Chaos and Structures in Nonlinear Plasmas
James Chen
1998-01-01
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
A. Ugulava; S. Chkhaidze; L. Chotorlishvili; Z. Rostomashvili
2009-02-17
The hodographs of magnetization of nonlinear nuclear magnetic resonance are investigated in the conditions of resonance on the unshifted frequency. It is shown that, depending on the value of amplitude of the variable field and value of frequency shift, topologically different hodographs separated from each other by separatrix are obtained.
Pathological tremors : Deterministic chaos or nonlinear
Timmer, Jens
Pathological tremors : Deterministic chaos or nonlinear stochastic oscillators? Jens Timmer \\Lambda Hospital of Freiburg, Breisacher Str. 64, 79110 Freiburg, Germany Abstract. Pathological tremors exhibit of the different methods suggest that the considered types of pathological tremors represent nonlinear stochastic
Scaling of chaos in strongly nonlinear lattices
Mulansky, Mario; Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, D-01187 Dresden; Institut für Theoretische Physik, TU Dresden, Zellescher Weg 17, D-01069 Dresden
2014-06-15
Although it is now understood that chaos in complex classical systems is the foundation of thermodynamic behavior, the detailed relations between the microscopic properties of the chaotic dynamics and the macroscopic thermodynamic observations still remain mostly in the dark. In this work, we numerically analyze the probability of chaos in strongly nonlinear Hamiltonian systems and find different scaling properties depending on the nonlinear structure of the model. We argue that these different scaling laws of chaos have definite consequences for the macroscopic diffusive behavior, as chaos is the microscopic mechanism of diffusion. This is compared with previous results on chaotic diffusion [M. Mulansky and A. Pikovsky, New J. Phys. 15, 053015 (2013)], and a relation between microscopic chaos and macroscopic diffusion is established.
Detecting nonlinearity and chaos in epidemic data
Ellner, S.; Gallant, A.R. [North Carolina State Univ., Raleigh, NC (United States). Dept. of Statistics; Theiler, J. [Santa Fe Inst., NM (United States)]|[Los Alamos National Lab., NM (United States)
1993-08-01
Historical data on recurrent epidemics have been central to the debate about the prevalence of chaos in biological population dynamics. Schaffer and Kot who first recognized that the abundance and accuracy of disease incidence data opened the door to applying a range of methods for detecting chaos that had been devised in the early 1980`s. Using attractor reconstruction, estimates of dynamical invariants, and comparisons between data and simulation of SEIR models, the ``case for chaos in childhood epidemics`` was made through a series of influential papers beginning in the mid 1980`s. The proposition that the precise timing and magnitude of epidemic outbreaks are deterministic but chaotic is appealing, since it raises the hope of finding determinism and simplicity beneath the apparently stochastic and complicated surface of the data. The initial enthusiasm for methods of detecting chaos in data has been followed by critical re-evaluations of their limitations. Early hopes of a ``one size fits all`` algorithm to diagnose chaos vs. noise in any data set have given way to a recognition that a variety of methods must be used, and interpretation of results must take into account the limitations of each method and the imperfections of the data. Our goals here are to outline some newer methods for detecting nonlinearity and chaos that have a solid statistical basis and are suited to epidemic data, and to begin a re-evaluation of the claims for nonlinear dynamics and chaos in epidemics using these newer methods. We also identify features of epidemic data that create problems for the older, better known methods of detecting chaos. When we ask ``are epidemics nonlinear?``, we are not questioning the existence of global nonlinearities in epidemic dynamics, such as nonlinear transmission rates. Our question is whether the data`s deviations from an annual cyclic trend (which would reflect global nonlinearities) are described by a linear, noise-driven stochastic process.
Digital Communication using Chaos and Nonlinear Lucas Illing
Illing, Lucas
Digital Communication using Chaos and Nonlinear Dynamics Lucas Illing Reed College, Portland, OR 97202 Abstract Digital communication using synchronized chaos is reviewed on the example communication in context, a simplified block di- agram of a typical traditional digital communication system
Pathological tremors: Deterministic chaos or nonlinear stochastic oscillators?
Timmer, Jens
Pathological tremors: Deterministic chaos or nonlinear stochastic oscillators? J. Timmera and Parkinsonian tremor exhibit a nonlinear oscillation. The oscillation is not strictly periodic have to be at least of third order. Second, the processes might be nonlinear stochastic oscillators
Household Chaos--Links with Parenting and Child Behaviour
ERIC Educational Resources Information Center
Coldwell, Joanne; Pike, Alison; Dunn, Judy
2006-01-01
Background: The study aimed to confirm previous findings showing links between household chaos and parenting in addition to examining whether household chaos was predictive of children's behaviour over and above parenting. In addition, we investigated whether household chaos acts as a moderator between parenting and children's behaviour. Method:…
Interactive Workshop Discusses Nonlinear Waves and Chaos
NASA Astrophysics Data System (ADS)
Tsurutani, Bruce; Morales, George; Passot, Thierry
2010-07-01
Eighth International Nonlinear Wave Workshop; La Jolla, California, 1-5 March 2010; Nonlinear waves and chaos were the focus of a weeklong series of informal and interactive discussions at the Eighth International Nonlinear Wave Workshop (NWW8), held in California. The workshop gathered nonlinear plasma and water wave experts from the United States, France, Czech Republic, Germany, Greece, Holland, India, and Japan. Attendees were from the fields of space, laboratory, and fusion plasma physics, astrophysics, and applied mathematics. Special focus was placed on nonlinear waves and turbulence in the terrestrial environment as well as in the interstellar medium from observational, laboratory, and theoretical perspectives. Discussions covered temperature anisotropies and related instabilities, the properties and origin of the so-called dissipation range, and various coherent structures of electromagnetic as well as electrostatic nature. Reconnection and shocks were also topics of discussion, as were properties of magnetospheric whistler and chorus waves. Examples and analysis techniques for superdiffusion and subdiffusion were identified. On this last topic, a good exchange of ideas and results occurred between a water wave expert and a plasma expert, with the rest of the audience listening intently.
Chaos Theory: Implications for Nonlinear Dynamics in Counseling.
ERIC Educational Resources Information Center
Stickel, Sue A.
The purpose of this paper is to explore the implications of chaos theory for counseling. The scientific notion of chaos refers to the tendency of dynamical, nonlinear systems toward irregular, sometimes unpredictable, yet deterministic behavior. Therapists, especially those working from a brief approach, have noted the importance of the client's…
Pathological tremors: Deterministic chaos or nonlinear stochastic oscillators?
Timmer, Jens
Pathological tremors: Deterministic chaos or nonlinear stochastic oscillators? J. Timmer a# Pathological tremors exhibit a nonlinear oscillation that is not strictly periodic. We investigate whether or of reflexes. 5,6 Pathological tremors like essential and Parkinsonian tremor exhibit a nonlinear oscillation
Specifying the Links between Household Chaos and Preschool Children's Development
ERIC Educational Resources Information Center
Martin, Anne; Razza, Rachel A.; Brooks-Gunn, Jeanne
2012-01-01
Household chaos has been linked to poorer cognitive, behavioural, and self-regulatory outcomes in young children, but the mechanisms responsible remain largely unknown. Using a diverse sample of families in Chicago, the present study tests for the independent contributions made by five indicators of household chaos: noise, crowding, family…
Chaos, patterns, coherent structures, and turbulence: Reflections on nonlinear science
NASA Astrophysics Data System (ADS)
Ecke, Robert E.
2015-09-01
The paradigms of nonlinear science were succinctly articulated over 25 years ago as deterministic chaos, pattern formation, coherent structures, and adaptation/evolution/learning. For chaos, the main unifying concept was universal routes to chaos in general nonlinear dynamical systems, built upon a framework of bifurcation theory. Pattern formation focused on spatially extended nonlinear systems, taking advantage of symmetry properties to develop highly quantitative amplitude equations of the Ginzburg-Landau type to describe early nonlinear phenomena in the vicinity of critical points. Solitons, mathematically precise localized nonlinear wave states, were generalized to a larger and less precise class of coherent structures such as, for example, concentrated regions of vorticity from laboratory wake flows to the Jovian Great Red Spot. The combination of these three ideas was hoped to provide the tools and concepts for the understanding and characterization of the strongly nonlinear problem of fluid turbulence. Although this early promise has been largely unfulfilled, steady progress has been made using the approaches of nonlinear science. I provide a series of examples of bifurcations and chaos, of one-dimensional and two-dimensional pattern formation, and of turbulence to illustrate both the progress and limitations of the nonlinear science approach. As experimental and computational methods continue to improve, the promise of nonlinear science to elucidate fluid turbulence continues to advance in a steady manner, indicative of the grand challenge nature of strongly nonlinear multi-scale dynamical systems.
Chaos, patterns, coherent structures, and turbulence: Reflections on nonlinear science.
Ecke, Robert E
2015-09-01
The paradigms of nonlinear science were succinctly articulated over 25 years ago as deterministic chaos, pattern formation, coherent structures, and adaptation/evolution/learning. For chaos, the main unifying concept was universal routes to chaos in general nonlinear dynamical systems, built upon a framework of bifurcation theory. Pattern formation focused on spatially extended nonlinear systems, taking advantage of symmetry properties to develop highly quantitative amplitude equations of the Ginzburg-Landau type to describe early nonlinear phenomena in the vicinity of critical points. Solitons, mathematically precise localized nonlinear wave states, were generalized to a larger and less precise class of coherent structures such as, for example, concentrated regions of vorticity from laboratory wake flows to the Jovian Great Red Spot. The combination of these three ideas was hoped to provide the tools and concepts for the understanding and characterization of the strongly nonlinear problem of fluid turbulence. Although this early promise has been largely unfulfilled, steady progress has been made using the approaches of nonlinear science. I provide a series of examples of bifurcations and chaos, of one-dimensional and two-dimensional pattern formation, and of turbulence to illustrate both the progress and limitations of the nonlinear science approach. As experimental and computational methods continue to improve, the promise of nonlinear science to elucidate fluid turbulence continues to advance in a steady manner, indicative of the grand challenge nature of strongly nonlinear multi-scale dynamical systems. PMID:26428558
Microcomputer Simulation of Nonlinear Systems: From Oscillations to Chaos.
ERIC Educational Resources Information Center
Raw, Cecil J. G.; Stacey, Larry M.
1989-01-01
Presents two short microcomputer programs which illustrate features of nonlinear dynamics, including steady states, periodic oscillations, period doubling, and chaos. Logistic maps are explained, inclusion in undergraduate chemistry and physics courses to teach nonlinear equations is discussed, and applications in social and biological sciences…
Chaos and Nonlinear Dynamics in a Quantum Artificial Economy
Carlos Pedro Gonçalves
2012-02-29
Chaos and nonlinear economic dynamics are addressed for a quantum coupled map lattice model of an artificial economy, with quantized supply and demand equilibrium conditions. The measure theoretic properties and the patterns that emerge in both the economic business volume dynamics' diagrams as well as in the quantum mean field averages are addressed and conclusions are drawn in regards to the application of quantum chaos theory to address signatures of chaotic dynamics in relevant discrete economic state variables.
Nonlinear system vibration---The appearance of chaos
Hunter, N.F. Jr.
1990-01-01
This paper begins with an examination of the differential equation for a single degree of freedom force excited oscillator and considers the state space behavior of linear, nonlinear, and chaotic single degree of freedom systems. The fundamental characteristics of classical chaos are reviewed: sensitivity to initial conditions, positive Lyapunov exponents, complex Poincare maps, fractal properties of motion in the state space, and broadening of the power spectrum of the system response. Illustrated examples of chaotic behavior include motion in a two well potential -- the chaos beam described in Moon and a hardening base excited Duffing system. Chaos-like phenomenon which occur with nonperiodic forcing are examined in the context of the two well potential and hardening Duffing systems. The paper concludes with some suggestions for detecting and modelling nonlinear or chaotic behavior. 19 refs., 19 figs.
Nonlinear Chemical Dynamics: Oscillations, Patterns, and Chaos Irving R. Epstein*
Showalter, Kenneth
of a remarkably accurate formula for the velocity of propagation of chemical waves3 in 1906. By the early 1920s oscillator, the iodate-catalyzed decomposition of hydrogen peroxide. Although ecologists were quick to pickNonlinear Chemical Dynamics: Oscillations, Patterns, and Chaos Irving R. Epstein* Department
12.006J / 18.353J Nonlinear Dynamics I: Chaos, Fall 2005
Rothman, Daniel H.
Introduction to the theory and phenomenology of nonlinear dynamics and chaos in dissipative systems. Forced and parametric oscillators. Phase space. Periodic, quasiperiodic, and aperiodic flows. Sensitivity to initial ...
Nonlinear Dynamics and Chaos: Applications in Atmospheric Sciences
A. M. Selvam
2010-11-30
Atmospheric flows, an example of turbulent fluid flows, exhibit fractal fluctuations of all space-time scales ranging from turbulence scale of mm -sec to climate scales of thousands of kilometers - years and may be visualized as a nested continuum of weather cycles or periodicities, the smaller cycles existing as intrinsic fine structure of the larger cycles. The power spectra of fractal fluctuations exhibit inverse power law form signifying long - range correlations identified as self - organized criticality and are ubiquitous to dynamical systems in nature and is manifested as sensitive dependence on initial condition or 'deterministic chaos' in finite precision computer realizations of nonlinear mathematical models of real world dynamical systems such as atmospheric flows. Though the selfsimilar nature of atmospheric flows have been widely documented and discussed during the last three to four decades, the exact physical mechanism is not yet identified. There now exists an urgent need to develop and incorporate basic physical concepts of nonlinear dynamics and chaos into classical meteorological theory for more realistic simulation and prediction of weather and climate. A review of nonlinear dynamics and chaos in meteorology and atmospheric physics is summarized in this paper.
Chaos in the fractional order nonlinear Bloch equation with delay
NASA Astrophysics Data System (ADS)
Baleanu, Dumitru; Magin, Richard L.; Bhalekar, Sachin; Daftardar-Gejji, Varsha
2015-08-01
The Bloch equation describes the dynamics of nuclear magnetization in the presence of static and time-varying magnetic fields. In this paper we extend a nonlinear model of the Bloch equation to include both fractional derivatives and time delays. The Caputo fractional time derivative (?) in the range from 0.85 to 1.00 is introduced on the left side of the Bloch equation in a commensurate manner in increments of 0.01 to provide an adjustable degree of system memory. Time delays for the z component of magnetization are inserted on the right side of the Bloch equation with values of 0, 10 and 100 ms to balance the fractional derivative with delay terms that also express the history of an earlier state. In the absence of delay, ? = 0 , we obtained results consistent with the previously published bifurcation diagram, with two cycles appearing at ? = 0.8548 with subsequent period doubling that leads to chaos at ? = 0.9436 . A periodic window is observed for the range 0.962 < ? < 0.9858 , with chaos arising again as ? nears 1.00. The bifurcation diagram for the case with a 10 ms delay is similar: two cycles appear at the value ? = 0.8532 , and the transition from two to four cycles at ? = 0.9259 . With further increases in the fractional order, period doubling continues until at ? = 0.9449 chaos ensues. In the case of a 100 millisecond delay the transitions from one cycle to two cycles and two cycles to four cycles are observed at ? = 0.8441 , and ? = 0.8635 , respectively. However, the system exhibits chaos at much lower values of ? (? = 0.8635). A periodic window is observed in the interval 0.897 < ? < 0.9341 , with chaos again appearing for larger values of ? . In general, as the value of ? decreased the system showed transitions from chaos to transient chaos, and then to stability. Delays naturally appear in many NMR systems, and pulse programming allows the user control over the process. By including both the fractional derivative and time delays in the Bloch equation, we have developed a delay-dependent model that predicts instability in this non-linear fractional order system consistent with the experimental observations of spin turbulence.
Chaos, creativity, and substance abuse: the nonlinear dynamics of choice.
Zausner, Tobi
2011-04-01
Artists create their work in conditions of disequilibrium, states of creative chaos that may appear turbulent but are capable of bringing forth new order. By absorbing information from the environment and discharging it negentropically as new work, artists can be modeled as dissipative systems. A characteristic of chaotic systems is a heightened sensitivity to stimuli, which can generate either positive experiences or negative ones that can lead some artists to substance abuse and misguided searches for a creative chaos. Alcohol and drug use along with inadequately addressed co-occurring emotional disorders interfere with artists' quest for the nonlinearity of creativity. Instead, metaphorically modeled by a limit cycle of addiction and then a spiral to disorder, the joys of a creative chaos become an elusive chimera for them rather than a fulfilling experience. Untreated mental illness and addiction to substances have shortened the lives of artists such as Vincent Van Gogh, Frida Kahlo, Henri de Toulouse-Lautrec, and Jackson Pollock, all of whom committed suicide. In contrast Edvard Munch and John Callahan, who chose to address their emotional problems and substance abuse, continued to live and remain creative. Choosing to access previously avoided moments of pain can activate the nonlinear power of self-transformation. PMID:21382261
Nonlinear dynamics, chaos and complex cardiac arrhythmias
NASA Technical Reports Server (NTRS)
Glass, L.; Courtemanche, M.; Shrier, A.; Goldberger, A. L.
1987-01-01
Periodic stimulation of a nonlinear cardiac oscillator in vitro gives rise to complex dynamics that is well described by one-dimensional finite difference equations. As stimulation parameters are varied, a large number of different phase-locked and chaotic rhythms is observed. Similar rhythms can be observed in the intact human heart when there is interaction between two pacemaker sites. Simplified models are analyzed, which show some correspondence to clinical observations.
Nonlinearly-enhanced energy transport in many dimensional quantum chaos
Brambila, D. S.; Fratalocchi, A.
2013-01-01
By employing a nonlinear quantum kicked rotor model, we investigate the transport of energy in multidimensional quantum chaos. This problem has profound implications in many fields of science ranging from Anderson localization to time reversal of classical and quantum waves. We begin our analysis with a series of parallel numerical simulations, whose results show an unexpected and anomalous behavior. We tackle the problem by a fully analytical approach characterized by Lie groups and solitons theory, demonstrating the existence of a universal, nonlinearly-enhanced diffusion of the energy in the system, which is entirely sustained by soliton waves. Numerical simulations, performed with different models, show a perfect agreement with universal predictions. A realistic experiment is discussed in two dimensional dipolar Bose-Einstein-Condensates (BEC). Besides the obvious implications at the fundamental level, our results show that solitons can form the building block for the realization of new systems for the enhanced transport of matter. PMID:23912934
Nonlinearly-enhanced energy transport in many dimensional quantum chaos.
Brambila, D S; Fratalocchi, A
2013-01-01
By employing a nonlinear quantum kicked rotor model, we investigate the transport of energy in multidimensional quantum chaos. This problem has profound implications in many fields of science ranging from Anderson localization to time reversal of classical and quantum waves. We begin our analysis with a series of parallel numerical simulations, whose results show an unexpected and anomalous behavior. We tackle the problem by a fully analytical approach characterized by Lie groups and solitons theory, demonstrating the existence of a universal, nonlinearly-enhanced diffusion of the energy in the system, which is entirely sustained by soliton waves. Numerical simulations, performed with different models, show a perfect agreement with universal predictions. A realistic experiment is discussed in two dimensional dipolar Bose-Einstein-Condensates (BEC). Besides the obvious implications at the fundamental level, our results show that solitons can form the building block for the realization of new systems for the enhanced transport of matter. PMID:23912934
Two types of chaos in non-linear mechanics
NASA Technical Reports Server (NTRS)
Zak, M.
1985-01-01
The two types of chaos, weak and strong, associated with the Liapunov and Hadamard instabilities respectively, are analyzed. The geometrical representation of weak chaos is considered, and criteria of this chaos are formulated using the geometrical interpretation of dynamics. Weak chaos in inertial motion of two-bar linkage is discussed. The analysis of strong chaos is restricted to a review of results published elsewhere.
Bifurcations, Chaos, Controlling and Synchronization of Certain Nonlinear Oscillators
NASA Astrophysics Data System (ADS)
Lakshmanan, M.
In this set of lectures, we review briefly some of the recent developments in the study of the chaotic dynamics of nonlinear oscillators, particularly of damped and driven type. By taking a representative set of examples such as the Duffing, Bonhoeffer-van der Pol and MLC circuit oscillators, we briefly explain the various bifurcations and chaos phenomena associated with these systems. We use numerical and analytical as well as analogue simulation methods to study these systems. Then we point out how controlling of chaotic motions can be effected by algorithmic procedures requiring minimal perturbations. Finally we briefly discuss how synchronization of identically evolving chaotic systems can be achieved and how they can be used in secure communications.
IP Fast Rerouting for Single-Link/Node Failure Kang Xi and H. Jonathan Chao
Chao, Jonathan
is critical to high quality service provisioning. The main challenge is how to achieve fast recovery without1 IP Fast Rerouting for Single-Link/Node Failure Recovery Kang Xi and H. Jonathan Chao Polytechnic University, Brooklyn, New York 11201 {kang, chao}@poly.edu Abstract--Failure recovery in IP networks
IP Fast Reroute for Double-Link Failure Recovery Kang Xi and H. Jonathan Chao
Chao, Jonathan
t service resumed use updated routing tables IPFRR triggered Fig. 2. Procedure of failure recovery. primaryIP Fast Reroute for Double-Link Failure Recovery Kang Xi and H. Jonathan Chao Polytechnic Institute of New York University, Brooklyn, NY {kxi,chao}@poly.edu Abstract--Failure recovery using IP fast reroute
Integrability and chaos in nonlinearly coupled optical beams
David, D.
1989-01-01
This paper presents a study, using dynamical systems methods, of the equations describing the polarization behavior of two nonlinearly coupled optical beams counterpropagating in a nonlinear medium. In the travelling-wave regime assumption, this system possesses a Lie-Poisson structure on the manifold C{sup 2} {times} C{sup 2}. In the case where the medium is assumed to be isotropic, this system exhibits invariance under the Hamiltonian action of two copies of the rotation group, S{sup 1}, and actually reduces to a lower-dimensional system on the two-sphere, S{sup 2}. We study the dynamics on the reduced space and examine the structure of the phase portrait by determining the fixed points and infinite-period homoclinic and heteroclinic orbits; we concentrate on presenting some exotic behaviour that occurs when some parameters are varied, and we also show special solutions associated with some of the above-mentioned orbits. Last, we demonstrate the existence of complex dynamics when the system is subject to certain classes of Hamiltonian perturbations. To this end, we make use of the Melnikov method to analytically show the occurrence of either horseshoe chaos, or Arnold diffusion. 19 refs.
BOOK REVIEW: Nonlinear Dynamics: Integrability, Chaos and Patterns
NASA Astrophysics Data System (ADS)
Grammaticos, B.
