we recover the essential laser controlling features experimentally discovered by Roy, Murphy, Jr., Maier, Gills, and Hunt [Phys. Rev. Lett. 68, 1259 (1992)].
Controlling chaos in Internet congestion control model
International Nuclear Information System (INIS)
Chen Liang; Wang Xiaofan; Han Zhengzhi
2004-01-01
The TCP end-to-end congestion control plus RED router queue management can be modeled as a discrete-time dynamical system, which may create complex bifurcating and chaotic behavior. Based on the basic features of the TCP-RED model, we propose a time-dependent delayed feedback control algorithm to control chaos in the system by perturbing the accessible RED parameter p max . This method is able to stabilized a router queue occupancy at a level without knowing the exact knowledge of the network. Further, we study the situation of the presence of the UDP traffic
Experimental chaos in nonlinear vibration isolation system
International Nuclear Information System (INIS)
Lou Jingjun; Zhu Shijian; He Lin; He Qiwei
2009-01-01
The chaotic vibration isolation method was studied thoroughly from an experimental perspective. The nonlinear load-deflection characteristic of the conical coil spring used in the experiment was surveyed. Chaos and subharmonic responses including period-2 and period-6 motions were observed. The line spectrum reduction and the drop of the acceleration vibration level in chaotic state and that in non-chaotic state were compared, respectively. It was concluded from the experiment that the nonlinear vibration isolation system in chaotic state has strong ability in line spectrum reduction.