2004-02-01
When the editorial office of Journal of Physics A: Mathematical and General of the Institute of Physics Publishing asked me to review a book on nonlinear dynamics I experienced an undeniable apprehension. Indeed, the domain is a rapidly expanding one and writing a book aiming at a certain degree of completeness looks like an almost impossible task. My uneasiness abated somewhat when I saw the names of the authors, two well-known specialists of the nonlinear domain, but it was only when I held the book in my hands that I felt really reassured. The book is not just a review of the recent (and less so) findings on nonlinear systems. It is also a textbook. The authors set out to provide a detailed, step by step, introduction to the domain of nonlinearity and its various subdomains: chaos, integrability and pattern formation (although this last topic is treated with far less detail than the other two). The public they have in mind is obviously that of university students, graduate or undergraduate, who are interested in nonlinear phenomena. I suspect that a non-negligible portion of readers will be people who have to teach topics which figure among those included in the book: they will find this monograph an excellent companion to their course. The book is written in a pedagogical way, with a profusion of examples, detailed explanations and clear diagrams. The point of view is that of a physicist, which to my eyes is a major advantage. The mathematical formulation remains simple and perfectly intelligible. Thus the reader is not bogged down by fancy mathematical formalism, which would have discouraged the less experienced ones. A host of exercises accompanies every chapter. This will give the novice the occasion to develop his/her problem-solving skills and acquire competence in the use of nonlinear techniques. Some exercises are quite straightforward, like `verify the relation 14.81'. Others are less so, such as `prepare a write-up on a) frequency-locking and b) devil's staircase'. I do not quite grasp the usefulness of such project-like exercises. Projects must be assigned by the person who indeed teaches the course. There are things that I really like a lot in this book. For instance, the section on `chaos in nonlinear electronic circuits' is particularly interesting. It offers a simple and rather inexpensive way to visualize chaos in the laboratory. The closing section of the book devoted to technological applications of nonlinear dynamics is also quite useful. The fact that the treatment remains rather elementary, based on review articles and monographs rather than research articles, adds to the intelligibility of the chapter, which will certainly prove stimulating to many a student. Of course, not everything can be perfect, and a 600-page book is bound to have some weak points. I find the treatment of quantum chaos rather sketchy and that of chaotic scattering even more so. Also, while the authors are aware of the importance of complex time in integrability, they do not attempt an explanation of the fundamental puzzle: `why, while the physical time is par excellence real, do we need a complex time in order to study the long-time behaviour of dynamical systems?'. Also the book devotes just four pages to integrable discrete systems. Given the tremendous development of this domain over the past decade, this short presentation is not doing justice to the subject. (However as the present reviewer is editing Springer Lecture Notes in Physics on precisely `Integrable Discrete Systems', to appear in early 2004, he would be the last one to complain about the absence of more details on the matter in the present book.) To sum it up, the monograph of Lakshmanan and Rajasekar is a book written by physicists and for physicists. It will be of interest to both the experienced practitioner and to the uninitiated. Its main quality resides in its thorough, pedagogical approach to the matter. Moreover the relaxed, not too formal, style makes for easy reading. Given that I am writing this review just a few days before Christmas I cannot hel
Nonlinear Dynamics In Quantum Physics -- Quantum Chaos and Quantum Instantons
H. Kröger
2003-02-21
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.
New Role for Nonlinear Dynamics and Chaos in Integrated Semiconductor Laser Technology
NASA Astrophysics Data System (ADS)
Yousefi, M.; Barbarin, Y.; Beri, S.; Bente, E. A. J. M.; Smit, M. K.; Nötzel, R.; Lenstra, D.
2007-01-01
Using an integrated colliding-pulse mode-locked semiconductor laser, we demonstrate the existence of nonlinear dynamics and chaos in photonic integrated circuits (PICs) by demonstrating a period-doubling transition into chaos. Unlike their stand-alone counterparts, the dynamics of PICs are more stable over the lifetime of the system, reproducible from batch to batch and on faster time scales due to the small sizes of PICs.
New role for nonlinear dynamics and chaos in integrated semiconductor laser technology.
Yousefi, M; Barbarin, Y; Beri, S; Bente, E A J M; Smit, M K; Nötzel, R; Lenstra, D
2007-01-26
Using an integrated colliding-pulse mode-locked semiconductor laser, we demonstrate the existence of nonlinear dynamics and chaos in photonic integrated circuits (PICs) by demonstrating a period-doubling transition into chaos. Unlike their stand-alone counterparts, the dynamics of PICs are more stable over the lifetime of the system, reproducible from batch to batch and on faster time scales due to the small sizes of PICs. PMID:17358775
Lee, Hae June
A universal characterization of nonlinear self-oscillation and chaos in various particle of nonlinear fluid simulations. © 1998 American Institute of Physics. S0003-6951 98 01012-2 The self-oscillation The comprehensive parameter space of self-oscillation and its period-doubling route to chaos are shown for bounded
Controlling spatiotemporal chaos in active dissipative-dispersive nonlinear systems
NASA Astrophysics Data System (ADS)
Gomes, S. N.; Pradas, M.; Kalliadasis, S.; Papageorgiou, D. T.; Pavliotis, G. A.
2015-08-01
We present an alternative methodology for the stabilization and control of infinite-dimensional dynamical systems exhibiting low-dimensional spatiotemporal chaos. We show that with an appropriate choice of time-dependent controls we are able to stabilize and/or control all stable or unstable solutions, including steady solutions, traveling waves (single and multipulse ones or bound states), and spatiotemporal chaos. We exemplify our methodology with the generalized Kuramoto-Sivashinsky equation, a paradigmatic model of spatiotemporal chaos, which is known to exhibit a rich spectrum of wave forms and wave transitions and a rich variety of spatiotemporal structures.
Pattern selection and low-dimensional chaos in systems of coupled nonlinear oscillators
Bishop, A.
1984-01-01
The longtime behavior of a number of one- and two-dimensional driven, dissipative, dispersive, many-degree-of-freedom systems is studied. It is shown numerically that the attractors are characterized by strong mode-locking into a small number of (nonlinear) modes. On the basis of the observed profiles, estimates of chaotic attractor dimensions, and projections into nonlinear mode bases, it is argued that the same few modes may (in these extended systems) give a unified picture of spatial pattern selection, low-dimensional chaos, and coexisting coherence and chaos. Analytic approaches to this class of problem are summarized.
Chaos in a double driven dissipative nonlinear oscillator
H. H. Adamyan; S. B. Manvelyan; G. Yu. Kryuchkyan
2001-06-19
We propose an anharmonic oscillator driven by two periodic forces of different frequencies as a new time-dependent model for investigating quantum dissipative chaos. Our analysis is done in the frame of statistical ensemble of quantum trajectories in quantum state diffusion approach. Quantum dynamical manifestation of chaotic behavior, including the emergence of chaos, properties of strange attractors, and quantum entanglement are studied by numerical simulation of ensemble averaged Wigner function and von Neumann entropy.
Socioeconomic Risk Moderates the Link Between Household Chaos and Maternal Executive Function
Socioeconomic Risk Moderates the Link Between Household Chaos and Maternal Executive Function Kirby.e., effortful regulation of attention and memory), and whether it varied as a function of socioeconomic risk (i), and 2) this link would be strongest in the most socioeco- nomically distressed or lowest-socioeconomic
Influence of nonlinear conductance and coscphi term on the onset of chaos in Josephson junctions
Aiello, A.; Barone, A.; Ovsyannikov, G.A.
1984-07-01
Chaotic behavior in a Josephson junction is investigated. Threshold curves for the onset of chaos in the rf current-frequency plane are computed by means of Kolmogorov entropy. Both the nonlinear dependence of the quasiparticle current I/sub N/(V) and the coscphi term have been considered to account for previously reported experimental results.
NASA Technical Reports Server (NTRS)
Hooker, John C.
1991-01-01
Three measures of nonlinear chaos (fractal dimension, Approximate Entropy (ApEn), and Lyapunov exponents) were studied as potential measures of cardiovascular condition. It is suggested that these measures have potential in the assessment of cardiovascular condition in environments of normal cardiovascular stress (normal gravity on the Earth surface), cardiovascular deconditioning (microgravity of space), and increased cardiovascular stress (lower body negative pressure (LBNP) treatments).
Title of Dissertation: NONLINEAR DYNAMICS OF EXTENDED SYSTEMS: CHAOS FRONTS, RARE INTENSE EVENTS,
Anlage, Steven
ABSTRACT Title of Dissertation: NONLINEAR DYNAMICS OF EXTENDED SYSTEMS: CHAOS FRONTS, RARE INTENSE EVENTS, AND GROWING NETWORKS Jong-Won Kim, Doctor of Philosophy, 2002 Dissertation directed by: Professor INTENSE EVENTS, AND GROWING NETWORKS by Jong-Won Kim Dissertation submitted to the Faculty of the Graduate
NASA Astrophysics Data System (ADS)
Kalaga, J. K.; Leo?ski, W.; Kowalewska-Kud?aszyk, A.
2014-12-01
A model of a nonlinear, damped kicked oscillator is discussed. For such a model intra-mode correlations described by mutual information parameter I[?] based on the Wehrl entropy are considered. Furthermore, the system's quantum evolution is compared to its classical counterpart. The mutual information parameter is discussed as a proposal for quantum chaos' witness.
Chaos Theory as a Model for Life Transitions Counseling: Nonlinear Dynamics and Life's Changes
ERIC Educational Resources Information Center
Bussolari, Cori J.; Goodell, Judith A.
2009-01-01
Chaos theory is presented for counselors working with clients experiencing life transitions. It is proposed as a model that considers disorder, unpredictability, and lack of control as normal parts of transition processes. Nonlinear constructs from physics are adapted for use in counseling. The model provides a method clients can use to…
Complexity, Chaos, and Nonlinear Dynamics: A New Perspective on Career Development Theory
ERIC Educational Resources Information Center
Bloch, Deborah P.
2005-01-01
The author presents a theory of career development drawing on nonlinear dynamics and chaos and complexity theories. Career is presented as a complex adaptive entity, a fractal of the human entity. Characteristics of complex adaptive entities, including (a) autopiesis, or self-regeneration; (b) open exchange; (c) participation in networks; (d)…
E. V. Felk; A. P. Kuznetsov; A. V. Savin
2013-11-13
The effect of small nonlinear dissipation on the dynamics of system with stochastic web which is linear oscillator driven by pulses is studied. The scenario of coexisting attractors evolution with the increase of nonlinear dissipation is revealed. It is shown that the period-doubling transition to chaos is possible only for third order resonance and only hard transitions can be seen for all other resonances.
INTRODUCTION: Introduction to Nonlinear Dynamics and Chaos Theory
NASA Astrophysics Data System (ADS)
McCauley, Joseph L.
1988-01-01
Chapters 1-3 of these lectures were given at the University of Oslo during my academic free half-year August l985-January 1986 which I spent at the Institute for Energy Technology (IFE). Chapter 4 was given by T Riste during my journeys to other Scandinavian institutions where I held seminars covering much of what is reflected in Chapter 5. That chapter represents a contribution to chaos theory that was carried out in collaboration with J Palmore. In place of the universal properties of unimodal maps, which are well-treated in the books by Cvitanovic and Schuster, I have instead based my elementary introduction to scaling and universality upon the damped driven pendulum and circle maps, which are of current interest to experimenters at IFE and elsewhere, as is reflected in the literature over the past year. Also, the circle map has not been so well-treated pedagogically in available texts. The discussion in Chapter 3 is not advanced, but it should prepare the reader for a better appreciation of the literature in that field. I should say that these lectures for the most part were written for students, for experimenters, and for curious theorists from other fields in physics, but not for the experts in nonlinear dynamics. For example, Chapter 3 ends where the hardest work begins. Tn preparing the lectures, I drew heavily upon the books by Arnol'd, Jorna, Jordan and Smith, Lichtenberg and Lieberman, and Schuster, and upon numerous journal articles. The level of the lectures is that of a second year graduate course at the University of Houston, but beginning with undergraduate-level topics in ordinary differential equations. Throughout, I have emphasized my interest in the connection of nonlinear dynamics to statistical mechanics, as well as my interest in "computer arithmetic". I hope that the reader will also find these subjects to be of interest since they have provided me with a great deal of intellectual enjoyment. My free-half-year at IFE would have been impossible without the aid and moral support provided by Tormod Riste. Gerd Jarrett helped and befriended me and my family in more ways than I should wish to count, and the entire physics staff at IFE, E Andersen, A F Andresen, G Jarrett, K Otnes, T Riste, A Skjeltorp and O. Steinsvoll helped to slake my heavy thirst for Norwegian history and culture, and agreed from the start to speak Norwegian to me daily in order to help me in my effort to learn to speak that language. Gerd Jarrett performed above and beyond the call of duty by tirelessly typing the original lecture notes, which appear as the internal report IFE/I-86/003 + KGF. I also owe thanks to Lynn Smith for typing the revisions that yielded this final version at the University of Houston. I willingly thank J Fröyland, J Palmore and F Ravndal for several helpful discussions and comments, and M Golubitsky, J Palmore, D Schiller and O Steinsvoll for proof-reading several of the chapters (blame for remaining errors is entirely my own, however). I also wish to thank P Alström, E Aurell, T Bohr, P Cvitanovic, E H Hauge, P C Hemmer, J Hertz, J Ketoja, T Kohonen, J Kurkijärvi, K Lindgren, J Myrheim, R Ritala and S Stenholm for interesting discussions during my journeys to other Scandinavian institutions. I am especially grateful to J Fröyland for guestfriendship at the University of Oslo, and to A K M F Hussain for encouraging in 1984 that I should put my lecture notes into print. Finally, my academic free-year was supported financially by the American Scandinavian Foundation, NORDITA and the University of Houston. All my travel costs within Scandinavia were paid by NORDITA
18.385 Nonlinear Dynamics and Chaos, Fall 2002
Rosales, Rodolfo
Nonlinear dynamics with applications. Intuitive approach with emphasis on geometric thinking, computational and analytical methods. Extensive use of demonstration software. Topics: Bifurcations. Phase plane. Nonlinear ...
Household chaos moderates the link between maternal attribution bias and parenting
Wang, Z.; Deater-Deckard, K.; Bell, M.A.
2013-01-01
Objective Parents who attribute child misbehavior to children's intentions and dismiss situational factors tend to show more hostility and less warmth in their parenting behavior, and are at greater risk for maltreatment. We extended this literature by investigating the role of household chaos as a moderator of the link between maternal attribution biases and parenting behaviors. Design The current sample included 160 mothers of 3- to7-year-old children. Mothers provided reports on their attribution biases and household chaos levels. Maternal negativity and positivity were measured using self-reports and observers’ ratings. Results The links between attribution bias and parenting behavior were stronger in more chaotic environments, with the moderating effect of chaos being particularly strong for internal attribution bias. Conclusions The findings point to the importance of social cognitive biases in the etiology of maternal behavior in family contexts that lack order and predictability. PMID:24358017
A. V. Dvornichenko
2012-11-06
We study an influence of nonlinear dissipation and external perturbations onto transition scenarious to chaos in Lorenz-Haken system. It will be show that varying in external potential parameters values leads to parameters domain formation of chaos realization. In the modified Lorenz-Haken system transitions from regular to chaotic dynamics can be of Ruelle-Takens scenario, Feigenbaum scenario, or through intermittency.
Minimal control synthesis adaptive control of nonlinear systems: utilizing the properties of chaos.
di Bernardo, M; Stoten, D P
2006-09-15
This paper discusses a novel approach to the control of chaos based on the use of the adaptive minimal control synthesis algorithm. The strategies presented are based on the explicit exploitation of different properties of chaotic systems including the boundedness of the chaotic attractors and their topological transitivity (or ergodicity). It is shown that chaos can be exploited to synthesize more efficient control techniques for nonlinear systems. For instance, by using the ergodicity of the chaotic trajectory, we show that a local adaptive control strategy can be used to synthesize a global controller. An application is to the swing-up control of a double inverted pendulum. PMID:16893794
12.006J / 18.353J / 2.050J Nonlinear Dynamics I: Chaos, Fall 2006
Rothman, Daniel
This course provides an introduction to the theory and phenomenology of nonlinear dynamics and chaos in dissipative systems. The content is structured to be of general interest to undergraduates in science and engineering.
Berman, G.P.; Bulgakov, E.N.; Campbell, D.K.; Krive, I.V.
1997-10-01
We consider Aharonov-Bohm oscillations in a mesoscopic semiconductor ring threaded by both a constant magnetic flux and a time-dependent, resonant magnetic field with one or two frequencies. Working in the ballistic regime, we establish that the theory of {open_quotes}quantum nonlinear resonance{close_quotes} applies, and thus that this system represents a possible solid-state realization of {open_quotes}quantum nonlinear resonance{close_quotes} and {open_quotes}quantum chaos.{close_quotes} In particular, we investigate the behavior of the time-averaged electron energy at zero temperature in the regimes of (i) an isolated quantum nonlinear resonance and (ii) the transition to quantum chaos, when two quantum nonlinear resonances overlap. The time-averaged energy exhibits sharp resonant behavior as a function of the applied constant magnetic flux, and has a staircase dependence on the amplitude of the external time-dependent field. In the chaotic regime, the resonant behavior exhibits complex structure as a function of flux and frequency. We compare and contrast the quantum chaos expected in these mesoscopic {open_quotes}solid-state atoms{close_quotes} with that observed in Rydberg atoms in microwave fields, and discuss the prospects for experimental observation of the effects we predict. {copyright} {ital 1997} {ital The American Physical Society}
Nonlinear elasticity of cross-linked networks
NASA Astrophysics Data System (ADS)
John, Karin; Caillerie, Denis; Peyla, Philippe; Raoult, Annie; Misbah, Chaouqi
2013-04-01
Cross-linked semiflexible polymer networks are omnipresent in living cells. Typical examples are actin networks in the cytoplasm of eukaryotic cells, which play an essential role in cell motility, and the spectrin network, a key element in maintaining the integrity of erythrocytes in the blood circulatory system. We introduce a simple mechanical network model at the length scale of the typical mesh size and derive a continuous constitutive law relating the stress to deformation. The continuous constitutive law is found to be generically nonlinear even if the microscopic law at the scale of the mesh size is linear. The nonlinear bulk mechanical properties are in good agreement with the experimental data for semiflexible polymer networks, i.e., the network stiffens and exhibits a negative normal stress in response to a volume-conserving shear deformation, whereby the normal stress is of the same order as the shear stress. Furthermore, it shows a strain localization behavior in response to an uniaxial compression. Within the same model we find a hierarchy of constitutive laws depending on the degree of nonlinearities retained in the final equation. The presented theory provides a basis for the continuum description of polymer networks such as actin or spectrin in complex geometries and it can be easily coupled to growth problems, as they occur, for example, in modeling actin-driven motility.
Nonlinear elasticity of cross-linked networks.
John, Karin; Caillerie, Denis; Peyla, Philippe; Raoult, Annie; Misbah, Chaouqi
2013-04-01
Cross-linked semiflexible polymer networks are omnipresent in living cells. Typical examples are actin networks in the cytoplasm of eukaryotic cells, which play an essential role in cell motility, and the spectrin network, a key element in maintaining the integrity of erythrocytes in the blood circulatory system. We introduce a simple mechanical network model at the length scale of the typical mesh size and derive a continuous constitutive law relating the stress to deformation. The continuous constitutive law is found to be generically nonlinear even if the microscopic law at the scale of the mesh size is linear. The nonlinear bulk mechanical properties are in good agreement with the experimental data for semiflexible polymer networks, i.e., the network stiffens and exhibits a negative normal stress in response to a volume-conserving shear deformation, whereby the normal stress is of the same order as the shear stress. Furthermore, it shows a strain localization behavior in response to an uniaxial compression. Within the same model we find a hierarchy of constitutive laws depending on the degree of nonlinearities retained in the final equation. The presented theory provides a basis for the continuum description of polymer networks such as actin or spectrin in complex geometries and it can be easily coupled to growth problems, as they occur, for example, in modeling actin-driven motility. PMID:23679463
ERIC Educational Resources Information Center
Crutchfield, James P.; And Others
1986-01-01
Discusses how the discovery of chaos has created a new paradigm in scientific modeling and how findings are contributing to changes in thought about many different branches of science. Includes explanations and examples of how chaotic behavior can be understood. (ML)
Bifurcation and chaos analysis of a nonlinear electromechanical coupling relative rotation system
NASA Astrophysics Data System (ADS)
Liu, Shuang; Zhao, Shuang-Shuang; Sun, Bao-Ping; Zhang, Wen-Ming
2014-09-01
Hopf bifurcation and chaos of a nonlinear electromechanical coupling relative rotation system are studied in this paper. Considering the energy in air-gap field of AC motor, the dynamical equation of nonlinear electromechanical coupling relative rotation system is deduced by using the dissipation Lagrange equation. Choosing the electromagnetic stiffness as a bifurcation parameter, the necessary and sufficient conditions of Hopf bifurcation are given, and the bifurcation characteristics are studied. The mechanism and conditions of system parameters for chaotic motions are investigated rigorously based on the Silnikov method, and the homoclinic orbit is found by using the undetermined coefficient method. Therefore, Smale horseshoe chaos occurs when electromagnetic stiffness changes. Numerical simulations are also given, which confirm the analytical results.
Nonlinear characteristics (chaos) of high-power microwave (HPM) sources
NASA Astrophysics Data System (ADS)
Gaudet, John A.; Luginsland, John W.; Wallace, Christopher B.
2000-07-01
Recent advances in the understanding of dynamical systems and chaotic behavior have resulted in the investigation of HPM source design issues. Modern dynamical systems theory can improve our understanding of the dynamics of space charge dominated beams and the RF waveforms generated by them. This paper will review the work done to date using time series analysis techniques to study the state space dynamics of high power microwave sources using simulation (particle-in-cell) code results. Low-dimensional chaos has been observed in simulation results from a variety of HPM sources, including the MILO (Magnetically Insulated Line Oscillator). Additionally, the particle behavior within the diode portion of HPM tubes can have chaotic characteristics. Knowing when these features occur and how they develop are important first steps in our ability to control and/or eliminate them. Central to understanding source behavior is the initial use of joint time frequency analysis to assess whether the dynamics are stationary or not. Subsequently we use delay coordinate embedding techniques to reconstruct an effective state space global dynamics. From this, Poincare sections are examined. Lyapunov exponents are then calculated to determine whether the behavior of the source is noise or deterministic chaos.
Nonlinear oscillations, bifurcations and chaos of functionally graded materials plate
Y. X. Hao; L. H. Chen; W. Zhang; J. G. Lei
2008-01-01
An analysis on the nonlinear dynamics of a simply supported functionally graded materials (FGMs) rectangular plate subjected to the transversal and in-plane excitations is presented in a thermal environment for the first time. Material properties are assumed to be temperature dependent. Based on Reddy's third-order plate theory, the nonlinear governing equations of motion for the FGM plates are derived using
Facilitating Joint Chaos and Fractal Analysis of Biosignals through Nonlinear Adaptive Filtering
Gao, Jianbo; Hu, Jing; Tung, Wen-wen
2011-01-01
Background Chaos and random fractal theories are among the most important for fully characterizing nonlinear dynamics of complicated multiscale biosignals. Chaos analysis requires that signals be relatively noise-free and stationary, while fractal analysis demands signals to be non-rhythmic and scale-free. Methodology/Principal Findings To facilitate joint chaos and fractal analysis of biosignals, we present an adaptive algorithm, which: (1) can readily remove nonstationarities from the signal, (2) can more effectively reduce noise in the signals than linear filters, wavelet denoising, and chaos-based noise reduction techniques; (3) can readily decompose a multiscale biosignal into a series of intrinsically bandlimited functions; and (4) offers a new formulation of fractal and multifractal analysis that is better than existing methods when a biosignal contains a strong oscillatory component. Conclusions The presented approach is a valuable, versatile tool for the analysis of various types of biological signals. Its effectiveness is demonstrated by offering new important insights into brainwave dynamics and the very high accuracy in automatically detecting epileptic seizures from EEG signals. PMID:21915312
Hazledine, Saul; Sun, Jongho; Wysham, Derin; Downie, J. Allan; Oldroyd, Giles E. D.; Morris, Richard J.
2009-01-01
Legume plants form beneficial symbiotic interactions with nitrogen fixing bacteria (called rhizobia), with the rhizobia being accommodated in unique structures on the roots of the host plant. The legume/rhizobial symbiosis is responsible for a significant proportion of the global biologically available nitrogen. The initiation of this symbiosis is governed by a characteristic calcium oscillation within the plant root hair cells and this signal is activated by the rhizobia. Recent analyses on calcium time series data have suggested that stochastic effects have a large role to play in defining the nature of the oscillations. The use of multiple nonlinear time series techniques, however, suggests an alternative interpretation, namely deterministic chaos. We provide an extensive, nonlinear time series analysis on the nature of this calcium oscillation response. We build up evidence through a series of techniques that test for determinism, quantify linear and nonlinear components, and measure the local divergence of the system. Chaos is common in nature and it seems plausible that properties of chaotic dynamics might be exploited by biological systems to control processes within the cell. Systems possessing chaotic control mechanisms are more robust in the sense that the enhanced flexibility allows more rapid response to environmental changes with less energetic costs. The desired behaviour could be most efficiently targeted in this manner, supporting some intriguing speculations about nonlinear mechanisms in biological signaling. PMID:19675679
SOMEADVANCES IN NONLINEAR SPEECH MODELING USING MODULATIONS, FRACTALS, AND CHAOS
Paragios, Nikos
@cs.ntua.gr. ABSTRACT In this paper we briefly summarize our ongoing work on modeling nonlinear structures in speech acoustics and 1D plane wave propagation of the sound in the vocal tract. This approximation leads aerodynamic phenomena during the speech production that cannot be accounted for by the lin ear model. In our
Chaos and the quantum: how nonlinear effects can explain certain quantum paradoxes
NASA Astrophysics Data System (ADS)
McHarris, Wm C.
2011-07-01
In recent years we have suggested that many of the so-called paradoxes resulting from the Copenhagen interpretation of quantum mechanics could well have more logical parallels based in nonlinear dynamics and chaos theory. Perhaps quantum mechanics might not be strictly linear as has been commonly postulated, and indeed, during the past year experimentalists have discovered signatures of chaos in a definitely quantum system. As an illustration of what can go wrong when quantum effects are forced into a linear interpretation, I examine Bell-type inequalities. In conventional derivations of such inequalities, classical systems are found to impose upper limits on the statistical correlations between, say, the properties of a pair of separated but entangled particles, whereas quantum systems allow greater correlations. Numerous experiments have upheld the quantum predictions (greater statistical correlations than allowed classically), which has led to inferences such as the instantaneous transmission of information between effectively infinitely separated particles — Einstein's "spooky action-at-a-distance," incompatible with relativity. I argue that there is nothing wrong with the quantum mechanical side of such derivations (the usual point of attack by those attempting to debunk Bell-type arguments), but implicit in the derivations on the classical side is the assumption of independent, uncorrelated particles. As a result, one is comparing uncorrelated probabilities versus conditional probabilities rather than comparing classical versus quantum mechanics, making moot the experimental inferences. Further, nonlinear classical systems are known to exhibit correlations that can easily be as great as and overlap with quantum correlations — so-called nonextensive thermodynamics with its nonadditive entropy has verified this with numerous examples. Perhaps quantum mechanics does contain fundamental nonlinear elements. Nonlinear dynamics and chaos theory could well provide a bridge between the determinism so dear to Einstein and the statisical interpretation of the Copenhagen school. Einstein and Bohr both could have been right in their debates.
Gauthier, Daniel
for our position sensor. Our work extends the Larsen effect, a phenomenon where positive audio feedbackSubwavelength Position Sensing Using Nonlinear Feedback and Wave Chaos Seth D. Cohen, Hugo L. D. de with a complex structured radio-frequency field generated using wave chaos and nonlinear feedback. We operate
Mutation and Chaos in Nonlinear Models of Heredity
Nawi, Ashraf Mohamed
2014-01-01
We shall explore a nonlinear discrete dynamical system that naturally occurs in population systems to describe a transmission of a trait from parents to their offspring. We consider a Mendelian inheritance for a single gene with three alleles and assume that to form a new generation, each gene has a possibility to mutate, that is, to change into a gene of the other kind. We investigate the derived models and observe chaotic behaviors of such models. PMID:25136693
A purely nonlinear route to transition approaching the edge of chaos in a boundary layer
NASA Astrophysics Data System (ADS)
Cherubini, S.; De Palma, P.; Robinet, J.-Ch; Bottaro, A.
2012-06-01
The understanding of transition in shear flows has recently progressed along new paradigms based on the central role of coherent flow structures and their nonlinear interactions. We follow such paradigms to identify, by means of a nonlinear optimization of the energy growth at short time, the initial perturbation which most easily induces transition in a boundary layer. Moreover, a bisection procedure has been used to identify localized flow structures living on the edge of chaos, found to be populated by hairpin vortices and streaks. Such an edge structure appears to act as a relative attractor for the trajectory of the laminar base state perturbed by the initial finite-amplitude disturbances, mediating the route to turbulence of the flow, via the triggering of a regeneration cycle of ? and hairpin structures at different space and time scales. These findings introduce a new, purely nonlinear scenario of transition in a boundary-layer flow.
Pattern selection and instability in nonlinear wave equation: an aspect of soliton and chaos
Imada, M.
1985-01-01
Pattern selection problems are found in a variety of phenomena. Fluid dynamical systems and nonlinear diffusion phenomena give typical examples of pattern formation problems in dissipative systems. In some cases the dissipation reduces the effective dimension of the system, and this fact leads to several strikingly universal behaviors which were initially found in simple model systems with a few degrees of freedom. Nonlinear wave equations themselves, however, describes systems without dissipation in which the situation is more complicated. In spite of this complexity, many completely integrable systems are known in nonlinear wave equations, where neither ergodicity nor chaos is expected. With addition of small perturbation to completely integrable systems, one can see the growth of instability and the role of coherent structures in the pattern selection problem. Two aspects are briefly discussed in the following sections.
Mutation and Chaos in Nonlinear Models of Heredity
Nasir Ganikhodjaev; Mansoor Saburov; Ashraf Mohamed Nawi
2013-04-21
In this short communication, we shall explore a nonlinear discrete dynamical system that naturally occurs in population systems to describe a transmission of a trait from parents to their offspring. We consider a Mendelian inheritance for a single gene with three alleles and assume that to form a new generation, each gene has a possibility to mutate, that is, to change into a gene of the other kind. We investigate the derived models. A numerical simulation assists us to get some clear picture about chaotic behaviors of such models.
NASA Astrophysics Data System (ADS)
Rizzato, Felipe; Lopes, Sérgio
1997-08-01
In this paper we examine the spatio-temporal dynamics of two nonlinearly coupled wave triplets(Phys. D, accepted (1997).). When spatial dependence is suppressed, the homogeneous manifold so obtained can be chaotic or regular. If chaotic, it drives energy diffusion from long to small wavelengths as soon as inhomogeneous perturbations are added to the system(Phys. Rev. E 54) 3239 (1996).. If regular, one has two possibilities: (i) energy diffusion is again present if the inhomogeneous modes are linearly unstable, or (ii) energy diffusion is totally absent if the inhomogeneous modes are linearly stable. We also discuss related topics as turbulence, spatio-temporal chaos, and thermalization.
Ductile Web Fracture Initiation in Steel Shear Links Shih-Ho Chao, S.M.ASCE1
Chao, Shih-Ho
Ductile Web Fracture Initiation in Steel Shear Links Shih-Ho Chao, S.M.ASCE1 ; Kapil Khandelwal, S-detailed short shear links can exhibit stable and ductile cyclic behavior. Recent tests of prevailing A992 rolled shapes revealed that shear links designed according to current seismic specifications can fail by ductile
Hamiltonian chaos in a nonlinear polarized optical beam
David, D.; Holm, D.D.; Tratnik, M.V. )
1989-01-01
This lecture concerns the applications of ideas about temporal complexity in Hamiltonian systems to the dynamics of an optical laser beam with arbitrary polarization propagating as a traveling wave in a medium with cubically nonlinear polarizability. We use methods from the theory of Hamiltonian systems with symmetry to study the geometry of phase space for this optical problem, transforming from C{sup 2} to S{sup 3} {times} S{sup 1}, first, and then to S{sup 2} {times} (J, {theta}), where (J, {theta}) is a symplectic action-angle pair. The bifurcations of the phase portraits of the Hamiltonian motion on S{sub 2} are classified and displayed graphically. These bifurcations take place when either J (the beam intensity), or the optical parameters of the medium are varied. After this bifurcation analysis has shown the existence of various saddle connections on S{sup 2}, the Melnikov method is used to demonstrate analytically that the traveling-wave dynamics of a polarized optical laser pulse develops chaotic behavior in the form of Smale horseshoes when propagating through spatially periodic perturbations in the optical parameters of the medium. 20 refs., 7 figs.
Turbulent Fluid Motion 6: Turbulence, Nonlinear Dynamics, and Deterministic Chaos
NASA Technical Reports Server (NTRS)
Deissler, Robert G.
1996-01-01
Several turbulent and nonturbulent solutions of the Navier-Stokes equations are obtained. The unaveraged equations are used numerically in conjunction with tools and concepts from nonlinear dynamics, including time series, phase portraits, Poincare sections, Liapunov exponents, power spectra, and strange attractors. Initially neighboring solutions for a low-Reynolds-number fully developed turbulence are compared. The turbulence is sustained by a nonrandom time-independent external force. The solutions, on the average, separate exponentially with time, having a positive Liapunov exponent. Thus, the turbulence is characterized as chaotic. In a search for solutions which contrast with the turbulent ones, the Reynolds number (or strength of the forcing) is reduced. Several qualitatively different flows are noted. These are, respectively, fully chaotic, complex periodic, weakly chaotic, simple periodic, and fixed-point. Of these, we classify only the fully chaotic flows as turbulent. Those flows have both a positive Liapunov exponent and Poincare sections without pattern. By contrast, the weakly chaotic flows, although having positive Liapunov exponents, have some pattern in their Poincare sections. The fixed-point and periodic flows are nonturbulent, since turbulence, as generally understood, is both time-dependent and aperiodic.
Dynamical Systems on Three Manifolds Part I: Knots, Links and Chaos
Yi Song; S. P. Banks; David Diaz
2007-06-16
In this paper, we give an explicit construction of dynamical systems (defined within a solid torus) containing any knot (or link) and arbitrarily knotted chaos. The first is achieved by expressing the knots in terms of braids, defining a system containing the braids and extending periodically to obtain a system naturally defined on a torus and which contains the given knotted trajectories. To get explicit differential equations for dynamical systems containing the braids, we will use a certain function to define a tube neigbourhood of the braid. The second one, generating chaotic systems, is realized by modeling the Smale horseshoe.
Chaos and related nonlinear noise phenomena in Josephson tunnel junctions
Miracky, R.F.
1984-07-01
The nonlinear dynamics of Josephson tunnel junctions shunted by a resistance with substantial self-inductance have been thoroughly investigated. The current-voltage characteristics of these devices exhibit stable regions of negative differential resistance. Very large increases in the low-frequency voltage noise with equivalent noise temperatures of 10/sup 6/ K or more, observed in the vicinity of these regions, arise from switching, or hopping, between subharmonic modes. Moderate increases in the noise, with temperatures of about 10/sup 3/ K, arise from chaotic behavior. Analog and digital simulations indicate that under somewhat rarer circumstances the same junction system can sustain a purely deterministic hopping between two unstable subharmonic modes, accompanied by excess low-frequency noise. Unlike the noise-induced case, this chaotic process occurs over a much narrower range in bias current and is destroyed by the addition of thermal noise. The differential equation describing the junction system can be reduced to a one-dimensional mapping in the vicinity of one of the unstable modes. A general analytical calculation of switching processes for a class of mappings yields the frequency dependence of the noise spectrum in terms of the parameters of the mapping. Finally, the concepts of noise-induced hopping near bifurcation thresholds are applied to the problem of the three-photon Josephson parametric amplifier. Analog simulations indicate that the noise rise observed in experimental devices arises from occasional hopping between a mode at the pump frequency ..omega../sub p/ and a mode at the half harmonic ..omega../sub p//2. The hopping is induced by thermal noise associated with the shunt resistance. 71 references.
Improving nonlinear modeling capabilities of functional link adaptive filters.
Comminiello, Danilo; Scarpiniti, Michele; Scardapane, Simone; Parisi, Raffaele; Uncini, Aurelio
2015-09-01
The functional link adaptive filter (FLAF) represents an effective solution for online nonlinear modeling problems. In this paper, we take into account a FLAF-based architecture, which separates the adaptation of linear and nonlinear elements, and we focus on the nonlinear branch to improve the modeling performance. In particular, we propose a new model that involves an adaptive combination of filters downstream of the nonlinear expansion. Such combination leads to a cooperative behavior of the whole architecture, thus yielding a performance improvement, particularly in the presence of strong nonlinearities. An advanced architecture is also proposed involving the adaptive combination of multiple filters on the nonlinear branch. The proposed models are assessed in different nonlinear modeling problems, in which their effectiveness and capabilities are shown. PMID:26057613
Resource Letter: CC-1: Controlling chaos
NASA Astrophysics Data System (ADS)
Gauthier, Daniel J.
2003-08-01
This Resource Letter provides a guide to the literature on controlling chaos. Journal articles, books, and web pages are provided for the following: controlling chaos, controlling chaos with weak periodic perturbations, controlling chaos in electronic circuits, controlling spatiotemporal chaos, targeting trajectories of nonlinear dynamical systems, synchronizing chaos, communicating with chaos, applications of chaos control in physical systems, and applications of chaos control in biological systems.
A Nonlinear Feedback Controller for a Single-Link
Ge, Shuzhi Sam
A Nonlinear Feedback Controller for a Single-Link Flexible Manipulator Based on a Finite Element In this article, a nonlinear dynamic model of a flexible manipulator is derived through finite element method associated with Lagrange approach. The flexible manipulator is modeled as an EulerBernoulli beam driven
The nonlinear bifurcation and chaos of coupled heave and pitch motions of a truss spar platform
NASA Astrophysics Data System (ADS)
Huang, Lei; Liu, Liqin; Liu, Chunyuan; Tang, Yougang
2015-10-01
This paper presents the results from a numerical study on the nonlinear dynamic behaviors including bifurcation and chaos of a truss spar platform. In view of the mutual influences between the heave and the pitch modes, the coupled heave and pitch motion equations of the spar platform hull were established in the regular waves. In order to analyze the nonlinear motions of the platform, three-dimensional maximum Lyapunov exponent graphs and the bifurcation graphs were constructed, the Poincaré maps and the power spectrums of the platform response were calculated. It was found that the platform motions are sensitive to wave frequency. With changing wave frequency, the platform undergoes complicated nonlinear motions, including 1/2 sub-harmonic motion, quasi-periodic motion and chaotic motion. When the wave frequency approaches the natural frequency of the heave mode of the platform, the platform moves with quasi-periodic motion and chaotic motional ternately. For a certain range of wave frequencies, the platform moves with totally chaotic motion. The range of wave frequencies which leads to chaotic motion of the platform increases with increasing wave height. The three-dimensional maximum Lyapunov exponent graphs and the bifurcation graphs reveal the nonlinear motions of the spar platform under different wave conditions.
Detecting Nonlinearity and Edge-of-Chaos Phenomena in Ordinal Data.
Heath, Rachel
2015-07-01
Some but not all algorithms for detecting nonlinearity in experimental data, such as prediction methods and Lyapunov spectra, require a much larger amount of stable continuous data than is generally available from individual human participants. A new method for detecting nonlinearity in relatively short data sets, Monotonic Ectropy, computes the change in Shannon information as ordinal scale values evolve over time by comparing runs of various lengths and directions. This method compares two successive ordinal scale changes with similar monotonic changes for three successive ordinal scale values. The resulting index discriminates a chaotic Henon series from both Gaussian noise and phase-randomised surrogate series, the latter containing the stochastic structure of the Henon series but without the nonlinearity. The empirical utility of the technique is illustrated using mood rating data obtained from two participants, one suffering from chronic depression, the other showing no signs of the disorder. Although Monotonic Ectropy discriminated between the mood ratings of the depressed and nondepressed subjects, evidence for nonlinearity was only obtained using Lempel-Ziv complexity, a measure based on symbolic dynamics. This was probably due to Monotonic Ectropy's unique sensitivity to edge-of-chaos phenomena. PMID:26058334
MZ twinning: chance or determinism? An essay in nonlinear dynamics (chaos).
Philippe, P
1994-01-01
Classically, researchers considered monozygotic twinning (MZT) a random phenomenon. This paper tests the hypothesis with the aid of nonlinear dynamics techniques. The latter can tell true randomness from chance-like variation. Chaos, the endpoint of the threshold state of a nonlinear deterministic system, can mimic constrained randomness. From a practical standpoint, recognizing chaos in a time series data set means that the paradigmatic multifactorial model of causation is essentially ruled out. Specifically, time series of MZ, DZ, and single maternities were analysed. First, spectral analysis was used to uncover periodicities embedded in the series. Second, a singular value decomposition was undertaken to reduce noise from the series. Third, phase space attractors were drawn up that describe the 'asymptotic' trajectory of the system at any time. Results suggested that DZ, MZ, and single maternities shared a similar 32-year periodicity. Owing to two interwoven similar periodicities, the single-maternity cycle kinetics proved to be faster than that of DZ's. The MZ series was the only one to display secondary interacting harmonics, thus eliciting a rather unusual trajectory in the bidimensional phase space. The MZ time points were not spread in a haphazard fashion; on the contrary, a fine structure was present that did not reduce to a limit cycle such as the one characterizing the DZ- or the single-maternity trajectory. It was concluded that a complex nonlinear dynamic underlies MZ twinning. Therefore, calling for extrinsic causes to account for what appears to be random variation overtime would be pointless. MZ twinning should rather be traced to a limited number of intrinsic and deterministic interacting system components. The most likely candidates are presented and discussed. PMID:7985991
Sprott, Julien Clinton
Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 9, No. 1, January, 2005. © 2005 Society for Chaos Theory in Psychology & Life Sciences. Dynamical Models of Happiness J. C. Sprott,1 University to life are discussed Key Words: happiness; hedonics; differential equations; chaos; van der Pol equation
NASA Astrophysics Data System (ADS)
Varney, Philip; Green, Itzhak
2015-02-01
The efficiency of rotating machines can be improved via precisely manufactured bearings with reduced clearances; consequently, the proclivity for rotor-stator contact is increased. A common model used to investigate rotor-stator contact in previous studies is the two degree-of-freedom (DOF) rotor with symmetric support stiffness, where the contact assumes a linear elastic normal restoring force proportional to the rotor-stator interference and a tangential dry Coulomb friction force. Switching between the contacting and non-contacting states creates strong nonlinearity in the equations of motion, and the dynamic response displays a rich profile of behaviors including periodic, quasiperiodic, and chaotic responses via period-doubling, sudden transitions, quasiperiodicity, and intermittency. For the first time, this work emphasizes an asymmetric support stiffness matrix with cross-coupling between the x and y direction stiffnesses. The influence of support asymmetry on the nonlinear rotor response is shown using rotor orbits, frequency spectra, Poincaré sections, and bifurcation diagrams. It is found that the cross-coupling stiffness coefficient kxy has negligible effect on the dynamic response until its magnitude is on the same order as the direct stiffness coefficients. Direct stiffness coefficient asymmetry is shown to affect the rotor's response, where even small asymmetries can qualitatively change the response. Additionally, the importance of including gravity is investigated, and a method is provided for determining the threshold shaft speed above which gravity can be ignored. The dominant route to chaos is period-doubling for the parameters considered here, though other routes to chaos are seen such as a direct transition from periodic to chaotic motion. Finally, observations pertaining to rotor modeling, design, and fault diagnostics are discussed.
Taylor, Richard
Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 12, No. 1, pp. 117-129. © 2008 Society for Chaos Theory in Psychology & Life Sciences Biophilic Fractals and the Visual Journey of Organic Screen
Taylor, Richard
Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 15, No. 1, pp. 129-136. © 2011 Society for Chaos Theory in Psychology & Life Sciences. The Art and Science of Foam Bubbles R. P. Taylor 1 of Nonlinear Dynamics, Psychology, and Life Sciences. Denis Weaire, Stefan Hutzler, Wiebke Drenckhan form
Nonlinear Dynamics and Chaos: Applications for Prediction of Weather and Climate
J. S. Pethkar; A. M. Selvam
2001-04-19
Turbulence, namely, irregular fluctuations in space and time characterize fluid flows in general and atmospheric flows in particular.The irregular,i.e., nonlinear space-time fluctuations on all scales contribute to the unpredictable nature of both short-term weather and long-term climate.It is of importance to quantify the total pattern of fluctuations for predictability studies. The power spectra of temporal fluctuations are broadband and exhibit inverse power law form with different slopes for different scale ranges. Inverse power-law form for power spectra implies scaling (self similarity) for the scale range over which the slope is constant. Atmospheric flows therefore exhibit multiple scaling or multifractal structure.Standard meteorological theory cannot explain satisfactorily the observed multifractal structure of atmospheric flows.Selfsimilar spatial pattern implies long-range spatial correlations. Atmospheric flows therefore exhibit long-range spatiotemporal correlations, namely,self-organized criticality,signifying order underlying apparent chaos. A recently developed non-deterministic cell dynamical system model for atmospheric flows predicts the observed self-organized criticality as intrinsic to quantumlike mechanics governing flow dynamics.The model predictions are in agreement with continuous periodogram spectral analysis of meteorological data sets.
Nonlinear inverse synthesis technique for optical links with lumped amplification.
Le, Son Thai; Prilepsky, Jaroslaw E; Turitsyn, Sergei K
2015-04-01
The nonlinear inverse synthesis (NIS) method, in which information is encoded directly onto the continuous part of the nonlinear signal spectrum, has been proposed recently as a promising digital signal processing technique for combating fiber nonlinearity impairments. However, because the NIS method is based on the integrability property of the lossless nonlinear Schrödinger equation, the original approach can only be applied directly to optical links with ideal distributed Raman amplification. In this paper, we propose and assess a modified scheme of the NIS method, which can be used effectively in standard optical links with lumped amplifiers, such as, erbium-doped fiber amplifiers (EDFAs). The proposed scheme takes into account the average effect of the fiber loss to obtain an integrable model (lossless path-averaged model) to which the NIS technique is applicable. We found that the error between lossless path-averaged and lossy models increases linearly with transmission distance and input power (measured in dB). We numerically demonstrate the feasibility of the proposed NIS scheme in a burst mode with orthogonal frequency division multiplexing (OFDM) transmission scheme with advanced modulation formats (e.g., QPSK, 16QAM, and 64QAM), showing a performance improvement up to 3.5 dB; these results are comparable to those achievable with multi-step per span digital back-propagation. PMID:25968670
Makarov, Vladimir A; Petnikova, V M; Potravkin, N N; Shuvalov, Vladimir V
2012-12-31
It is found that chirped elliptically polarised cnoidal waves can propagate and aperiodic regimes, resembling polarisation chaos, can emerge in an isotropic medium with local and nonlocal components of cubic nonlinearity and second-order frequency dispersion. In the particular case of the formation of the waveguides of the same profile for two circularly polarised components of the light field relevant analytical solutions are derived and the frequencies of chirped components are shown to vary in concord with periodic changes of their intensities. In this case, the nature of the changes in the polarisation state during the light wave propagation depends on the values of nonlinear phase shifts of circularly polarised components of the field during the period and is sensitive to changes in the initial conditions. (nonlinear optical phenomena)
Louis Ehwerhemuepha; Godfrey E. Akpojotor
2013-06-05
The presence of physical systems whose characteristics change in a seemingly erratic manner gives rise to the study of chaotic systems. The characteristics of these systems are due to their hypersensitivity to changes in initial conditions. In order to understand chaotic systems, some sort of simulation and visualization is pertinent. Consequently, in this work, we have simulated and graphically visualized chaos in a driven nonlinear pendulum as a means of introducing chaotic systems. The visualized results obtained which highlight the hypersensitivity of the pendulum to initial conditions can be used to effectively introduce the physics of chaotic system. The simulation and visualization programme is written in Python codes.
Sprott, Julien Clinton
Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 8, No. 3, July, 2004. © 2004 Society for Chaos Theory in Psychology & Life Sciences Dynamical Models of Love J. C. Sprott1 , University may be positive or negative. A similar linear model has been proposed by Rinaldi (1998a) in which
Sprott, Julien Clinton
405 Nonlinear Dynamics, Psychology, and Life Sciences, Vol.10, No.3, pp.405-407. © 2006 Society for Chaos Theory in Psychology & Life Sciences Book Review Images of a Complex World: The Art and Poetry Theory in Psychology and Life Sciences, practitioners in diverse disciplines have come together to foster
Taylor, Richard
Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 19, No. 1, pp. 1-12. © 2015 Society for Chaos Theory in Psychology & Life Sciences. Human Physiological Benefits of Viewing Nature: EEG. P. Taylor, University of Oregon, Eugene, OR Abstract: Psychological and physiological benefits
Sprott, Julien Clinton
Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 12, No. 1, pp. 117-129. © 2008 Society for Chaos Theory in Psychology & Life Sciences Biophilic Fractals and the Visual Journey of Organic Screen, Draves regards his images as evolving artificial life forms and the parameters that generate them
Goldstone, Robert
for Chaos Theory in Psychology & Life Sciences. Innovation, Imitation, and Problem-Solving in a NetworkedNonlinear Dynamics, Psychology, and Life Sciences, Vol. 15, No. 2, pp. 229-252. © 2011 Society played a simple innovation game in a complex problem space, with score feedback provided after each
Chaos-based communications at high bit rates using commercial fibre-optic links.
Argyris, Apostolos; Syvridis, Dimitris; Larger, Laurent; Annovazzi-Lodi, Valerio; Colet, Pere; Fischer, Ingo; García-Ojalvo, Jordi; Mirasso, Claudio R; Pesquera, Luis; Shore, K Alan
2005-11-17
Chaotic signals have been proposed as broadband information carriers with the potential of providing a high level of robustness and privacy in data transmission. Laboratory demonstrations of chaos-based optical communications have already shown the potential of this technology, but a field experiment using commercial optical networks has not been undertaken so far. Here we demonstrate high-speed long-distance communication based on chaos synchronization over a commercial fibre-optic channel. An optical carrier wave generated by a chaotic laser is used to encode a message for transmission over 120 km of optical fibre in the metropolitan area network of Athens, Greece. The message is decoded using an appropriate second laser which, by synchronizing with the chaotic carrier, allows for the separation of the carrier and the message. Transmission rates in the gigabit per second range are achieved, with corresponding bit-error rates below 10(-7). The system uses matched pairs of semiconductor lasers as chaotic emitters and receivers, and off-the-shelf fibre-optic telecommunication components. Our results show that information can be transmitted at high bit rates using deterministic chaos in a manner that is robust to perturbations and channel disturbances unavoidable under real-world conditions. PMID:16292256
Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series
NASA Astrophysics Data System (ADS)
Sugihara, George; May, Robert M.
1990-04-01
An approach is presented for making short-term predictions about the trajectories of chaotic dynamical systems. The method is applied to data on measles, chickenpox, and marine phytoplankton populations, to show how apparent noise associated with deterministic chaos can be distinguished from sampling error and other sources of externally induced environmental noise.
Schieber, Jay D.
Universality and speedup in equilibrium and nonlinear rheology predictions of the fixed slip-link by the The Society of Rheology Articles you may be interested in Numerical study of a slip-link model for polymer of the discrete slip-link model and their effect on nonlinear rheology predictions J. Rheol. 57, 535 (2013); 10
Approximations of the discrete slip-link model and their effect on nonlinear rheology predictions
Schieber, Jay D.
Approximations of the discrete slip-link model and their effect on nonlinear rheology predictions of Rheology Related Articles Concentration fluctuations in polymer solutions under extensional flow J. Rheol://www.journalofrheology.org/masthead #12;Approximations of the discrete slip-link model and their effect on nonlinear rheology predictions
An algebraic criterion for the onset of chaos in nonlinear dynamic systems
NASA Technical Reports Server (NTRS)
Unal, A.; Tobak, M.
1987-01-01
The correspondence between iterated integrals and a noncommutative algebra is used to recast the given dynamical system from the time domain to the Laplace-Borel transform domain. It is then shown that the following algebraic criterion has to be satisfied for the outset of chaos: the limit (as tau approaches infinity and x sub 0 approaches infinity) of ((sigma(k=0) (tau sup k) / (k* x sub 0 sup k)) G II G = 0, where G is the generating power series of the trajectories, the symbol II is the shuffle product (le melange) of the noncommutative algebra, x sub 0 is a noncommutative variable, and tau is the correlation parameter. In the given equation, symbolic forms for both G and II can be obtained by use of one of the currently available symbolic languages such as PLI, REDUCE, and MACSYMA. Hence, the criterion is a computer-algebraic one.
D. M. Basko
2011-09-22
The subject of this study is the long-time equilibration dynamics of a strongly disordered one-dimensional chain of coupled weakly anharmonic classical oscillators. It is argued that chaos in this system has a very particular spatial structure: it can be viewed as a dilute gas of chaotic spots. Each chaotic spot corresponds to a stochastic pump which drives the Arnold diffusion of the oscillators surrounding it, thus leading to their relaxation and thermalization. The most important mechanism of relaxation at long distances is provided by random migration of the chaotic spots along the chain, which bears analogy with variable-range hopping of electrons in strongly disordered solids. The cor- resonding macroscopic transport equations are obtained.
Non-linear dynamics for clinicians: chaos theory, fractals, and complexity at the bedside
of pacemaker cells in the heart or neurons in the brain. Their non-linear coupling generates behaviours unfettered randomness, usually with catastrophic implications) is quite different from this special usage
Nonlinear Viscoelasticity of Actin Transiently Cross-linked with Mutant -Actinin-4
Nonlinear Viscoelasticity of Actin Transiently Cross-linked with Mutant -Actinin-4 Norman Y. Yao1 examine the bulk mechanical behavior of in vitro actin networks cross-linked with wild-type and mutant properties of actin networks cross-linked with mutant Actn4 may represent physical determinants
NSDL National Science Digital Library
Harrison, David M.
This site, from the University of Toronto, provides an overview of chaos theory and concisely explains the characteristics of chaotic systems. The bifurcation of a rabbit population, with the transition to chaos, is presented with several graphs. There are links to various animations and a list of other examples.
Nonlinear vibration and radiation from a panel with transition to chaos induced by acoustic waves
NASA Technical Reports Server (NTRS)
Maestrello, Lucio; Frendi, Abdelkader; Brown, Donald E.
1992-01-01
The dynamic response of an aircraft panel forced at resonance and off-resonance by plane acoustic waves at normal incidence is investigated experimentally and numerically. Linear, nonlinear (period doubling) and chaotic responses are obtained by increasing the sound pressure level of the excitation. The response time history is sensitive to the input level and to the frequency of excitation. The change in response behavior is due to a change in input conditions, triggered either naturally or by modulation of the bandwidth of the incident waves. Off-resonance, bifurcation is diffused and difficult to maintain, thus the panel response drifts into a linear behavior. The acoustic pressure emanated by the panel is either linear or nonlinear as is the vibration response. The nonlinear effects accumulate during the propagation with distance. Results are also obtained on the control of the panel response using damping tape on aluminum panel and using a graphite epoxy panel having the same size and weight. Good agreement is obtained between the experimental and numerical results.
NASA Astrophysics Data System (ADS)
Tél, Tamás
2015-09-01
We intend to show that transient chaos is a very appealing, but still not widely appreciated, subfield of nonlinear dynamics. Besides flashing its basic properties and giving a brief overview of the many applications, a few recent transient-chaos-related subjects are introduced in some detail. These include the dynamics of decision making, dispersion, and sedimentation of volcanic ash, doubly transient chaos of undriven autonomous mechanical systems, and a dynamical systems approach to energy absorption or explosion.
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. PMID:26428572
Periodic solutions and chaos in a non-linear model for the delayed cellular immune response
NASA Astrophysics Data System (ADS)
Canabarro, A. A.; Gléria, I. M.; Lyra, M. L.
2004-10-01
We model the cellular immune response using a set of non-linear delayed differential equations. We observe that the stationary solution becomes unstable above a critical immune response time. The exponents characterizing the approach to this bifurcation point as well as the critical slow dynamics are obtained. In the periodic regime, the minimum virus load is substantially reduced with respect to the stationary solution. Further increasing the delay time, the dynamics display a series of bifurcations evolving to a chaotic regime characterized by a set of 2D portraits.
Nonlinear Viscoelastic Mechanics of Cross-linked Rubbers
NASA Technical Reports Server (NTRS)
Freed, Alan D.; Leonov, Arkady I.; Gray, Hugh R. (Technical Monitor)
2002-01-01
The paper develops a general theory for finite rubber viscoelasticity, and specifies it in the form, convenient for solving problems important for rubber, tire and space industries. Based on the quasi-linear approach of non-equilibrium thermodynamics, a general nonlinear theory has been developed for arbitrary nonisothermal deformations of viscoelastic solids. In this theory, the constitutive equations are presented as the sum of known equilibrium (rubber elastic) and non-equilibrium (liquid polymer viscoelastic) terms. These equations are then simplified using several modeling arguments. Stability constraints for the proposed constitutive equations are also discussed. It is shown that only strong ellipticity criteria are applicable for assessing stability of the equations governing viscoelastic solids.
Using Lyapunov exponents to predict the onset of chaos in nonlinear oscillators.
Ryabov, Vladimir B
2002-07-01
An analytic technique for predicting the emergence of chaotic instability in nonlinear nonautonomous dissipative oscillators is proposed. The method is based on the Lyapunov-type stability analysis of an arbitrary phase trajectory and the standard procedure of calculating the Lyapunov characteristic exponents. The concept of temporally local Lyapunov exponents is then utilized for specifying the area in the phase space where any trajectory is asymptotically stable, and, therefore, the existence of chaotic attractors is impossible. The procedure of linear coordinate transform optimizing the linear part of the vector field is developed for the purpose of maximizing the stability area in the vicinity of a stable fixed point. By considering the inverse conditions of asymptotic stability, this approach allows formulating a necessary condition for chaotic motion in a broad class of nonlinear oscillatory systems, including many cases of practical interest. The examples of externally excited one- and two-well Duffing oscillators and a planar pendulum demonstrate efficiency of the proposed method, as well as a good agreement of the theoretical predictions with the results of numerical experiments. The comparison of the proposed method with Melnikov's criterion shows a potential advantage of using the former one at high values of dissipation parameter and/or multifrequency type of excitation in dynamical systems. PMID:12241468
Quantum-mechanical research on nonlinear resonance and the problem of quantum chaos.
Ugulava, A; Chotorlishvili, L; Nickoladze, K
2004-08-01
The quantum-mechanical investigation of nonlinear resonance in terms of approximation to moderate nonlinearity is reduced to the investigation of eigenfunctions and eigenvalues of the Mathieu-Schrodinger equation. The eigenstates of the Mathieu-Schrodinger equation are nondegenerate in a certain area of pumping amplitude values in the neighborhood of the classical separatrix. Outside this area, the system finds itself in a degenerate state for both small and large pumping amplitude values. Degenerate energy terms arise as a result of merging and branching of pairs of nondegenerate energy terms. Equations are obtained for finding the merging points of energy terms. These equations are solved by numerical methods. The main objective of this paper is to establish a quantum analog of the classical stochastic layer formed in the separatrix area. With this end in view, we consider a nonstationary quantum-mechanical problem of perturbation of the state of the Mathieu-Schrodinger equation. It is shown that in passing through the branching point the system may pass from the pure state to the mixed one. At multiple passages through branching points there develops the irreversible process of "creeping" of the system to quantum states. In that case, the observed population of a certain number of levels can be considered, in our opinion, to be a quantum analog of the stochastic layer. The number of populated levels is defined by a perturbation amplitude. PMID:15447577
Nonlinear A. C. response of YBCO weak link bridges and quantum circuit theory
Jiang, H.; Widom, A.; How, H.; Yuan, T.; Vittoria, C. )
1993-11-01
The authors have fabricated microbridge weak links on YBCO films with artificial single grain boundary. The weak link bridges show typical Shapiro step behavior upon application of microwave radiation at 20GHz. However, application of signals at 0.1-4MHz induced nonlinear responses at temperatures below [Tc] of the weak link bridges. The ac nonlinearity was independent of external magnetic fields and microwave radiation up to 20GHz. They propose a circuit theory model based upon a quantum macroscopic Hamiltonian of the Josephson junction to explain the experimental results. The theoretical predictions are in good agreement with the experimental results.
Minimal seeds for shear flow turbulence: using nonlinear transient growth to touch the edge of chaos
Pringle, Chris C T; Kerswell, Rich R
2011-01-01
We propose a general strategy for determining the minimal finite amplitude isturbance to trigger transition to turbulence in shear flows. This involves constructing a variational problem that searches over all disturbances of fixed initial amplitude, which respect the boundary conditions, incompressibility and the Navier--Stokes equations, to maximise a chosen functional over an asymptotically long time period. The functional must be selected such that it identifies turbulent velocity fields by taking significantly enhanced values compared to those for laminar fields. We illustrate this approach using the ratio of the final to initial perturbation kinetic energies (energy growth) as the functional and the energy norm to measure amplitudes in the context of pipe flow. Our results indicate that the variational problem yields a smooth converged solution providing the amplitude is below the threshold amplitude for transition. This optimal is the nonlinear analogue of the well-studied (linear) transient growth opt...
Periodic Solutions and Chaos in a Nonlinear Model for the Delayed Immune Response
NASA Astrophysics Data System (ADS)
Canabarro, Askery
2005-11-01
We model the cellular immune response using a set of non- Newtonian delayed nonlinear differential equations. The production of defense cells is taken to be proportional to the abundance of pathogenic particles in a previous time. We observe that the stationary solution becomes unstable above a critical immune response time ?c. In the periodic regime, the minimum virus load is substantially reduced with respect to the stationary solution. Further increasing the delay time, the dynamics display a series of bifurcations evolving to a chaotic regime characterized by a set of 2D portraits. Time series data of the immune state of patients look rather irregular, pointing out to the possibility of a chaotic dynamics.
Bradley, Elizabeth
1990-12-01
Most of the recent literature on chaos and nonlinear dynamics is written either for popular science magazine readers or for advanced mathematicians. This paper gives a broad introduction to this interesting and rapidly ...
Coherence and chaos in condensed matter
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. (LSP)
Measurement of nonlinear rheology of cross-linked biopolymer gels Chase P. Broedersz,ab
, and their transient nature complicates the mechanical response by enabling stress relaxation and network flow.16 is the control variable that is increased linearly in time while the stress is measured, the elastic responseMeasurement of nonlinear rheology of cross-linked biopolymer gels Chase P. Broedersz,ab Karen E
Berry, Michael Victor
the end of the writing, I encountered papers by Martin Gutzwiller and was tremendously impressed by them Gutzwiller had thought about chaos at that time and it wasn't mentioned in our review. The publishers sent is making very spectacular discoveries about a phenomenon that underlies those papers by Gutzwiller that you
Dynamic non-linear response of cross-linked actin networks: an energy dissipation approach
NASA Astrophysics Data System (ADS)
Majumdar, Sayantan; Gardel, Margaret L.
2014-03-01
Cross-linked bio-polymer networks that primarily maintain the shape and rigidity in eukaryotic cells show striking non-linear mechanical properties. Here, we study the steady-state energy dissipation (Ediss) over a complete sinusoidal shear strain cycle for a macroscopic assembly of reconstituted network of actin filaments cross-linked with Filamin A, over wide range of strain amplitude and frequency values. For small values of the applied strain amplitudes (linear regime) Ediss increases monotonously with the increasing frequency over the entire frequency range studied but in the non-linear regime (larger applied strain amplitudes), a clear saturation in Ediss is observed at higher frequencies. Also, the normalized dissipated energy distribution binned over the fixed strain intervals along the shear cycle show frequency dependence in the nonlinear regime but remains frequency independent in the linear regime. Remarkably, the monotonously increasing behavior of Ediss with frequency is also observed in the non-linear regime when a more rigid cross-linker A-Actinin is used, suggesting the importance of flexibility of cross-linkers in controlling the non-linear mechanical response in this class of materials. MRSEC Kadanoff-Rice Post Doctoral Fellowship.
Nonlinear Optimization-Based Device-Free Localization with Outlier Link Rejection
Xiao, Wendong; Song, Biao; Yu, Xiting; Chen, Peiyuan
2015-01-01
Device-free localization (DFL) is an emerging wireless technique for estimating the location of target that does not have any attached electronic device. It has found extensive use in Smart City applications such as healthcare at home and hospitals, location-based services at smart spaces, city emergency response and infrastructure security. In DFL, wireless devices are used as sensors that can sense the target by transmitting and receiving wireless signals collaboratively. Many DFL systems are implemented based on received signal strength (RSS) measurements and the location of the target is estimated by detecting the changes of the RSS measurements of the wireless links. Due to the uncertainty of the wireless channel, certain links may be seriously polluted and result in erroneous detection. In this paper, we propose a novel nonlinear optimization approach with outlier link rejection (NOOLR) for RSS-based DFL. It consists of three key strategies, including: (1) affected link identification by differential RSS detection; (2) outlier link rejection via geometrical positional relationship among links; (3) target location estimation by formulating and solving a nonlinear optimization problem. Experimental results demonstrate that NOOLR is robust to the fluctuation of the wireless signals with superior localization accuracy compared with the existing Radio Tomographic Imaging (RTI) approach. PMID:25853406
Nonlinear optimization-based device-free localization with outlier link rejection.
Xiao, Wendong; Song, Biao; Yu, Xiting; Chen, Peiyuan
2015-01-01
Device-free localization (DFL) is an emerging wireless technique for estimating the location of target that does not have any attached electronic device. It has found extensive use in Smart City applications such as healthcare at home and hospitals, location-based services at smart spaces, city emergency response and infrastructure security. In DFL, wireless devices are used as sensors that can sense the target by transmitting and receiving wireless signals collaboratively. Many DFL systems are implemented based on received signal strength (RSS) measurements and the location of the target is estimated by detecting the changes of the RSS measurements of the wireless links. Due to the uncertainty of the wireless channel, certain links may be seriously polluted and result in erroneous detection. In this paper, we propose a novel nonlinear optimization approach with outlier link rejection (NOOLR) for RSS-based DFL. It consists of three key strategies, including: (1) affected link identification by differential RSS detection; (2) outlier link rejection via geometrical positional relationship among links; (3) target location estimation by formulating and solving a nonlinear optimization problem. Experimental results demonstrate that NOOLR is robust to the fluctuation of the wireless signals with superior localization accuracy compared with the existing Radio Tomographic Imaging (RTI) approach. PMID:25853406
Strong and weak chaos in weakly nonintegrable many-body Hamiltonian systems
Mario Mulansky; Karsten Ahnert; Arkady Pikovsky; Dima Shepelyansky
2011-03-15
We study properties of chaos in generic one-dimensional nonlinear Hamiltonian lattices comprised of weakly coupled nonlinear oscillators, by numerical simulations of continuous-time systems and symplectic maps. For small coupling, the measure of chaos is found to be proportional to the coupling strength and lattice length, with the typical maximal Lyapunov exponent being proportional to the square root of coupling. This strong chaos appears as a result of triplet resonances between nearby modes. In addition to strong chaos we observe a weakly chaotic component having much smaller Lyapunov exponent, the measure of which drops approximately as a square of the coupling strength down to smallest couplings we were able to reach. We argue that this weak chaos is linked to the regime of fast Arnold diffusion discussed by Chirikov and Vecheslavov. In disordered lattices of large size we find a subdiffusive spreading of initially localized wave packets over larger and larger number of modes. The relations between the exponent of this spreading and the exponent in the dependence of the fast Arnold diffusion on coupling strength are analyzed. We also trace parallels between the slow spreading of chaos and deterministic rheology.
Dissipative Chaos in Quantum Distributions
T. V. Gevorgyan; A. R. Shahinyan; G. Yu. Kryuchkyan
2011-01-30
We discuss some problems of dissipative chaos for open quantum systems in the framework of semiclassical and quantum distributions. For this goal, we propose a driven nonlinear oscillator with time-dependent coefficients, i.e. with time-dependent Kerr-nonlinearity and time-modulated driving field. This model showing both regular and chaotic dynamics in the classical limit is realized in several experimental schemes. Quantum dissipative chaos is analyzed on the base of numerical method of quantum trajectories. Three quantities are studied: the Wigner function of oscillatory mode from the point of view of quantum-assemble theory and both semiclassical Poincare section and quantum Poincare section calculated on a single quantum trajectory. The comparatively analysis of these distributions for various operational chaotic regimes of the models is performed, as well as scaling invariance in dissipative chaos and quantum interference effects assisted by chaos are discussed.
Chaos in driven Alfven systems
NASA Technical Reports Server (NTRS)
Hada, T.; Kennel, C. F.; Buti, B.; Mjolhus, E.
1990-01-01
The chaos in a one-dimensional system, which would be nonlinear stationary Alfven waves in the absence of an external driver, is characterized. The evolution equations are numerically integrated for the transverse wave magnetic field amplitude and phase using the derivative nonlinear Schroedinger equation (DNLS), including resistive wave damping and a long-wavelength monochromatic, circularly polarized driver. A Poincare map analysis shows that, for the nondissipative (Hamiltonian) case, the solutions near the phase space (soliton) separatrices of this system become chaotic as the driver amplitude increases, and 'strong' chaos appears when the driver amplitude is large. The dissipative system exhibits a wealth of dynamical behavior, including quasiperiodic orbits, period-doubling bifurcations leading to chaos, sudden transitions to chaos, and several types of strange attractors.
Chaos in driven Alfven systems
Hada, T.; Kennel, C.F. Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA ); Buti, B. ); Mjolhus, E. )
1990-11-01
The chaos in a one-dimensional system, which would be nonlinear stationary Alfven waves in the absence of an external driver, is characterized. The evolution equations are numerically integrated for the transverse wave magnetic field amplitude and phase using the derivative nonlinear Schroedinger equation (DNLS), including resistive wave damping and a long-wavelength monochromatic, circularly polarized driver. A Poincare map analysis shows that, for the nondissipative (Hamiltonian) case, the solutions near the phase space (soliton) separatrices of this system become chaotic as the driver amplitude increases, and strong'' chaos appears when the driver amplitude is large. The dissipative system exhibits a wealth of dynamical behavior, including quasiperiodic orbits, period-doubling bifurcations leading to chaos, sudden transitions to chaos, and several types of strange attractors.
Chaos in laser-matter interactions
Ackerhalt, J.; Milonni, P.; Shih, M.L.
1987-01-01
This is a set of lecture notes given by the authors at the Universities of Rochester, Arkansas and Puerto Rico. This volume introduces the main ideas of chaos and its applications to a broad range of problems in quantum optics, electronics and laser physics. Contents: Introduction; Nonlinearity; The Period Doubling Route to Chaos; The Duffing Oscillator; Strange Attractors; Two-Frequency Route to Chaos; Intermittency; Dimensions of Attractors; Noise, The Lorenz Model and the Single-Mode Laser; Chaotic Lasers: Theory and Experiment; Hamiltonian Systems; The Henon-Heiles System; The Standard Mapping; Fat Fractals; Ergodicity and Mixing; Chaos and the Microwave Ionization of Hydrogen; The Kicked Pendulum: Classical Theory and Quantum Theory; Chaos and Multiple-Photon Excitation of Molecular Vibrations; Chaos and Molecular Rotations; Ideas in Quantum Chaos; Outlook.
Impact of nonlinearity phenomenon FWM in DWDM optical link considering dispersive fiber
NASA Astrophysics Data System (ADS)
Puche, William S.; Amaya, Ferney O.; Sierra, Javier E.
2013-12-01
The increasing demand of network traffic requires new research centers; improve their communications networks, due to the excessive use of mobile and portable devices wanting to have greater access to the network by downloading interactive content quickly and effectively. For our case analyze optical network link through simulation results assuming a DWDM (Dense wavelength Division Multiplexing) optical link, considering the nonlinearity phenomenon FWM (Four Mixed Wavelength) in order to compare their performance, assuming transmission bit rates to 2.5 Gbps and 10 Gbps, using three primary wavelengths of 1450 nm, 1550 nm and 1650 nm for the transmission of information, whose separation is 100 GHz to generate 16 channels or user information. Tests were conducted to analyze optical amplifiers EDFAs link robustness at a maximum distance of 200 km and identify parameters OSNR, SNR and BER, for a robust and effective transmission
Rokui, M R; Khorasani, K
2000-01-01
The aim of this paper is to develop and implement a nonlinear adaptive control scheme for a single-link flexible manipulator. The controller is designed based on a discrete-time nonlinear model of the arm. The model is derived by using the forward difference method (Euler approximation). The output redefinition concept is then used so that the associated zero dynamics corresponding to the new output is guaranteed to be exponentially stable. An indirect adaptive linearizing controller is developed for the resulting minimum phase system where the "payload mass" is assumed to be unknown but its upper bound is assumed to be known a priori. The performance of the adaptively controlled closed-loop system is investigated by both numerical simulations and experimental results. The proposed controller is also compared experimentally with those of nonadaptive feedback linearization and conventional proportional derivative (PD) control strategies. PMID:18244737
Frank Steiner
1994-02-07
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 formula 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.
Ma, Fang; Bai, Dong-Sheng; Xu, Hong-Liang
2014-09-01
It is well known that settling transparency-efficiency tradeoff is important to design nonlinear optical (NLO) materials. In this work, we constructed one-dimensional polymeric cyanoacetylene (NCCCH)n by hydrogen-bond-directed-linking to understand this tradeoff from molecular level. Results show that the first hyperpolarizability of (NCCCH)n (n=2-8) gradually increased with the increase of n, and what is more important is that the red-shifts, associated with the increase of n, were very little. It is proposed that these polymeric structures possess double-degenerated charge transitions, which contribute to the hyperpolarizability in an additive fashion, and that the coupled oscillators are gradually improved, which lead to the increase of the first hyperpolarizability. Therefore, we propose the hydrogen-bond-directed-linking idea is helpful to develop the potential high-performance NLO materials. PMID:25145287
Reflective confocal laser scanning microscopy and nonlinear microscopy of cross-linked rabbit cornea
NASA Astrophysics Data System (ADS)
Krueger, Alexander; Hovakimyan, Marina; Ramirez, Diego F.; Stachs, Oliver; Guthoff, Rudolf F.; Heisterkamp, Alexander
2009-07-01
Cross-linking of the cornea with application of Ribovlavin and UV-A light is an evolving clinical treatment of the eye disease keratoconus. Despite the positive clinical track record of corneal cross-linking, the complex wound healing process after the treatment is still under investigation. In this study an animal model was used to clarify the state of wound healing 5 weeks after treatment. Cross-linked rabbit corneae were imaged with reflective confocal laser scanning and nonlinear microscopy, namely second harmonic imaging microscopy (SHIM) and two-photon excited autofluorescence. First results show that the NAD(P) H-autofluorescence of the corneal keratocytes and their scattering signal still show a signature of the treatment five weeks after the cross-linking procedure. The SHIM signals show the structural morphology of the fibrous collagen sheets in the stroma of the cornea. SHIM detected in the forward direction differs substantially from backward SHIM, but no signature of treatment was found in both detection channels of the SHIM signal.
PT-Symmetry-Breaking Chaos in Optomechanics.
Lü, Xin-You; Jing, Hui; Ma, Jin-Yong; Wu, Ying
2015-06-26
We demonstrate PT-symmetry-breaking chaos in an optomechanical system, which features an ultralow driving threshold. In principle, this chaos will emerge once a driving laser is applied to the cavity mode and lasts for a period of time. The driving strength is inversely proportional to the starting time of chaos. This originally comes from the dynamical enhancement of nonlinearity by field localization in the PT-symmetry-breaking phase. Moreover, this chaos is switchable by tuning the system parameters so that a PT-symmetry phase transition occurs. This work may fundamentally broaden the regimes of cavity optomechanics and nonlinear optics. It offers the prospect of exploring ultralow-power-laser-triggered chaos and its potential applications in secret communication. PMID:26197125
NASA Astrophysics Data System (ADS)
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.
G. J. Milburn; S. Dyrting
2000-01-01
I shall discuss the quantum and classical dynamics of a class of nonlinear Hamiltonian systems. The discussion will be restricted to systems with one degree of freedom. Such systems cannot exhibit chaos, unless the Hamiltonians are time dependent. Thus we shall consider systems with a potential function that has a higher than quadratic dependence on the position and, furthermore, we
Apthorp, Deborah; Nagle, Fintan; Palmisano, Stephen
2014-01-01
Visually-induced illusions of self-motion (vection) can be compelling for some people, but they are subject to large individual variations in strength. Do these variations depend, at least in part, on the extent to which people rely on vision to maintain their postural stability? We investigated by comparing physical posture measures to subjective vection ratings. Using a Bertec balance plate in a brightly-lit room, we measured 13 participants' excursions of the centre of foot pressure (CoP) over a 60-second period with eyes open and with eyes closed during quiet stance. Subsequently, we collected vection strength ratings for large optic flow displays while seated, using both verbal ratings and online throttle measures. We also collected measures of postural sway (changes in anterior-posterior CoP) in response to the same visual motion stimuli while standing on the plate. The magnitude of standing sway in response to expanding optic flow (in comparison to blank fixation periods) was predictive of both verbal and throttle measures for seated vection. In addition, the ratio between eyes-open and eyes-closed CoP excursions during quiet stance (using the area of postural sway) significantly predicted seated vection for both measures. Interestingly, these relationships were weaker for contracting optic flow displays, though these produced both stronger vection and more sway. Next we used a non-linear analysis (recurrence quantification analysis, RQA) of the fluctuations in anterior-posterior position during quiet stance (both with eyes closed and eyes open); this was a much stronger predictor of seated vection for both expanding and contracting stimuli. Given the complex multisensory integration involved in postural control, our study adds to the growing evidence that non-linear measures drawn from complexity theory may provide a more informative measure of postural sway than the conventional linear measures. PMID:25462216
Chaos in World Politics: A Reflection
NASA Astrophysics Data System (ADS)
Ferreira, Manuel Alberto Martins; Filipe, José António Candeias Bonito; Coelho, Manuel F. P.; Pedro, Isabel C.
Chaos theory results from natural scientists' findings in the area of non-linear dynamics. The importance of related models has increased in the last decades, by studying the temporal evolution of non-linear systems. In consequence, chaos is one of the concepts that most rapidly have been expanded in what research topics respects. Considering that relationships in non-linear systems are unstable, chaos theory aims to understand and to explain this kind of unpredictable aspects of nature, social life, the uncertainties, the nonlinearities, the disorders and confusion, scientifically it represents a disarray connection, but basically it involves much more than that. The existing close relationship between change and time seems essential to understand what happens in the basics of chaos theory. In fact, this theory got a crucial role in the explanation of many phenomena. The relevance of this kind of theories has been well recognized to explain social phenomena and has permitted new advances in the study of social systems. Chaos theory has also been applied, particularly in the context of politics, in this area. The goal of this chapter is to make a reflection on chaos theory - and dynamical systems such as the theories of complexity - in terms of the interpretation of political issues, considering some kind of events in the political context and also considering the macro-strategic ideas of states positioning in the international stage.
Physics and Applications of Laser Diode Chaos
Sciamanna, Marc
2015-01-01
An overview of chaos in laser diodes is provided which surveys experimental achievements in the area and explains the theory behind the phenomenon. The fundamental physics underpinning this behaviour and also the opportunities for harnessing laser diode chaos for potential applications are discussed. The availability and ease of operation of laser diodes, in a wide range of configurations, make them a convenient test-bed for exploring basic aspects of nonlinear and chaotic dynamics. It also makes them attractive for practical tasks, such as chaos-based secure communications and random number generation. Avenues for future research and development of chaotic laser diodes are also identified.
Proceedings of the 2nd Experimental Chaos Conference
NASA Astrophysics Data System (ADS)
Ditto, William; Pecora, Lou; Shlesinger, Michael; Spano, Mark; Vohra, Sandeep
1995-02-01
The Table of Contents for the full book PDF is as follows: * Introduction * Spatiotemporal Phenomena * Experimental Studies of Chaotic Mixing * Using Random Maps in the Analysis of Experimental Fluid Flows * Transition to Spatiotemporal Chaos in a Reaction-Diffusion System * Ion-Dynamical Chaos in Plasmas * Optics * Chaos in a Synchronously Driven Optical Resonator * Chaos, Patterns and Defects in Stimulated Scattering Phenomena * Test of the Normal Form for a Subcritical Bifurcation * Observation of Bifurcations and Chaos in a Driven Fiber Optic Coil * Applications -- Communications * Robustness and Signal Recovery in a Synchronized Chaotic System * Synchronizing Nonautonomous Chaotic Circuits * Synchronization of Pulse-Coupled Chaotic Oscillators * Ocean Transmission Effects on Chaotic Signals * Controlling Symbolic Dynamics for Communication * Applications -- Control * Analysis of Nonlinear Actuators Using Chaotic Waveforms * Controlling Chaos in a Quasiperiodic Electronic System * Control of Chaos in a CO2 Laser * General Research * Video-Based Analysis of Bifurcation Phenomena in Radio-Frequency-Excited Inert Gas Plasmas * Transition from Soliton to Chaotic Motion During the Impact of a Nonlinear Structure * Sonoluminescence in a Single Bubble: Periodic, Quasiperiodic and Chaotic Light Source * Quantum Chaos Experiments Using Microwave Cavities * Experiments on Quantum Chaos With and Without Time Reversibility * When Small Noise Imposed on Deterministic Dynamics Becomes Important * Biology * Chaos Control for Cardiac Arrhythmias * Irregularities in Spike Trains of Cat Retinal Ganglion Cells * Broad-Band Synchronization in Monkey Neocortex * Applicability of Correlation Dimension Calculations to Blood Pressure Signal in Rats * Tests for Deterministic Chaos in Noisy Time Series * The Crayfish Mechanoreceptor Cell: A Biological Example of Stochastic Resonance * Chemistry * Chaos During Heterogeneous Chemical Reactions * Stabilizing and Tracking Unstable Periodic Orbits and Stationary States in Chemical Systems * Recursive Proportional-Feedback and Its Use to Control Chaos in an Electrochemical System * Temperature Patterns on Catalytic Surfaces * Meteorology/Oceanography * Nonlinear Evolution of Water Waves: Hilbert's View * Fractal Properties of Isoconcentration Surfaces in a Smoke Plume * Fractal Dimensions of Remotely Sensed Atmospheric Signals * Are Ocean Surface Waves Chaotic? * Dynamical Attractor Reconstruction for a Marine Stratocumulus Cloud
NSDL National Science Digital Library
Dolphins have an uncanny sense of sonar, based partly on their ability to figure out exactly what type of sound signal to use to analyze their surroundings. This radio broadcast reports on research using chaos theory to analyze how the dolphin does this. The clip is 2 minutes in length.
436 Acc. Chem. Res. 1987,20,436-442 Chemical Chaos: From Hints to Confirmation
. The intrinsically nonlinear properties of chemical kinetics suggest the possibility of chaos in chemical system436 Acc. Chem. Res. 1987,20,436-442 Chemical Chaos: From Hints to Confirmation F. ARGOUL,A. ARNEODO^,^ but there is a healthy skepticism regarding the actual existence of chaos in real well- controlled chemical reactions
Chaos theory as a model for interpreting information systems in organizations
Neil Mcbride
2005-01-01
Chaos theory concerns the qualitative study of unstable aperiodic behaviour in deterministic non-linear dynamical systems. Concepts from chaos theory have recently been applied as a model for interpreting organizational change and understanding organizational behaviour. This paper applies these concepts to the study of information systems in organizations. Key concepts from chaos theory are identified and used to develop an interpretive
Chaos and Forecasting - Proceedings of the Royal Society Discussion Meeting
NASA Astrophysics Data System (ADS)
Tong, Howell
1995-04-01
The Table of Contents for the full book PDF is as follows: * Preface * Orthogonal Projection, Embedding Dimension and Sample Size in Chaotic Time Series from a Statistical Perspective * A Theory of Correlation Dimension for Stationary Time Series * On Prediction and Chaos in Stochastic Systems * Locally Optimized Prediction of Nonlinear Systems: Stochastic and Deterministic * A Poisson Distribution for the BDS Test Statistic for Independence in a Time Series * Chaos and Nonlinear Forecastability in Economics and Finance * Paradigm Change in Prediction * Predicting Nonuniform Chaotic Attractors in an Enzyme Reaction * Chaos in Geophysical Fluids * Chaotic Modulation of the Solar Cycle * Fractal Nature in Earthquake Phenomena and its Simple Models * Singular Vectors and the Predictability of Weather and Climate * Prediction as a Criterion for Classifying Natural Time Series * Measuring and Characterising Spatial Patterns, Dynamics and Chaos in Spatially-Extended Dynamical Systems and Ecologies * Non-Linear Forecasting and Chaos in Ecology and Epidemiology: Measles as a Case Study
Quantum Chaos generates Regularities
Otsuka, Takaharu; Shimizu, Noritaka
2005-07-08
The mechanism of the dominance (preponderance) of the 0+ ground state for random interactions is proposed to be the chaotic realization of the highest rotational symmetry. This is a consequence of a general principle on the chaos and symmetry that the highest symmetry is given to the ground state if sufficient mixing occurs in a chaotic way by a random interaction. Under this symmetry-realization mechanism, the ground-state parity and isospin can be predicted so that the positive parity is favored over the negative parity and the isospin T = 0 state is favored over higher isospin. It is further suggested how one can enhance the realization of highest symmetries within random interactions. Thus, chaos and symmetry are shown to be linked deeply.
NASA Astrophysics Data System (ADS)
Maldonado, Armando; Bixler, David
2012-03-01
Chaos Theory is an interesting and important branch of physics. Many physical systems, such as weather or fluid flow, exhibit chaotic behavior. Experiments in simple mechanical or electrical systems, as well as simple simulations can be used as methods of studying chaos. Using a mechanical method, we connected a speaker and to a frequency modulator to bounce a table tennis ball. We recorded the ball's motion at different frequencies using a video camera. Using Tracker software we observed it's position versus it's velocity in order to analyze its chaotic behavior. For a simple simulation, we used the visual-based programming in LabView to examine chaotic behavior produced by some non-linear differential equations. Results from both the mechanical system and the simulations will be discussed. For future work, we plan to continue to explore some chaotic simulations and perform a sequence of experiments with an electrical system. Exploring these nonlinear chaotic systems can help us to better understand and model many phenomena found in nature.
Instability, subharmonics, and chaos in power electronic systems
JONATHAN H. B. DEANE; DAVID C. HAMILL
1990-01-01
The concept of chaos is applied to a variety of nonlinear power electronic circuits. With the onset of instability, the phenomena of subharmonics, quasi-periodicity, and chaos are predicted and observed. The following examples are dealt with: diodes with charge storage (with application to resonant converters); a ferroresonant circuit; a controlled thyristor rectifier circuit; and a Buck converter controlled by pulse-width
Applying Chaos Theory to Lesson Planning and Delivery
ERIC Educational Resources Information Center
Cvetek, Slavko
2008-01-01
In this article, some of the ways in which thinking about chaos theory can help teachers and student-teachers to accept uncertainty and randomness as natural conditions in the classroom are considered. Building on some key features of complex systems commonly attributed to chaos theory (e.g. complexity, nonlinearity, sensitivity to initial…
Investigation of Robot-Environment Interaction using Chaos Theory
Nehmzow, Ulrich
of systems exhibiting deterministic chaos: 2 #12;Figure 3: 'Billiard Ball' Behaviour in Square Arena how dynamical systems theory and chaos theory can be used to quantify robot-environment interaction (see figure 1). This triangle of robot, task and environment constitutes a non-linear system, whose
Monitoring chaos of cardiac rhythms
Mayer-Kress, G.
1989-01-01
Chaos theory provides a new paradigm in monitoring complexity changes in heart rate variability. Even in cases where the spectral analysis only shows broad band characteristics estimations of dimensional complexity parameters can show quantitative changes in the degree of chaos present in the interbeat interval dynamics. We introduce the concept of dimensional complexity as dynamical monitoring parameter and discuss its properties in connection with control data and data taken during cardiac arrest. Whereas dimensional complexity provides a quantitative indicator of overall chaotic behavior, recurrence plots allow direct visualization of recurrences in arbitrary high dimensional pattern-space. In combination these two methods from non-linear dynamics exemplify a new approach in the problem of heart rate monitoring and identification of precursors of cardiac arrest. Finally we mention a new method of chaotic control, by which selective and highly effective perturbations of nonlinear dynamical systems could be used for improved pacing patterns. 11 refs., 6 figs.
Sprott, Julien Clinton
, in which the natives harvested most of the trees, leading to a rapid18 decline in the human population not previously reported. Such behavior may more realistically depict the10 population dynamics of general that is ubiquitous in such12 systems.13 Key Words: chaos, Easter Island, ecology, population dynamics, Turing14
NASA Astrophysics Data System (ADS)
Casati, Giulio; Chirikov, Boris
2006-11-01
Preface; Acknowledgments; Introduction: 1. The legacy of chaos in quantum mechanics G. Casati and B. V. Chirikov; Part I. Classical Chaos and Quantum Localization: 2. Stochastic behaviour of a quantum pendulum under a periodic perturbation G. Casati, B. V. Chirikov, F. M. Izrailev and J. Ford; 3. Quantum dynamics of a nonintegrable system D. R. Grempel, R. E. Prange and S. E. Fishman; 4. Excitation of molecular rotation by periodic microwave pulses. A testing ground for Anderson localization R. Blümel, S. Fishman and U. Smilansky; 5. Localization of diffusive excitation in multi-level systems D. K. Shepelyansky; 6. Classical and quantum chaos for a kicked top F. Haake, M. Kus and R. Scharf; 7. Self-similarity in quantum dynamics L. E. Reichl and L. Haoming; 8. Time irreversibility of classically chaotic quantum dynamics K. Ikeda; 9. Effect of noise on time-dependent quantum chaos E. Ott, T. M. Antonsen Jr and J. D. Hanson; 10. Dynamical localization, dissipation and noise R. F. Graham; 11. Maximum entropy models and quantum transmission in disordered systems J.-L. Pichard and M. Sanquer; 12. Solid state 'atoms' in intense oscillating fields M. S. Sherwin; Part II. Atoms in Strong Fields: 13. Localization of classically chaotic diffusion for hydrogen atoms in microwave fields J. E. Bayfield, G. Casati, I. Guarneri and D. W. Sokol; 14. Inhibition of quantum transport due to 'scars' of unstable periodic orbits R. V. Jensen, M. M. Sanders, M. Saraceno and B. Sundaram; 15. Rubidium Rydberg atoms in strong fields G. Benson, G. Raithel and H. Walther; 16. Diamagnetic Rydberg atom: confrontation of calculated and observed spectra C.-H. Iu, G. R. Welch, M. M. Kash, D. Kleppner, D. Delande and J. C. Gay; 17. Semiclassical approximation for the quantum states of a hydrogen atom in a magnetic field near the ionization limit M. Y. Kuchiev and O. P. Sushkov; 18. The semiclassical helium atom D. Wintgen, K. Richter and G. Tanner; 19. Stretched helium: a model for quantum chaos in two-electron atoms R. Blümel and W. P. Reinhardt; Part III. Semiclassical Approximations: 20. Semiclassical theory of spectral rigidity M. V. Berry; 21. Semiclassical structure of trace formulas R. G. Littlejohn; 22. h-Expansion for quantum trace formulas P. Gaspard; 23. Pinball scattering B. Eckhardt, G. Russberg, P. Cvitanovic, P. E. Rosenqvist and P. Scherer; 24. Logarithm breaking time in quantum chaos G. P. Berman and G. M. Zaslavsky; 25. Semiclassical propagation: how long can it last? M. A. Sepulveda, S. Tomsovic and E. J. Heller; 26. The quantized Baker's transformation N. L. Balazs and A. Voros; 27. Classical structures in the quantized baker transformation M. Saraceno; 28. Quantum nodal points as fingerprints of classical chaos P. Leboeuf and A. Voros; 29. Chaology of action billiards A. M. Ozorio de Almeida and M. A. M. de Aguiar; Part IV. Level Statistics and Random Matrix Theory: 30. Characterization of chaotic quantum spectra and universality of level fluctuation laws O. Bohigas, M. J. Giannono, and C. Schmit; 31. Quantum chaos, localization and band random matrices F. M. Izrailev; 32. Structural invariance in channel space: a step toward understanding chaotic scattering in quantum mechanics T. H. Seligman; 33. Spectral properties of a Fermi accelerating disk R. Badrinarayanan and J. J. José; 34. Spectral properties of systems with dynamical localization T. Dittrich and U. Smilansky; 35. Unbound quantum diffusion and fractal spectra T. Geisel, R. Ketzmerick and G. Petschel; 36. Microwave studies in irregularly shaped billiards H.-J. Stöckmann, J. Stein and M. Kollman; Index.
NASA Astrophysics Data System (ADS)
Casati, Giulio; Chirikov, Boris
1995-04-01
Preface; Acknowledgments; Introduction: 1. The legacy of chaos in quantum mechanics G. Casati and B. V. Chirikov; Part I. Classical Chaos and Quantum Localization: 2. Stochastic behaviour of a quantum pendulum under a periodic perturbation G. Casati, B. V. Chirikov, F. M. Izrailev and J. Ford; 3. Quantum dynamics of a nonintegrable system D. R. Grempel, R. E. Prange and S. E. Fishman; 4. Excitation of molecular rotation by periodic microwave pulses. A testing ground for Anderson localization R. Blümel, S. Fishman and U. Smilansky; 5. Localization of diffusive excitation in multi-level systems D. K. Shepelyansky; 6. Classical and quantum chaos for a kicked top F. Haake, M. Kus and R. Scharf; 7. Self-similarity in quantum dynamics L. E. Reichl and L. Haoming; 8. Time irreversibility of classically chaotic quantum dynamics K. Ikeda; 9. Effect of noise on time-dependent quantum chaos E. Ott, T. M. Antonsen Jr and J. D. Hanson; 10. Dynamical localization, dissipation and noise R. F. Graham; 11. Maximum entropy models and quantum transmission in disordered systems J.-L. Pichard and M. Sanquer; 12. Solid state 'atoms' in intense oscillating fields M. S. Sherwin; Part II. Atoms in Strong Fields: 13. Localization of classically chaotic diffusion for hydrogen atoms in microwave fields J. E. Bayfield, G. Casati, I. Guarneri and D. W. Sokol; 14. Inhibition of quantum transport due to 'scars' of unstable periodic orbits R. V. Jensen, M. M. Sanders, M. Saraceno and B. Sundaram; 15. Rubidium Rydberg atoms in strong fields G. Benson, G. Raithel and H. Walther; 16. Diamagnetic Rydberg atom: confrontation of calculated and observed spectra C.-H. Iu, G. R. Welch, M. M. Kash, D. Kleppner, D. Delande and J. C. Gay; 17. Semiclassical approximation for the quantum states of a hydrogen atom in a magnetic field near the ionization limit M. Y. Kuchiev and O. P. Sushkov; 18. The semiclassical helium atom D. Wintgen, K. Richter and G. Tanner; 19. Stretched helium: a model for quantum chaos in two-electron atoms R. Blümel and W. P. Reinhardt; Part III. Semiclassical Approximations: 20. Semiclassical theory of spectral rigidity M. V. Berry; 21. Semiclassical structure of trace formulas R. G. Littlejohn; 22. h-Expansion for quantum trace formulas P. Gaspard; 23. Pinball scattering B. Eckhardt, G. Russberg, P. Cvitanovic, P. E. Rosenqvist and P. Scherer; 24. Logarithm breaking time in quantum chaos G. P. Berman and G. M. Zaslavsky; 25. Semiclassical propagation: how long can it last? M. A. Sepulveda, S. Tomsovic and E. J. Heller; 26. The quantized Baker's transformation N. L. Balazs and A. Voros; 27. Classical structures in the quantized baker transformation M. Saraceno; 28. Quantum nodal points as fingerprints of classical chaos P. Leboeuf and A. Voros; 29. Chaology of action billiards A. M. Ozorio de Almeida and M. A. M. de Aguiar; Part IV. Level Statistics and Random Matrix Theory: 30. Characterization of chaotic quantum spectra and universality of level fluctuation laws O. Bohigas, M. J. Giannono, and C. Schmit; 31. Quantum chaos, localization and band random matrices F. M. Izrailev; 32. Structural invariance in channel space: a step toward understanding chaotic scattering in quantum mechanics T. H. Seligman; 33. Spectral properties of a Fermi accelerating disk R. Badrinarayanan and J. J. José; 34. Spectral properties of systems with dynamical localization T. Dittrich and U. Smilansky; 35. Unbound quantum diffusion and fractal spectra T. Geisel, R. Ketzmerick and G. Petschel; 36. Microwave studies in irregularly shaped billiards H.-J. Stöckmann, J. Stein and M. Kollman; Index.
The missing link: a nonlinear post-Friedmann framework for small and large scales
Irene Milillo; Daniele Bertacca; Marco Bruni; Andrea Maselli
2015-05-09
We present a nonlinear post-Friedmann framework for structure formation, generalizing to cosmology the weak-field (post-Minkowskian) approximation, unifying the treatment of small and large scales. We consider a universe filled with a pressureless fluid and a cosmological constant $\\Lambda$, the theory of gravity is Einstein's general relativity and the background is the standard flat $\\Lambda$CDM cosmological model. We expand the metric and the energy-momentum tensor in powers of $1/c$, keeping the matter density and peculiar velocity as exact fundamental variables. We assume the Poisson gauge, including scalar and tensor modes up to $1/c^4$ order and vector modes up to $1/c^5$ terms. Through a redefinition of the scalar potentials as a resummation of the metric contributions at different orders, we obtain a complete set of nonlinear equations, providing a unified framework to study structure formation from small to superhorizon scales, from the nonlinear Newtonian to the linear relativistic regime. We explicitly show the validity of our scheme in the two limits: at leading order we recover the fully nonlinear equations of Newtonian cosmology; when linearized, our equations become those for scalar and vector modes of first-order relativistic perturbation theory in the Poisson gauge. Tensor modes are nondynamical at the $1/c^4$ order we consider: they are purely nonlinear and describe a distortion of the spatial slices determined at this order by a constraint, quadratic in the scalar and vector variables. The main results of our analysis are as follows: (a) at leading order a purely Newtonian nonlinear energy current sources a frame-dragging gravitomagnetic vector potential, and (b) in the leading-order Newtonian regime and in the linear relativistic regime the two scalar metric potentials are the same, while the nonlinearity of general relativity makes them different.
Experimental Chaos - Proceedings of the 3rd Conference
NASA Astrophysics Data System (ADS)
Harrison, Robert G.; Lu, Weiping; Ditto, William; Pecora, Lou; Spano, Mark; Vohra, Sandeep
1996-10-01
The Table of Contents for the full book PDF is as follows: * Preface * Spatiotemporal Chaos and Patterns * Scale Segregation via Formation of Domains in a Nonlinear Optical System * Laser Dynamics as Hydrodynamics * Spatiotemporal Dynamics of Human Epileptic Seizures * Experimental Transition to Chaos in a Quasi 1D Chain of Oscillators * Measuring Coupling in Spatiotemporal Dynamical Systems * Chaos in Vortex Breakdown * Dynamical Analysis * Radial Basis Function Modelling and Prediction of Time Series * Nonlinear Phenomena in Polyrhythmic Hand Movements * Using Models to Diagnose, Test and Control Chaotic Systems * New Real-Time Analysis of Time Series Data with Physical Wavelets * Control and Synchronization * Measuring and Controlling Chaotic Dynamics in a Slugging Fluidized Bed * Control of Chaos in a Laser with Feedback * Synchronization and Chaotic Diode Resonators * Control of Chaos by Continuous-time Feedback with Delay * A Framework for Communication using Chaos Sychronization * Control of Chaos in Switching Circuits * Astrophysics, Meteorology and Oceanography * Solar-Wind-Magnetospheric Dynamics via Satellite Data * Nonlinear Dynamics of the Solar Atmosphere * Fractal Dimension of Scalar and Vector Variables from Turbulence Measurements in the Atmospheric Surface Layer * Mechanics * Escape and Overturning: Subtle Transient Behavior in Nonlinear Mechanical Models * Organising Centres in the Dynamics of Parametrically Excited Double Pendulums * Intermittent Behaviour in a Heating System Driven by Phase Transitions * Hydrodynamics * Size Segregation in Couette Flow of Granular Material * Routes to Chaos in Rotational Taylor-Couette Flow * Experimental Study of the Laminar-Turbulent Transition in an Open Flow System * Chemistry * Order and Chaos in Excitable Media under External Forcing * A Chemical Wave Propagation with Accelerating Speed Accompanied by Hydrodynamic Flow * Optics * Instabilities in Semiconductor Lasers with Optical Injection * Spatio-Temporal Dynamics of a Bimode CO2 Laser with Saturable Absorber * Chaotic Homoclinic Phenomena in Opto-Thermal Devices * Observation and Characterisation of Low-Frequency Chaos in Semiconductor Lasers with External Feedback * Condensed Matter * The Application of Nonlinear Dynamics in the Study of Ferroelectric Materials * Cellular Convection in a Small Aspect Ratio Liquid Crystal Device * Driven Spin-Wave Dynamics in YIG Films * Quantum Chaology in Quartz * Small Signal Amplification Caused by Nonlinear Properties of Ferroelectrics * Composite Materials Evolved from Chaos * Electronics and Circuits * Controlling a Chaotic Array of Pulse-Coupled Fitzhugh-Nagumo Circuits * Experimental Observation of On-Off Intermittency * Phase Lock-In of Chaotic Relaxation Oscillators * Biology and Medicine * Singular Value Decomposition and Circuit Structure in Invertebrate Ganglia * Nonlinear Forecasting of Spike Trains from Neurons of a Mollusc * Ultradian Rhythm in the Sensitive Plants: Chaos or Coloured Noise? * Chaos and the Crayfish Sixth Ganglion * Hardware Coupled Nonlinear Oscillators as a Model of Retina
Chaos and Quantum Chaos in Nuclear Systems
Luca Salasnich
1995-10-15
The presence of chaos and quantum chaos is shown in two different nuclear systems. We analyze the chaotic behaviour of the classical SU(2) Yang--Mills--Higgs system, and then we study quantum chaos in the nuclear shell model calculating the spectral statistics of $A=46$--$50$ atomic nuclei.
Chaos Experiments Wave Chaos and Electromagnetic
Anlage, Steven
Chaos Experiments Wave Chaos and Electromagnetic Interference in Enclosures ·Faculty: Steven M;Electromagnetic Coupling in Computer Circuits connectors cables circuit boards Integrated circuits Schematic can be said about coupling without solving in detail the complicated EM problem ? · Wave Chaos Chaotic
ERIC Educational Resources Information Center
Lee, Sik-Yum; Song, Xin-Yuan; Cai, Jing-Heng
2010-01-01
Analysis of ordered binary and unordered binary data has received considerable attention in social and psychological research. This article introduces a Bayesian approach, which has several nice features in practical applications, for analyzing nonlinear structural equation models with dichotomous data. We demonstrate how to use the software…
Missing link: A nonlinear post-Friedmann framework for small and large scales
NASA Astrophysics Data System (ADS)
Milillo, Irene; Bertacca, Daniele; Bruni, Marco; Maselli, Andrea
2015-07-01
We present a nonlinear post-Friedmann framework for structure formation, generalizing to cosmology the weak-field (post-Minkowskian) approximation, unifying the treatment of small and large scales. We consider a universe filled with a pressureless fluid and a cosmological constant ? , the theory of gravity is Einstein's general relativity and the background is the standard flat ? CDM cosmological model. We expand the metric and the energy-momentum tensor in powers of 1 /c , keeping the matter density and peculiar velocity as exact fundamental variables. We assume the Poisson gauge, including scalar and tensor modes up to 1 /c4 order and vector modes up to 1 /c5 terms. Through a redefinition of the scalar potentials as a resummation of the metric contributions at different orders, we obtain a complete set of nonlinear equations, providing a unified framework to study structure formation from small to superhorizon scales, from the nonlinear Newtonian to the linear relativistic regime. We explicitly show the validity of our scheme in the two limits: at leading order we recover the fully nonlinear equations of Newtonian cosmology; when linearized, our equations become those for scalar and vector modes of first-order relativistic perturbation theory in the Poisson gauge. Tensor modes are nondynamical at the 1 /c4 order we consider (gravitational waves only appear at higher order): they are purely nonlinear and describe a distortion of the spatial slices determined at this order by a constraint, quadratic in the scalar and vector variables. The main results of our analysis are as follows: (a) at leading order a purely Newtonian nonlinear energy current sources a frame-dragging gravitomagnetic vector potential, and (b) in the leading-order Newtonian regime and in the linear relativistic regime, the two scalar metric potentials are the same, while the nonlinearity of general relativity makes them different. Possible applications of our formalism include the calculations of the vector potential and the difference between the two scalar potentials from Newtonian N-body simulations, and the extension of Newtonian approximations used in structure formation studies, to include relativistic effects.
Borbone, Fabio; Carella, Antonio; Roviello, Antonio; Casalboni, Mauro; De Matteis, Fabio; Stracci, Glauco; della Rovere, Fabio; Evangelisti, Andrea; Dispenza, Massimiliano
2011-10-27
In this paper we report the synthesis and characterization of a trihydroxylated nonlinear optical (NLO) azochromophore and its functionalization with 2,4-tolylendiisocyanate (TDI) to give an amorphous mixture of isomers that was used as a starting compound for the preparation of cross-linked electro-optic (EO) thin films. An unedited type of thermal cross-linking reaction was used, exploiting the reactivity of isocyanate groups themselves in the presence of N,N-dimethylacetamide, without the addition of any hydroxylated comonomer as usual in the preparation of polyurethanes. Thin films were prepared by spin coating and corona poled during thermal cross-linking. A d(33) value of 33 pm/V was obtained by second-harmonic generation (SHG) measurements on poled films, and an excellent stability of SHG signal was shown upon aging at 130 °C and during dynamic thermal stability measurements. PMID:21916511
P T -Symmetry-Breaking Chaos in Optomechanics
NASA Astrophysics Data System (ADS)
Lü, Xin-You; Jing, Hui; Ma, Jin-Yong; Wu, Ying
2015-06-01
We demonstrate P T -symmetry-breaking chaos in an optomechanical system, which features an ultralow driving threshold. In principle, this chaos will emerge once a driving laser is applied to the cavity mode and lasts for a period of time. The driving strength is inversely proportional to the starting time of chaos. This originally comes from the dynamical enhancement of nonlinearity by field localization in the P T -symmetry-breaking phase. Moreover, this chaos is switchable by tuning the system parameters so that a P T -symmetry phase transition occurs. This work may fundamentally broaden the regimes of cavity optomechanics and nonlinear optics. It offers the prospect of exploring ultralow-power-laser-triggered chaos and its potential applications in secret communication.
$\\mathcal{PT}$-Symmetry-Breaking Chaos in Optomechanics
Xin-You Lü; Hui Jing; Jin-Yong Ma; Ying Wu
2015-06-30
We demonstrate a $\\mathcal{PT}$-symmetry-breaking chaos in optomechanical system (OMS), which features an ultralow driving threshold. In principle, this chaos will emerge once a driving laser is applied to the cavity mode and lasts for a period of time. The driving strength is inversely proportional to the starting time of chaos. This originally comes from the dynamical enhancement of nonlinearity by field localization in $\\mathcal{PT}$-symmetry-breaking phase ($\\mathcal{PT}$BP). Moreover, this chaos is switchable by tuning the system parameters so that a $\\mathcal{PT}$-symmetry phase transition occurs. This work may fundamentally broaden the regimes of cavity optomechanics and nonlinear optics. It offers the prospect of exploring ultralow-power-laser triggered chaos and its potential applications in secret communication.
On the synchronization of a class of electronic circuits that exhibit chaos
Sprott, Julien Clinton
On the synchronization of a class of electronic circuits that exhibit chaos Er-Wei Bai a,*, Karl E Accepted 19 June 2001 Abstract The synchronization of two nonlinear electronic circuits that exhibit chaos that electronic circuits that consist of possibly one or two nonlinear elements can be used to verify several
Chaos in the Solar Cycle: using data to drive predictions Matthew Young
theory. Finally, we present results of nonlinear analysis of solar motion and propose that further of chaos theory and nonlinear time series analysis to solar data in order to further our understanding reviews of the history of sunspot records, the mathematical framework of chaos theory, and solar dynamo
Nonlinear optics technology. Volume 2: Phase conjugated optical communication link, phase 3
NASA Astrophysics Data System (ADS)
Brock, J.; Caponi, M.; Horwitz, A.; Lembo, L.; Novoseller, D.
1991-01-01
A laser communication link that uses phase conjugation (PC) to correct for atmospheric aberrations due to turbulence was investigated. Significant improvements over conventional optical communication links were demonstrated through experiments and analysis. A 1.1 km four wave mixing (FWM) PC optical communication link propagating through the atmosphere was demonstrated and characterized over a range of atmospheric turbulence conditions and compared to the performance of a conventional link. Four wave mixing was performed in sodium vapor near the sodium D2 resonance line (lambda = 589 nm). Signals with amplitude modulation of 10 kHz to 1 MHz were successfully transmitted and received over this link. Measurements of intensity variance demonstrated that the beam returned by the phase conjugator is corrected for atmospheric turbulence, displaying significantly less intensity variance than a beam returned by a conventional mirror. A 30 m FWM PC communication link was tested with a uniform turbulence generator (turbox) in the laboratory and compared to theoretical performance predictions.
Nonlinear dynamics experiments in plasmas
Nurujjaman, Md
2009-01-01
The study of nonlinear dynamics or chaos theory has emerged in the last three decades or so as an important interdisciplinary area of research encompassing a wide range of fields like: fluids, plasmas, biomedical sciences, finance, turbulence, astronomy, material sciences, etc. In plasma chaos was first experimentally observed by Boswell. Different other nonlinear dynamics related phenomena like, the intermittency route to a chaos, Homoclinic chaos, Period adding route to chaos and period subtracting, mode locking, period pulling, etc., had been observed by several researchers. In this thesis, we have presented (a) anode glow related observation of chaos to order transition and homoclinic bifurcation; (b) coherence resonance and stochastic resonance; and self organized criticality behavior in glow discharge plasma.
Experimental evidence of chaos from memristors
L. V. Gambuzza; L. Fortuna; M. Frasca; E. Gale
2015-04-24
Until now, most memristor-based chaotic circuits proposed in the literature are based on mathematical models which assume ideal characteristics such as piece-wise linear or cubic non-linearities. The idea, illustrated here and originating from the experimental approach for device characterization, is to realize a chaotic system exploiting the non-linearity of only one memristor with a very simple experimental set-up using feedback. In this way a simple circuit is obtained and chaos is experimentally observed and is confirmed by the calculation of the largest Lyapunov exponent. Numerical results using the Strukov model support the existence of robust chaos in our circuit. This is the first experimental demonstration of chaos in a real memristor circuit and suggests that memristors are well placed for hardware encryption.
Experimental Evidence of Chaos from Memristors
NASA Astrophysics Data System (ADS)
Gambuzza, Lucia Valentina; Fortuna, Luigi; Frasca, Mattia; Gale, Ella
Until now, most memristor-based chaotic circuits proposed in the literature are based on mathematical models which assume ideal characteristics such as piecewise-linear or cubic nonlinearities. The idea, illustrated here and originating from the experimental approach for device characterization, is to realize a chaotic system exploiting the nonlinearity of only one memristor with a very simple experimental set-up using feedback. In this way, a simple circuit is obtained and chaos is experimentally observed and is confirmed by the calculation of the largest Lyapunov exponent. Numerical results using the Strukov model support the existence of robust chaos in our circuit. To our knowledge, this is the first experimental demonstration of chaos in a real memristor circuit and suggests that memristors are well placed for hardware encryption.
Improvement and empirical research on chaos control by theory of "chaos?+?chaos?=?order".
Fulai, Wang
2012-12-01
This paper focuses on advancing the understanding of Parrondian effects and their paradoxical behavior in nonlinear dynamical systems. Some examples are given to show that a dynamics combined by more than two discrete chaotic dynamics in deterministic manners can give rise to order when combined. The chaotic maps in our study are more general than those in the current literatures as far as "chaos + chaos?=?order" is concerned. Some problems left over in the current literatures are solved. It is proved both theoretically and numerically that, given any m chaotic dynamics generated by the one-dimensional real Mandelbrot maps, it is no possible to get a periodic system when all the m chaotic dynamics are alternated in random manner, but for any integer m(m ? 2) a dynamics combined in deterministic manner by m Mandelbrot chaotic dynamics can be found to give rise to a periodic dynamics of m periods. Numerical and mathematical analysis prove that the paradoxical phenomenon of "chaos + chaos?=?order" also exist in the dynamics generated by non-Mandelbrot maps. PMID:23278080
Kot, M.
1990-07-01
A recurrent theme of much recent research is that seemingly random fluctuations often occur as the result of simple deterministic mechanisms. Hence, much of the recent work in nonlinear dynamics has centered on new techniques for identifying order in seemingly chaotic systems. To determine the robustness of these techniques, chaos must, to some extent, be brought into the laboratory. Preliminary investigations of the forced double-Monod equations, a model for a predator and a prey in a chemostat with periodic variation in inflowing substrate concentration, suggest that simple microbial systems may provide the perfect framework for determining the efficacy and relevance of the new nonlinear dynamics in dealing with complex population dynamics. This research has two main goals, that is the mathematical analysis and computer simulation of the periodically forced double-Monod equations and of related models; and experimental (chemostat) population studies that evaluate the accuracy and generality of the models, and that judge the usefulness of various new techniques of nonlinear dynamics to the study of populations.
Dissipative Chaos in Semiconductor Superlattices
Kirill N. Alekseev; Gennady P. Berman; David K. Campbell; Ethan H. Cannon; Matthew C. Cargo
1996-04-29
We consider the motion of ballistic electrons in a miniband of a semiconductor superlattice (SSL) under the influence of an external, time-periodic electric field. We use the semi-classical balance-equation approach which incorporates elastic and inelastic scattering (as dissipation) and the self-consistent field generated by the electron motion. The coupling of electrons in the miniband to the self-consistent field produces a cooperative nonlinear oscillatory mode which, when interacting with the oscillatory external field and the intrinsic Bloch-type oscillatory mode, can lead to complicated dynamics, including dissipative chaos. For a range of values of the dissipation parameters we determine the regions in the amplitude-frequency plane of the external field in which chaos can occur. Our results suggest that for terahertz external fields of the amplitudes achieved by present-day free electron lasers, chaos may be observable in SSLs. We clarify the nature of this novel nonlinear dynamics in the superlattice-external field system by exploring analogies to the Dicke model of an ensemble of two-level atoms coupled with a resonant cavity field and to Josephson junctions.
Experimental Techniques for Investigating Chaos in Electronics
Tse, Chi K. "Michael"
18 Experimental Techniques for Investigating Chaos in Electronics Chi K. Tse 1 Department of Electronic and Information Engineering The Hong Kong Polytechnic University Hong Kong, China encktse@polyu.edu.hk Abstract In the study of nonlinear phenomena in electronics, experiments are indispensable for the purpose
Chaos, brain and divided consciousness.
Bob, Petr
2007-01-01
Modern trends in psychology and cognitive neuroscience suggest that applications of nonlinear dynamics, chaos and self-organization seem to be particularly important for research of some fundamental problems regarding mind-brain relationship. Relevant problems among others are formations of memories during alterations of mental states and nature of a barrier that divides mental states, and leads to the process called dissociation. This process is related to a formation of groups of neurons which often synchronize their firing patterns in a unique spatial maner. Central theme of this study is the relationship between level of moving and oscilating mental processes and their neurophysiological substrate. This opens a question about principles of organization of conscious experiences and how these experiences arise in the brain. Chaotic self-organization provides a unique theoretical and experimental tool for deeper understanding of dissociative phenomena and enables to study how dissociative phenomena can be linked to epileptiform discharges which are related to various forms of psychological and somatic manifestations. Organizing principles that constitute human consciousness and other mental phenomena from this point of view may be described by analysis and reconstruction of underlying dynamics of psychological or psychophysiological measures. These nonlinear methods in this study were used for analysis of characteristic changes in EEG and bilateral electrodermal activity (EDA) during reliving of dissociated traumatic and stressful memories and during psychopathological states. Analysis confirms a possible role of chaotic transitions in the processing of dissociated memory. Supportive finding for a possible chaotic process related to dissociation found in this study represent also significant relationship of dissociation, epileptiform discharges measured by typical psychopathological manifestations and characteristic laterality changes in bilateral EDA in patients with schizophrenia and depression. Increased level of psychopathological symptoms indicates close relationship to the right-left EDA asymmetry and asymmetry of information entropy calculated by non-linear recurrence quantification analysis of EDA records. Because epileptiform activity has specific chaotic behaviour and calculated information entropy from EDA records reflects the complexity of the deterministic structure in the system there is a relevant assumption that unilaterally increased complexity may produce interhemispheric disbalance and increased chaoticity which hypothetically may serve as a dynamic source of epileptiform discharges related to trauma induced kindling mechanism. Specific form of chaotic inner organization which cannot be explained only as a consequence of external causality support also psychophysiological data that lead to the so-called self-organizing theory of dreaming by Kahn and Hobson. This study suggests that self-organizing theory of dreaming is particularly important with respect to problem of memory formation and processing during dissociative states characteristic for dreams. Recent data and also findings of this study support the research utility of chaos theory in psychology and neuroscience, and also its conceptual view of dynamic ordering factors and self-organization underlying psychological processes and brain physiology. PMID:17867519
Magnetic field induced dynamical chaos
Ray, Somrita; Baura, Alendu; Bag, Bidhan Chandra
2013-12-15
In this article, we have studied the dynamics of a particle having charge in the presence of a magnetic field. The motion of the particle is confined in the x–y plane under a two dimensional nonlinear potential. We have shown that constant magnetic field induced dynamical chaos is possible even for a force which is derived from a simple potential. For a given strength of the magnetic field, initial position, and velocity of the particle, the dynamics may be regular, but it may become chaotic when the field is time dependent. Chaotic dynamics is very often if the field is time dependent. Origin of chaos has been explored using the Hamiltonian function of the dynamics in terms of action and angle variables. Applicability of the present study has been discussed with a few examples.
California at Davis, University of
Computation at the Onset of Chaos James P. Crutchfield Karl Young Physics Department* University of Information, W. Zurek, editor, Addison-Wesley, Reading, Massachusetts (1989). *JPC's Internet address is chaos
ERIC Educational Resources Information Center
Barton, Ray
1990-01-01
Presented is an educational game called "The Chaos Game" which produces complicated fractal images. Two basic computer programs are included. The production of fractal images by the Sierpinski gasket and the Chaos Game programs is discussed. (CW)
High-dimensional chaos from self-sustained collisions of solitons
Yildirim, O. Ozgur, E-mail: donhee@seas.harvard.edu, E-mail: oozgury@gmail.com [Cavium, Inc., 600 Nickerson Rd., Marlborough, Massachusetts 01752 (United States); Ham, Donhee, E-mail: donhee@seas.harvard.edu, E-mail: oozgury@gmail.com [Harvard University, 33 Oxford St., Cambridge, Massachusetts 02138 (United States)
2014-06-16
We experimentally demonstrate chaos generation based on collisions of electrical solitons on a nonlinear transmission line. The nonlinear line creates solitons, and an amplifier connected to it provides gain to these solitons for their self-excitation and self-sustenance. Critically, the amplifier also provides a mechanism to enable and intensify collisions among solitons. These collisional interactions are of intrinsically nonlinear nature, modulating the phase and amplitude of solitons, thus causing chaos. This chaos generated by the exploitation of the nonlinear wave phenomena is inherently high-dimensional, which we also demonstrate.
Nonlinear oceanic-atmospheric oscil-lations have been linked to hydro-
linked to increased commercial landings of blue crabs (Callinectes sapidus) in Texas (More, 1969 drought severity index, or by a combination of the NAO and precipitation. to both commercial landings). Vegetated and ephemeral structured habitats provide chemical cues for settlement, food, and refuge
ERIC Educational Resources Information Center
Huwe, Terence K.
2009-01-01
"Embracing the chaos" is an ongoing challenge for librarians. Embracing the chaos means librarians must have a plan for responding to the flood of new products, widgets, web tools, and gizmos that students use daily. In this article, the author argues that library instruction and access services have been grappling with that chaos with some degree…
ERIC Educational Resources Information Center
Bedford, Crayton W.
1998-01-01
Outlines a course on fractal geometry and chaos theory. Discusses how chaos theory and fractal geometry have begun to appear as separate units in the mathematics curriculum and offers an eight unit course by pulling together units related to chaos theory and fractal geometry. Contains 25 references. (ASK)
Evolution of Channels Draining Mount St. Helens: Linking Non-Linear and Rapid, Threshold Responses
NASA Astrophysics Data System (ADS)
Simon, A.
2010-12-01
The catastrophic eruption of Mount St. Helens buried the valley of the North Fork Toutle River (NFT) to a depth of up to 140 m. Initial integration of a new drainage network took place episodically by the “filling and spilling” (from precipitation and seepage) of depressions formed during emplacement of the debris avalanche deposit. Channel incision to depths of 20-30 m occurred in the debris avalanche and extensive pyroclastic flow deposits, and headward migration of the channel network followed, with complete integration taking place within 2.5 years. Downstream reaches were converted from gravel-cobble streams with step-pool sequences to smoothed, infilled channels dominated by sand-sized materials. Subsequent channel evolution was dominated by channel widening with the ratio of changes in channel width to changes in channel depth ranging from about 60 to 100. Widening resulted in significant adjustment of hydraulic variables that control sediment-transport rates. For a given discharge over time, flow depths were reduced, relative roughness increased and flow velocity and boundary shear stress decreased non-linearly. These changes, in combination with coarsening of the channel bed with time resulted in systematically reduced rates of degradation (in upstream reaches), aggradation (in downstream reaches) and sediment-transport rates through much of the 1990s. Vertical adjustments were, therefore, easy to characterize with non-linear decay functions with bed-elevation attenuating with time. An empirical model of bed-level response was then created by plotting the total dimensionless change in elevation against river kilometer for both initial and secondary vertical adjustments. High magnitude events generated from the generated from upper part of the mountain, however, can cause rapid (threshold) morphologic changes. For example, a rain-on-snow event in November 2006 caused up to 9 m of incision along a 6.5 km reach of Loowit Creek and the upper NFT. The event triggered a debris flow which cutoff tributary channels to Glacier Creek and redirected Step and Loowit Creeks thereby forcing enhanced flow volumes through the main channel. Very coarse, armored bed materials were mobilized allowing for deep incision into the substrate. Incision continues today at slower rates but it is again the lateral shifting and widening of the channels that is dominant. Low and moderate flows undercut the toe of 30 m-high pyroclastic flow deposits causing significant erosion. As the channel continues to widen incision will attenuate non-linearly. Channels such as the multiple Step Creek channels will coalesce as narrow ridges erode by undercutting and mass failure much as reaches of lower Loowit Creek did in the late 1980’s. The resulting enlarged and over-widened sections will then again (as in downstream reaches) have lowered transporting power.
Stochastic Representation of Chaos using Terminal Attractors
NASA Technical Reports Server (NTRS)
Zak, Michail
2005-01-01
A nonlinear version of the Liouville equation based upon terminal attractors is proposed for describing post-instability motions of dynamical systems with exponential divergence of trajectories such as those leading to chaos and turbulence. As a result, the post-instability motions are represented by expectations, variances, and higher moments of the state variables as functions of time. The proposed approach can be applied to conservative chaos, and in particular, to n-bodies problem, as well as to dissipative systems, and in particular, to chaotic attractors and turbulence.
Phased-array cancellation of nonlinear FWM in coherent OFDM dispersive multi-span links.
Nazarathy, Moshe; Khurgin, Jacob; Weidenfeld, Rakefet; Meiman, Yehuda; Cho, Pak; Noe, Reinhold; Shpantzer, Isaac; Karagodsky, Vadim
2008-09-29
We develop an analytic model of Coherent Optical Orthogonal Frequency Division Multiplexing (OFDM) propagation and detection over multi-span long-haul fiber links, comprehensively and rigorously analyzing the impairments due the combined effects of FWM, Dispersion and ASE noise. Consistent with prior work of Innoe and Schadt in the WDM context, our new closed-form expressions for the total FWM received power fluctuations in the wake of dispersive phase mismatch in OFDM transmission, indicate that the FWM contributions of the multitude of spans build-up on a phased-array basis. For particular ultra-long haul link designs, the effectiveness of dispersion in reducing FWM is far greater than previously assumed in OFDM system analysis. The key is having the dominant FWM intermodulation products due to the multiple spans, destructively interfere, mutually cancelling their FWM intermodulation products, analogous to operating at the null of a phased-array antenna system. By applying the new analysis tools, this mode of effectively mitigating the FWM impairment, is shown under specific dispersion and spectral management conditions, to substantially suppress the FWM power fluctuations. Accounting for the phased-array concept and applying the compact OFDM design formulas developed here, we analyzed system performance of a 40 Gbps coherent OFDM system, over standard G.652 fiber, with cyclic prefix based electronic dispersion compensation but no optical compensation along the link. The transmission range for 10-3 target BER is almost tripled from 2560 km to 6960 km, relative to a reference system performing optical dispersion compensation in every span (ideally accounting for FWM and ASE noise and the cyclic prefix overhead, but excluding additional impairments). PMID:18825217
NASA Astrophysics Data System (ADS)
Greenfield, Margo; McGrane, Shawn; Bolme, Cindy; Chavez, David; Veauthier, Jacqueline; Hanson, Susan; Myers, Thomas; Scharff, Jason
2015-06-01
In general, conventional molecular explosives are white to off-white in color and only absorb ultraviolet light. A novel approach to synthetically link optically active energetic chromophores to existing molecular energetic materials has resulted in increased photoactivity in the visible (532 nm) region of the electromagnetic spectrum. Tetrazine, an energetic optically active chromophore, which absorbs around 532 nm, has been derivatized with various energetic materials including pentaeythritol tetranitrate (PETN), nitroglycerine (NG) and dinitroazetidine (DNAZ). We report the corresponding photochemistry and photochemical quantum yields of these new materials under various wavelength and intensity regimes.
Ordering chaos by random shortcuts.
Qi, Feng; Hou, Zhonghuai; Xin, Houwen
2003-08-01
In this Letter, the effects of random shortcuts in an array of coupled nonlinear chaotic pendulums and their ability to control the dynamical behavior of the system are investigated. We show that random shortcuts can induce periodic synchronized spatiotemporal motions, even though all oscillators are chaotic when uncoupled. This process exhibits a nonmonotonic dependence on the density of shortcuts. Specifically, there is an optimal amount of random shortcuts, which can induce the most ordered motion characterized by the largest order parameter that is introduced to measure the spatiotemporal order. Our results imply that topological randomness can tame spatiotemporal chaos. PMID:12935078
Abraham, N.B.; Arecchi, F.T.; Lugiato, L.A.
1988-01-01
The following topics are considered: laser and maser instabilities, classical and quantum noise, transverse effects, dynamics in optical bistability and nonlinear optical media, and methods of analysis in nonlinear dynamics. Particular papers are presented on multistability and chaos in a two-photon microscopic maser, quantum chaos in quantum optics, spatial chaos in bistable optical arrays, four-wave mixing and dynamics, and bifurcation problems in nonlinear optics.
NASA Astrophysics Data System (ADS)
Arwas, Geva; Vardi, Amichay; Cohen, Doron
2015-03-01
The hallmark of superfluidity is the appearance of a quantized metastable circulating current. The Landau criterion links the metastability of a vortex state to its spectral stability, i.e. to the inaccessibility of elementary excitations connecting it to other states with the same energy. In low dimensional systems, superfluid vortex states can exist due to their dynamical stability even if they are spectrally unstable. This traditional paradigm associate superfluid vortex states with stationary stable fixed points in phase space. Hence, Bogoliubov de Gennes (BdG) stability analysis is normally used to determine the feasibility of such states. In this work we challenge this traditional criterion and highlight the role of chaos in the analysis, thus explaining the existence of current carrying eigenstates which are neither spectrally-stable nor dynamically- stable.
Valentini, F.; Vecchio, A.; Donato, S.; Carbone, V.; Veltri, P. [Dipartimento di Fisica and CNISM, Università della Calabria, I-87036 Rende (CS) (Italy); Briand, C.; Bougeret, J., E-mail: francesco.valentini@fis.unical.it [LESIA-Observatoire de Paris, CNRS, UPMC Université Paris 06, Université Paris-Diderot, 5 place J. Janssen, F-92190 Meudon (France)
2014-06-10
The local heating of the solar-wind gas during its expansion represents one of the most intriguing problems in space plasma physics and is at present the subject of a relevant scientific effort. The possible mechanisms that could account for local heat production in the interplanetary medium are most likely related to the turbulent character of the solar-wind plasma. Nowadays, many observational and numerical analyses are devoted to the identification of fluctuation channels along which energy is carried from large to short wavelengths during the development of the turbulent cascade; these fluctuation channels establish the link between macroscopic and microscopic scales. In this Letter, by means of a quantitative comparison between in situ measurements in the solar wind from the STEREO spacecraft and numerical results from kinetic simulations, we identify an electrostatic channel of fluctuations that develops along the turbulent cascade in a direction parallel to the ambient magnetic field. This channel appears to be efficient in transferring the energy from large Alfvénic to short electrostatic acoustic-like scales up to a range of wavelengths where it can finally be turned into heat, even when the electron to proton temperature ratio is of the order of unity.
Parabolic Resonance: A Route to Hamiltonian Spatiotemporal Chaos
Shlizerman, Eli; Rom-Kedar, Vered [Faculty of Mathematics and Computer Science, Weizmann Institute of Science, Post Office Box 26, Rehovot 76100 (Israel)
2009-01-23
We show that initial data near an unperturbed stable plane wave can evolve into a regime of spatiotemporal chaos in the slightly forced conservative periodic one-dimensional nonlinear Schroedinger equation. Statistical measures are employed to demonstrate that this spatiotemporal chaos is intermittent: there are windows in time for which the solution gains spatial coherence. The parameters and initial profiles that lead to such intermittency are predicted by utilizing a novel geometrical description of the integrable unforced equation.
Chai, Dongyul; Juhasz, Tibor; Brown, Donald J.; Jester, James V.
2013-01-01
Abstract. In this study we test the hypothesis that nonlinear optical (NLO) multiphoton photoactivation of riboflavin using a focused femtosecond (FS) laser light can be used to induce cross-linking (CXL) and mechanically stiffen collagen as a potential clinical therapy for the treatment of keratoconus and corneal ectasia. Riboflavin-soaked, compressed collagen hydrogels are cross-linked using a FS laser tuned to 760 nm and set to either 100 mW (NLO CXL I) or 150 mW (NLO CXL II) of laser power. FS pulses are focused into the hydrogel using a 0.75 NA objective lens, and the hydrogel is three-dimensionally scanned. Measurement of hydrogel stiffness by indentation testing show that the calculated elastic modulus (E) values are significantly increased over twofold following NLO CXL I and II compared with baseline values (P<0.05). Additionally, no significant differences are detected between NLO CXL and single photon, UVA CXL (P>0.05). This data suggests that NLO CXL has a comparable effect to conventional UVA CXL in mechanically stiffening collagen and may provide a safe and effective approach to localize CXL at different regions and depths within the cornea. PMID:23515869
Hung, Yu-Han; Hwang, Sheng-Kwang
2013-09-01
For radio-over-fiber links, microwave-modulated optical carriers with high optical modulation depth are preferred because high optical modulation depth allows generation of high microwave power after photodetection, leading to high detection sensitivity, long transmission distance, and large link gain. This study investigates the period-one nonlinear dynamics of semiconductor lasers for optical modulation depth improvement to achieve photonic microwave amplification through modulation sideband enhancement. In our scheme, only typical semiconductor lasers are required as the amplification unit. The amplification is achieved for a broad microwave range, from less than 25 GHz to more than 60 GHz, and for a wide gain range, from less than 10 dB to more than 30 dB. The microwave phase quality is mainly preserved while the microwave power is largely amplified, improving the signal-to-noise ratio up to at least 25 dB. The bit-error ratio at 1.25 Gbits/s is better than 10(-9), and a sensitivity improvement of up to at least 15 dB is feasible. PMID:23988956
NASA Astrophysics Data System (ADS)
Chai, Dongyul; Juhasz, Tibor; Brown, Donald J.; Jester, James V.
2013-03-01
In this study we test the hypothesis that nonlinear optical (NLO) multiphoton photoactivation of riboflavin using a focused femtosecond (FS) laser light can be used to induce cross-linking (CXL) and mechanically stiffen collagen as a potential clinical therapy for the treatment of keratoconus and corneal ectasia. Riboflavin-soaked, compressed collagen hydrogels are cross-linked using a FS laser tuned to 760 nm and set to either 100 mW (NLO CXL I) or 150 mW (NLO CXL II) of laser power. FS pulses are focused into the hydrogel using a 0.75 NA objective lens, and the hydrogel is three-dimensionally scanned. Measurement of hydrogel stiffness by indentation testing show that the calculated elastic modulus (E) values are significantly increased over twofold following NLO CXL I and II compared with baseline values (P<0.05). Additionally, no significant differences are detected between NLO CXL and single photon, UVA CXL (P>0.05). This data suggests that NLO CXL has a comparable effect to conventional UVA CXL in mechanically stiffening collagen and may provide a safe and effective approach to localize CXL at different regions and depths within the cornea.
NASA Astrophysics Data System (ADS)
Gaponov-Grekhov, Andrei V.; Rabinovich, Mikhail I.; Engelbrecht, Jüri
Since 1972 the Schools on Nonlinear Physics in Gorky have been a meeting place for Soviet Scientists working in this field. Since 1989 the proceedings appear in English. They present a good cross section of nonlinear physics in the USSR. This third volume emerged from material presented at the 1989 School. It contains sections dealing with nonlinear problems in physics and astrophysics, quantum and solid state physics, dynamical chaos and self-organization.
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
Quantum Chaos and Statistical Mechanics
Mark Srednicki
1994-06-14
We briefly review the well known connection between classical chaos and classical statistical mechanics, and the recently discovered connection between quantum chaos and quantum statistical mechanics.
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. PMID:24894264
Energy enhancement and chaos control in microelectromechanical systems Kwangho Park,1
Lai, Ying-Cheng
For a resonator in an electrostatic microelectromechanical system MEMS , nonlinear coupling between appliedEnergy enhancement and chaos control in microelectromechanical systems Kwangho Park,1 Qingfei Chen MEMS resonators, and propose a control strategy to convert chaos into periodic motions with enhanced
California at Davis, University of
Computation at the Onset of Chaos James P. Crutchfield Karl Young Physics Department * University of Information, W. Zurek, editor, AddisonWesley, Reading, Massachusetts (1989). * JPC's Internet address
NASA Astrophysics Data System (ADS)
Spano, Mark
1997-04-01
The publication by Ott, Grebogi and Yorke(E. Ott, C. Grebogi and J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990).) of their theory of chaos control in 1990 led to an explosion of experimental work applying their theory to mechanical systems and electronic circuits, lasers and chemical reactors, and heart and brain tissue, to name only a few. In this talk the basics of chaos control as implemented in a simple mechanical system will be described, as well as extensions of the method to biological applications. Finally, current advances in the field, including the maintenance of chaos and the control of high dimensional chaos, will be discussed.
Quantum Chaos and Quantum Computing Structures
Carlos Pedro Gonçalves
2012-08-13
A system of quantum computing structures is introduced and proven capable of making emerge, on average, the orbits of classical bounded nonlinear maps on \\mathbb{C} through the iterative action of path-dependent quantum gates. The effects of emerging nonlinear dynamics and chaos upon the quantum averages of relevant observables and quantum probabilities are exemplified for a version of Chirikov's standard map on \\mathbb{C} . Both the individual orbits and ensemble properties are addressed so that the Poincar\\'e map for Chirikov's standard map, in the current quantum setting, is reinterpreted in terms of a quantum ensemble which is then formally introduced within the formalized system of quantum computing structures, in terms of quantum register machines, revealing three phases of quantum ensemble dynamics: the regular, the chaotic and an intermediate phase called complex quantum stochastic phase which shares similarities to the edge of chaos notion from classical cellular automata and classical random boolean networks' evolutionary computation.
Chaos control of parametric driven Duffing oscillators
Jin, Leisheng; Mei, Jie; Li, Lijie
2014-03-31
Duffing resonators are typical dynamic systems, which can exhibit chaotic oscillations, subject to certain driving conditions. Chaotic oscillations of resonating systems with negative and positive spring constants are identified to investigate in this paper. Parametric driver imposed on these two systems affects nonlinear behaviours, which has been theoretically analyzed with regard to variation of driving parameters (frequency, amplitude). Systematic calculations have been performed for these two systems driven by parametric pumps to unveil the controllability of chaos.
Spatiotemporal communication with synchronized optical chaos
J. Garcia-Ojalvo; R. Roy
2000-11-06
We propose a model system that allows communication of spatiotemporal information using an optical chaotic carrier waveform. The system is based on broad-area nonlinear optical ring cavities, which exhibit spatiotemporal chaos in a wide parameter range. Message recovery is possible through chaotic synchronization between transmitter and receiver. Numerical simulations demonstrate the feasibility of the proposed scheme, and the benefit of the parallelism of information transfer with optical wavefronts.
Controlling spatiotemporal chaos via small external forces
Shunguang Wu; Kaifen He; Zuqia Huang
1999-08-08
The spatiotemporal chaos in the system described by a one-dimensional nonlinear drift-wave equation is controlled by directly adding a periodic force with appropriately chosen frequencies. By dividing the solution of the system into a carrier steady wave and its perturbation, we find that the controlling mechanism can be explained by a slaving principle. The critical controlling time for a perturbation mode increases exponentially with its wave number.
Spatiotemporal intermittency and chaos in stimulated Raman backscattering
NASA Astrophysics Data System (ADS)
Škori?, M. M.; Jovanovi?, M. S.; Rajkovi?, M. R.
1996-04-01
Spatiotemporal dynamics of stimulated Raman backscattering in a finite, weakly dissipative plasma, with non-linear phase detuning taken into account, is examined numerically. The non-linear model of a three-wave interaction, involving quadratic coupling of slowly varying complex amplitudes of the laser pump, the backscattering and the electron plasma waves, exhibits spatiotemporal intermittency and chaos following a quasi-periodic scenario. Qualitative analysis of spatiotemporal patterns reveals increasing complexity both for the backscattered and the electron plasma wave as the relative pump strength increases. The transition from spatiotemporal intermittency to chaos is identified using methods from the theory of critical phenomena.
Cyberterrorism: Postmodern State of Chaos
Jonathan Matusitz
2008-01-01
This paper examines cyberterrorism and its potential to create a postmodern state of chaos. In general, chaos refers to a state of extreme confusion and disorder. This analysis breaks new ground in that it describes chaos theory as a foundation for better understanding cyberterrorism and explains how chaos theory and game theory are tightly coupled. The author also contrasts modern,
Cyberterrorism: Postmodern State of Chaos
Jonathan Matusitz
2010-01-01
This paper examines cyberterrorism and its potential to create a postmodern state of chaos. In general, chaos refers to a state of extreme confusion and disorder. This analysis breaks new ground in that it describes chaos theory as a foundation for better understanding cyberterrorism and explains how chaos theory and game theory are tightly coupled. The author also contrasts modern,
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. PMID:23556962
ERIC Educational Resources Information Center
Moseley, Bryan; Dustin, Daniel
2008-01-01
In this article, the authors advance a metaphor born of chaos theory that views the college classroom as a complex dynamical system. The authors reason further that "teaching as chaos" provides a more accurate representation of the teaching-learning process than the existing linear scientific metaphors on which traditional learning assessments are…
ERIC Educational Resources Information Center
Murphy, David
2011-01-01
About 20 years ago, while lost in the midst of his PhD research, the author mused over proposed titles for his thesis. He was pretty pleased with himself when he came up with "Chaos Rules" (the implied double meaning was deliberate), or more completely, "Chaos Rules: An Exploration of the Work of Instructional Designers in Distance Education." He…
Understanding chaos via nuclei
Cejnar, Pavel; Stránský, Pavel
2014-01-08
We use two models of nuclear collective dynamics-the geometric collective model and the interacting boson model-to illustrate principles of classical and quantum chaos. We propose these models as a suitable testing ground for further elaborations of the general theory of chaos in both classical and quantum domains.
Chaos and order in models of black hole pairs
Levin, Janna
2006-12-15
Chaos in the orbits of black hole pairs has by now been confirmed by several independent groups. While the chaotic behavior of binary black hole orbits is no longer argued, it remains difficult to quantify the importance of chaos to the evolutionary dynamics of a pair of comparable mass black holes. None of our existing approximations are robust enough to offer convincing quantitative conclusions in the most highly nonlinear regime. It is intriguing to note that, in three different approximations to a black hole pair built of a spinning black hole and a nonspinning companion, two approximations exhibit chaos and one approximation does not. The fully relativistic scenario of a spinning test mass around a Schwarzschild black hole shows chaos, as does the post-Newtonian Lagrangian approximation. However, the approximately equivalent post-Newtonian Hamiltonian approximation does not show chaos when only one body spins. It is well known in dynamical systems theory that one system can be regular while an approximately related system is chaotic, so there is no formal conflict. However, the physical question remains: Is there chaos for comparable mass binaries when only one object spins? We are unable to answer this question given the poor convergence of the post-Newtonian approximation to the fully relativistic system. A resolution awaits better approximations that can be trusted in the highly nonlinear regime.
Spirals, chaos, and new mechanisms of wave propagation.
Chen, P S; Garfinkel, A; Weiss, J N; Karagueuzian, H S
1997-02-01
The chaos theory is based on the idea that phenomena that appear disordered and random may actually be produced by relatively simple deterministic mechanisms. The disordered (aperiodic) activation that characterizes a chaotic motion is reached through one of a few well-defined paths that are characteristic of nonlinear dynamical systems. Our group has been studying VF using computerized mapping techniques. We found that in electrically induced VF, reentrant wavefronts (spiral waves) are present both in the initial tachysystolic stage (resembling VT) and the later tremulous incoordination stage (true VF). The electrophysiological characteristics associated with the transition from VT to VF is compatible with the quasiperiodic route to chaos as described in the Ruelle-Takens theorem. We propose that specific restitution of action potential duration (APD) and conduction velocity properties can cause a spiral wave (the primary oscillator) to develop additional oscillatory modes that lead to spiral meander and breakup. When spiral waves begin to meander and are modulated by other oscillatory processes, the periodic activity is replaced by unstable quasiperiodic oscillation, which then undergoes transition to chaos, signaling the onset of VF. We conclude that VF is a form of deterministic chaos. The development of VF is compatible with quasiperiodic transition to chaos. These results indicate that both the prediction and the control of fibrillation are possible based on the chaos theory and with the advent of chaos control algorithms. PMID:9058845
Decrease of cardiac chaos in congestive heart failure
NASA Astrophysics Data System (ADS)
Poon, Chi-Sang; Merrill, Christopher K.
1997-10-01
The electrical properties of the mammalian heart undergo many complex transitions in normal and diseased states. It has been proposed that the normal heartbeat may display complex nonlinear dynamics, including deterministic chaos,, and that such cardiac chaos may be a useful physiological marker for the diagnosis and management, of certain heart trouble. However, it is not clear whether the heartbeat series of healthy and diseased hearts are chaotic or stochastic, or whether cardiac chaos represents normal or abnormal behaviour. Here we have used a highly sensitive technique, which is robust to random noise, to detect chaos. We analysed the electrocardiograms from a group of healthy subjects and those with severe congestive heart failure (CHF), a clinical condition associated with a high risk of sudden death. The short-term variations of beat-to-beat interval exhibited strongly and consistently chaotic behaviour in all healthy subjects, but were frequently interrupted by periods of seemingly non-chaotic fluctuations in patients with CHF. Chaotic dynamics in the CHF data, even when discernible, exhibited a high degree of random variability over time, suggesting a weaker form of chaos. These findings suggest that cardiac chaos is prevalent in healthy heart, and a decrease in such chaos may be indicative of CHF.
Marat Akhmet; Mehmet Onur Fen
2012-09-09
A new phenomenon, entrainment of chaos, which is understood as a seizure of an irregular behavior by limit cycles, is discussed. As a result, chaotic cycles appear if the chaos amplitude is small. Otherwise, the chaos is not necessarily cyclic, if the perturbations are strong and/or diameter of the limit cycle is small. Sensitivity as a main and a unique ingredient is considered and, in addition, period-doubling route to chaos is chosen for extension. The results may be of strong importance for engineering sciences, brainwaves and biomusicology phenomena as well as can be developed for hydrodynamics. Theoretical results are supported by simulations and discussions over Chua's oscillators, entrainment of chaos by toroidal attractors and controlling problems. Moreover, through an example, by means of the Lyapunov functions method, a chaotic attractor is provided.
Quantum chaos in Aharonov-Bohm oscillations
Berman, G.P.; Campbell, D.K.; Bulgakov, E.N.; Krive, I.V.
1995-10-01
Aharonov-Bohm oscillations in a mesoscopic ballistic ring are considered under the influence of a resonant magnetic field with one and two frequencies. The authors investigate the oscillations of the time-averaged electron energy at zero temperature in the regime of an isolated quantum nonlinear resonance and at the transition to quantum chaos, when two quantum nonlinear resonances overlap. It is shown that the time-averaged energy exhibits resonant behavior as a function of the magnetic flux, and has a ``staircase`` dependence on the amplitude of the external field. The delocalization of the quasi-energy eigenfunctions is analyzed.
Quantum weak chaos in a degenerate system
V. Ya. Demikhovskii; D. I. Kamenev; G. A. Luna-Acosta
1998-09-27
Quantum weak chaos is studied in a perturbed degenerate system --- a charged particle interacting with a monochromatic wave in a transverse magnetic field. The evolution operator for an arbitrary number of periods of the external field is built and its structure is explored in terms of the QE (quasienergy eigenstates) under resonance condition (wave frequency $=$ cyclotron frequency) in the regime of weak classical chaos. The new phenomenon of diffusion via the quantum separatrices and the influence of chaos on diffusion are investigated and, in the quasi classical limit, compared with its classical dynamics. We determine the crossover from purely quantum diffusion to a diffusion which is the quantum manifestation of classical diffusion along the stochastic web. This crossover results from the non-monotonic dependence of the characteristic localization length of the QE states on the wave amplitude. The width of the quantum separatrices was computed and compared with the width of the classical stochastic web. We give the physical parameters which can be realized experimentally to show the manifestation of quantum chaos in nonlinear acoustic resonance.
NASA Astrophysics Data System (ADS)
Kandrup, H. E.
2002-09-01
This talk summarises a combined theoretical and numerical investigation of the role of chaos and transient chaos in time-dependent Hamiltonian systems which aim to model elliptical galaxies. The existence of large amounts of chaos in near-equilibrium configurations is of potential importance because configurations incorporating large numbers of chaotic orbits appear to be substantially more susceptible than nearly integrable systems to various irregularities associated with, e.g., internal substructures, satellite galaxies, and/or the effects of a high density environment. Alternatively, transient chaos, reflecting exponential sensitivity over comparatively short time intervals, can prove important by significantly increasing the overall efficiency of violent relaxation so as to facilitate a more rapid evolution towards a `well-mixed' equilibrium. Completely conclusive `smoking gun' evidence for chaos and chaotic mixing has not yet been obtained, although evidence for the presence of chaos can in principle be extracted from such data sets as provided by the Sloan Digital Sky Survey. Interestingly, however, arguments completely analogous to those applied to self-gravitating systems also suggest the presence of chaos in charged particle beams, a setting which is amenable to controlled experiments.
Reliability of the 0-1 test for chaos
NASA Astrophysics Data System (ADS)
Hu, Jing; Tung, Wen-Wen; Gao, Jianbo; Cao, Yinhe
2005-11-01
In time series analysis, it has been considered of key importance to determine whether a complex time series measured from the system is regular, deterministically chaotic, or random. Recently, Gottwald and Melbourne have proposed an interesting test for chaos in deterministic systems. Their analyses suggest that the test may be universally applicable to any deterministic dynamical system. In order to fruitfully apply their test to complex experimental data, it is important to understand the mechanism for the test to work, and how it behaves when it is employed to analyze various types of data, including those not from clean deterministic systems. We find that the essence of their test can be described as to first constructing a random walklike process from the data, then examining how the variance of the random walk scales with time. By applying the test to three sets of data, corresponding to (i) 1/f? noise with long-range correlations, (ii) edge of chaos, and (iii) weak chaos, we show that the test mis-classifies (i) both deterministic and weakly stochastic edge of chaos and weak chaos as regular motions, and (ii) strongly stochastic edge of chaos and weak chaos, as well as 1/f? noise as deterministic chaos. Our results suggest that, while the test may be effective to discriminate regular motion from fully developed deterministic chaos, it is not useful for exploratory purposes, especially for the analysis of experimental data with little a priori knowledge. A few speculative comments on the future of multiscale nonlinear time series analysis are made.
Nonlinear and Complex Dynamics in Real Systems
Barnett, William A.; Serletis, Apostolos; Serletis, Demitre
2006-06-01
In this article we provide a review of the literature with respect to fluctuations in real systems and chaos. In doing so, we contrast the order and organization hypothesis of real systems to nonlinear chaotic dynamics and discuss some techniques...
A generalization of Chao's estimator for covariate information.
Böhning, Dankmar; Vidal-Diez, Alberto; Lerdsuwansri, Rattana; Viwatwongkasem, Chukiat; Arnold, Mark
2013-12-01
This note generalizes Chao's estimator of population size for closed capture-recapture studies if covariates are available. Chao's estimator was developed under unobserved heterogeneity in which case it represents a lower bound of the population size. If observed heterogeneity is available in form of covariates we show how this information can be used to reduce the bias of Chao's estimator. The key element in this development is the understanding and placement of Chao's estimator in a truncated Poisson likelihood. It is shown that a truncated Poisson likelihood (with log-link) with all counts truncated besides ones and twos is equivalent to a binomial likelihood (with logit-link). This enables the development of a generalized Chao estimator as the estimated, expected value of the frequency of zero counts under a truncated (all counts truncated except ones and twos) Poisson regression model. If the regression model accounts for the heterogeneity entirely, the generalized Chao estimator is asymptotically unbiased. A simulation study illustrates the potential in gain of bias reduction. Comparisons of the generalized Chao estimator with the homogeneous zero-truncated Poisson regression approach are supplied as well. The method is applied to a surveillance study on the completeness of farm submissions in Great Britain. PMID:24164233
Regularity and chaos in 0+ states of the interacting boson model using quantum measures
S. Karampagia; Dennis Bonatsos; R. F. Casten
2015-05-11
Statistical measures of chaos have long been used in the study of chaotic dynamics in the framework of the interacting boson model. The use of large number of bosons renders additional studies of chaos possible, that can provide a direct comparison with similar classical studies of chaos. We intend to provide complete quantum chaotic dynamics at zero angular momentum in the vicinity of the arc of regularity and link the results of the study of chaos using statistical measures with those of the study of chaos using classical measures. Statistical measures of chaos are applied on the spectrum and the transition intensities of 0+ states in the framework of the interacting boson model. The energy dependence of chaos is provided for the first time using statistical measures of chaos. The position of the arc of regularity was also found to be stable in the limit of large boson numbers. The results of the study of chaos using statistical measures are consistent with previous studies using classical measures of chaos, as well as with studies using statistical measures of chaos, but for small number of bosons and states with angular momentum greater than 2.
Nuclear Collective Dynamics and Chaos
NASA Astrophysics Data System (ADS)
Sakata, Fumihiko; Marumori, Toshio
1992-09-01
present status and future problems in both the classical-level theory and full quantum theory of nuclear collective dynamics are discussed by putting special emphasis on their relation to the classical and quantum order-to-chaos transition dynamics, respectively. The nonlinear dynamics between the collective and single-particle excitation modes of motion specific for the finite, self-sustained and self-organizing system as the nucleus is discussed within the time-dependent Hartree-Fock (TDHF) theory, the basic equation of which is shown to be formally equivalent to the Hamilton's canonical equations of motion in the classical nonlinear dynamical system. An importance to relate the structure of the TDHF symplectic manifold with an inexhaustible rich structure of the classical phase space in the nonlinear system is stressed. A full quantum theory of nuclear collective dynamics is proposed under a dictation of what has been developed in the classical-level TDHF theory. It is shown that the proposed quantum theory enables us to explore exceeding complexity of the Hilbert space. It is discussed that a resonant denominator known as a source of the extraordinary rich structure of the phase space trajectories, also plays a decisive role in generating a rich structure of the quantum Hilbert space.
Nonlinear Structure in Shanghai Stock Index
Qi-fa Xu
2009-01-01
The typical character of financial market is nonlinear. The nonlinear structure in financial market is explored through the method of time-series analysis and the theory of nonlinear dynamics. The empirical result shows that return series of Shanghai Stock Index is a little degree of freedom chaos system with self-similar nonlinear structure. The nonlinear structure cannot be simulated adequately by ARCH(4)
Resource Letter: CC-1: Controlling chaos Daniel J. Gauthier
Gauthier, Daniel
damped pendulum, can show exceedingly erratic, noise-like behavior that is a manifestation of nonlinear systems falls into just a few universal categories. For example, the route to chaos for a pendulum experiments conducted with an optical device can be used to understand some aspects of the behavior
Organisational Leadership and Chaos Theory: Let's Be Careful
ERIC Educational Resources Information Center
Galbraith, Peter
2004-01-01
This article addresses issues associated with applications of ideas from "chaos theory" to educational administration and leadership as found in the literature. Implications are considered in relation to claims concerning the behaviour of non-linear dynamic systems, and to the nature of the interpretations and recommendations that are made. To aid…
Chaos in a three-species food chain
A. Hastings; T. Powell
1991-01-01
A continuous time model of a food chain incorporating nonlinear functional (and numerical) responses exhibits chaotic dynamics in long-term behavior when biologically reasonable parameter values are chosen. The appearance of chaos in this model suggests the chaotic dynamics may be common in natural food webs. One approach to the study of an ecological community begins with an important object: its
Thinking about Chaos: Non-Quantitative Approaches to Teacher Education.
ERIC Educational Resources Information Center
Rockler, Michael J.
1991-01-01
Explains the chaos theory and its effect on education, relating it to quantum physics. The article suggests implications for education (predictions about student achievement are limited, the brain learns in nonlinear ways, and the knowledge base in teacher education needs modification to account for recent discoveries in science and mathematics).…
Bifurcations and chaos in a circular Couette system
Shusheng Liu; Yongda Sun; Lu Chai
1988-01-01
The techniques of the laser light scattering and the flow visualization are used to study the bifurcations and chaos in a circular Couette system. Two different routes to turbulence are observed. A physical understanding of the results is given based on the nonlinear interaction. Bibtex entry for this abstract Preferred format for this abstract (see Preferences) Find Similar Abstracts: Use:
Ecosystem Simulations and Chaos on the Graphing Calculator
ERIC Educational Resources Information Center
Sinn, Robb
2007-01-01
An eighth grade algebra class used graphing calculators to simulate ecosystems. One simulation introduced mathematical chaos. The activities exposed the students to nonlinear patterns and modeling. The rate-of-change investigations related the ideas of intercept and slope to the changing equilibrium. The chaotic model intrigued them and was useful…
Campbell, D.
1987-01-01
Provided is 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.
Chaos, Fractals, and Polynomials.
ERIC Educational Resources Information Center
Tylee, J. Louis; Tylee, Thomas B.
1996-01-01
Discusses chaos theory; linear algebraic equations and the numerical solution of polynomials, including the use of the Newton-Raphson technique to find polynomial roots; fractals; search region and coordinate systems; convergence; and generating color fractals on a computer. (LRW)
ERIC Educational Resources Information Center
Peterson, Ivars
1991-01-01
Described are the idea of chaos and the ability to control the chaotic behavior of a real-world physical system. Included is an explanation of the methodology and applications in biology and chemistry. (KR)
Exploiting chaos for applications
NASA Astrophysics Data System (ADS)
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.
Tracking quasi-classical chaos in ultracold boson gases
Maxence Lepers; Véronique Zehnlé; Jean Claude Garreau
2008-08-05
We study the dynamics of a ultra-cold boson gas in a lattice submitted to a constant force. We track the route of the system towards chaos created by the many-body-induced nonlinearity and show that relevant information can be extracted from an experimentally accessible quantity, the gas mean position. The threshold nonlinearity for the appearance of chaotic behavior is deduced from KAM arguments and agrees with the value obtained by calculating the associated Lyapunov exponent.
Stochastic Representation of Chaos Using Terminal Attractors
NASA Technical Reports Server (NTRS)
Zak, Michail
2006-01-01
A nonlinear version of the Liouville equation based on terminal attractors is part of a mathematical formalism for describing postinstability motions of dynamical systems characterized by exponential divergences of trajectories leading to chaos (including turbulence as a form of chaos). The formalism can be applied to both conservative systems (e.g., multibody systems in celestial mechanics) and dissipative systems (e.g., viscous fluids). The development of the present formalism was undertaken in an effort to remove positive Lyapunov exponents. The means chosen to accomplish this is coupling of the governing dynamical equations with the corresponding Liouville equation that describes the evolution of the flow of error probability. The underlying idea is to suppress the divergences of different trajectories that correspond to different initial conditions, without affecting a target trajectory, which is one that starts with prescribed initial conditions.
Quantum chaos in QCD and hadrons
Harald Markum; Willibald Plessas; Rainer Pullirsch; Bianka Sengl; Robert F. Wagenbrunn
2005-05-13
This article is the written version of a talk delivered at the Workshop on Nonlinear Dynamics and Fundamental Interactions in Tashkent and starts with an introduction into quantum chaos and its relationship to classical chaos. The Bohigas-Giannoni-Schmit conjecture is formulated and evaluated within random-matrix theory. In accordance to the title, the presentation is twofold and begins with research results on quantum chromodynamics and the quark-gluon plasma. We conclude with recent research work on the spectroscopy of baryons. Within the framework of a relativistic constituent quark model we investigate the excitation spectra of the nucleon and the delta with regard to a possible chaotic behavior for the cases when a hyperfine interaction of either Goldstone-boson-exchange or one-gluon-exchange type is added to the confinement interaction. Agreement with predictions from the experimental hadron spectrum is established.
Heller, E.J.; Davis, M.J.
1982-06-10
This paper reviews some of the opinions on quantum chaos put forth at the 1981 American Conference on Theoretical Chemistry and presents evidence to support the author's point of view. The degree of correspondence between classical and quantum onset and extent of chaos differs markedly according to the definition adopted for quantum chaos. At one extreme, a quantum generalization of the classical Kolmolgorov entropy which give zero entrophy for quantum systems with a discrete spectrum regardless of the classical properties, was a suitable foundation for the definition of quantum chaos. At the other, the quantum phase space definition shows generally excellent correspondence to the classical phase space measures. The authors preferred this approach. Another point of controversy is the question of whether the spectrum of energy levels (or its variation with some parameter of the Hamiltonian) is enough to characterize the quantum chaos (or lack of it), or whether more information is needed (i.e., eigenfunctions). The authors conclude that one does not want to rely upon eigenvalues alone to characterize the degree of chaos in the quantum dynamics.
Sprott, Julien Clinton
2010-01-01
. For example, the van der Pol equation has an x2 in the damping term [van der Pol, 1926], while the Rayleigh in the case of small damping. Moreover, the chaos persists as the damping is reduced to zero. Keywords: Chaos( x, x), contains at least one nonlinearity in the damping ( x) term or the restor- ing force (x) term
Experimental Characterization of Transition to Chaos in the Presence of Noise Ying-Cheng Lai,1,2
Lai, Ying-Cheng
Experimental Characterization of Transition to Chaos in the Presence of Noise Bin Xu,1 Ying; published 23 April 2003) Transition to chaos in the presence of noise is an important problem in nonlinear exponent to the noise variation near the transition. Here we present experimental observation of noise
Fractal Patterns and Chaos Games
ERIC Educational Resources Information Center
Devaney, Robert L.
2004-01-01
Teachers incorporate the chaos game and the concept of a fractal into various areas of the algebra and geometry curriculum. The chaos game approach to fractals provides teachers with an opportunity to help students comprehend the geometry of affine transformations.
Application of Chaos Theory to Psychological Models
NASA Astrophysics Data System (ADS)
Blackerby, Rae Fortunato
This dissertation shows that an alternative theoretical approach from physics--chaos theory--offers a viable basis for improved understanding of human beings and their behavior. Chaos theory provides achievable frameworks for potential identification, assessment, and adjustment of human behavior patterns. Most current psychological models fail to address the metaphysical conditions inherent in the human system, thus bringing deep errors to psychological practice and empirical research. Freudian, Jungian and behavioristic perspectives are inadequate psychological models because they assume, either implicitly or explicitly, that the human psychological system is a closed, linear system. On the other hand, Adlerian models that require open systems are likely to be empirically tenable. Logically, models will hold only if the model's assumptions hold. The innovative application of chaotic dynamics to psychological behavior is a promising theoretical development because the application asserts that human systems are open, nonlinear and self-organizing. Chaotic dynamics use nonlinear mathematical relationships among factors that influence human systems. This dissertation explores these mathematical relationships in the context of a sample model of moral behavior using simulated data. Mathematical equations with nonlinear feedback loops describe chaotic systems. Feedback loops govern the equations' value in subsequent calculation iterations. For example, changes in moral behavior are affected by an individual's own self-centeredness, family and community influences, and previous moral behavior choices that feed back to influence future choices. When applying these factors to the chaos equations, the model behaves like other chaotic systems. For example, changes in moral behavior fluctuate in regular patterns, as determined by the values of the individual, family and community factors. In some cases, these fluctuations converge to one value; in other cases, they diverge in still other cases, they oscillate periodically among two or more precise values. At certain values, the equations iterate random results, with no convergence, divergence or periodicity: "chaos." At still other values, the equations behave chaotically for many iterations; then a periodic oscillation emerges from the chaos. These emergent patterns provide a significantly better model fit to the dynamic reality of psychological behavior because qualitatively reorganized behavior is logically possible and incorporated in the model's metaphysical assumptions.
ARITHMETIC QUANTUM CHAOS JENS MARKLOF
Marklof, Jens
ARITHMETIC QUANTUM CHAOS JENS MARKLOF 1. Introduction The central objective in the study of quantum (Berry and Tabor 1977; Bohigas, Giannoni and Schmit 1984). Arithmetic quantum chaos (AQC) refers chaos is to characterize universal properties of quantum systems that reflect the regular or chaotic
QUANTUM CHAOS IN QUANTUM NETWORKS()
Shepelyansky, Dima
QUANTUM CHAOS IN QUANTUM NETWORKS() Chepelianskii Alexei LycÂ´ee Pierre de Fermat and Quantware MIPS Computers and Quantum Chaos", June 28 - 30, 2001, Villa Olmo, Como, Italy #12;SHORT DESCRIPTION OF THE RESULTS Quantum chaos in a quantum small world We introduce and study a quantum small world model
Rey Juan Carlos, Universidad
. Introduction This paper is concerned with the appearance of homoclinic and heteroclinic instabilities and chaos and airplane wings, the beating of a heart, and the nonlinear model of a machine tool chatter [6]. A self
Quantum Chaos & Quantum Computers
D. L. Shepelyansky
2000-06-15
The standard generic quantum computer model is studied analytically and numerically and the border for emergence of quantum chaos, induced by imperfections and residual inter-qubit couplings, is determined. This phenomenon appears in an isolated quantum computer without any external decoherence. The onset of quantum chaos leads to quantum computer hardware melting, strong quantum entropy growth and destruction of computer operability. The time scales for development of quantum chaos and ergodicity are determined. In spite the fact that this phenomenon is rather dangerous for quantum computing it is shown that the quantum chaos border for inter-qubit coupling is exponentially larger than the energy level spacing between quantum computer eigenstates and drops only linearly with the number of qubits n. As a result the ideal multi-qubit structure of the computer remains rather robust against imperfections. This opens a broad parameter region for a possible realization of quantum computer. The obtained results are related to the recent studies of quantum chaos in such many-body systems as nuclei, complex atoms and molecules, finite Fermi systems and quantum spin glass shards which are also reviewed in the paper.
Experimental observation of quantum chaos in a beam of light.
Lemos, Gabriela B; Gomes, Rafael M; Walborn, Stephen P; Souto Ribeiro, Paulo H; Toscano, Fabricio
2012-01-01
The manner in which unpredictable chaotic dynamics manifests itself in quantum mechanics is a key question in the field of quantum chaos. Indeed, very distinct quantum features can appear due to underlying classical nonlinear dynamics. Here we observe signatures of quantum nonlinear dynamics through the direct measurement of the time-evolved Wigner function of the quantum-kicked harmonic oscillator, implemented in the spatial degrees of freedom of light. Our setup is decoherence-free and we can continuously tune the semiclassical and chaos parameters, so as to explore the transition from regular to essentially chaotic dynamics. Owing to its robustness and versatility, our scheme can be used to experimentally investigate a variety of nonlinear quantum phenomena. As an example, we couple this system to a quantum bit and experimentally investigate the decoherence produced by regular or chaotic dynamics. PMID:23169052
Foukzon, Jaykov
2008-01-01
Advanced numerical-analytical study of the three-dimensional nonlinear stochastic partial differential equation, analogous to that proposed by V. N. Nikolaevski to describe longitudinal seismic waves, is presented. The equation has a threshold of short-wave instability and symmetry, providing long-wave dynamics. Proposed new mechanism for quantum "super chaos" generating in nonlinear dynamical systems. The hypothesis is said, that strong physical turbulence could be identified with quantum chaos of considered type.
ERIC Educational Resources Information Center
Shamama-tus-Sabah, Syeda; Gilani, Nighat; Wachs, Theodore D.
2011-01-01
Recent findings from Western developed countries have linked home chaos to children's cognitive performance and behavioral problems. In the present paper we test whether the same pattern of associations can be replicated in a non-Western developing country. Our sample was 203 Pakistani primary school children. To assess home chaos the Confusion,…
Chaos in a Fractional Order Chua System
NASA Technical Reports Server (NTRS)
Lorenzo, Carl F.; Hartley, Tom T.; Qammar, Helen Killory
1996-01-01
This report studies the effects of fractional dynamics in chaotic systems. In particular, Chua's system is modified to include fractional order elements. Varying the total system order incrementally from 2.6 to 3.7 demonstrates that systems of 'order' less than three can exhibit chaos as well as other nonlinear behavior. This effectively forces a clarification of the definition of order which can no longer be considered only by the total number of differentiations or by the highest power of the Laplace variable.
A Description of Quantum Chaos
Kei Inoue; Andrzej Kossakowski; Masanori Ohya
2004-06-30
A measure describing the chaos of a dynamics was introduced by two complexities in information dynamics, and it is called the chaos degree. In particular, the entropic chaos degree has been used to characterized several dynamical maps such that logistis, Baker's, Tinckerbel's in classical or quantum systems. In this paper, we give a new treatment of quantum chaos by defining the entropic chaos degree for quantum transition dynamics, and we prove that every non-chaotic quantum dynamics, e.g., dissipative dynamics, has zero chaos degree. A quantum spin 1/2 system is studied by our chaos degree, and it is shown that this degree well describes the chaotic behavior of the spin system.
CHARACTERIZATION OF NON-LINEAR CELLULAR AUTOMATA MODEL FOR PATTERN RECOGNITION
Ganguly, Niloy
CHARACTERIZATION OF NON-LINEAR CELLULAR AUTOMATA MODEL FOR PATTERN RECOGNITION Niloy Ganguly 1 to be at the edge of chaos. Keywords: Cellular Automata, GA, Edge of Chaos, Pattern Recognition. 1 Introduction establishes the non-linear Cellular Automata (CA) as a powerful pattern recognizer. The special class of CA
Parametrization of nonlinear and chaotic oscillations in driven beam-plasma diodes
Min Sup Hur; Hae June Lee; Jae Koo Lee
1998-01-01
Nonlinear phenomena in a driven plasma diode are studied using a fluid code and the particle-in-cell simulation code xpdp1. When a uniform electron beam is injected to a bounded diode filled with uniform ion background, the beam is destabilized by the Pierce instability and a perturbation grows to exhibit nonlinear oscillations including chaos. Two standard routes to chaos, period doubling
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. PMID:26428568
A DC-to-Three-Phase-AC High-Frequency Link Converter With Compensation for Nonlinear Distortion
Dipankar De; Venkataramanan Ramanarayanan
2010-01-01
This paper focuses on a new high-frequency (HF) link dc-to-three-phase-ac power converter. The least number of switching devices among other HF link dc-to-three-phase-ac converters, improved power density due to the absence of devices of bidirectional voltage-blocking capability, simple commutation requirements, and isolation between input and output are the integral features of this topology. The commutation process of the converter requires
NASA Astrophysics Data System (ADS)
Geddada, Nagesh; Karanki, Srinivas B.; Mishra, Mahesh K.
2014-06-01
This paper proposes a modified four-leg distribution static compensator (DSTATCOM) topology for compensation of unbalanced and nonlinear loads in three-phase four-wire distribution system. DSTATCOM, connected in parallel to the load, supplies reactive and harmonic powers demanded by unbalanced nonlinear loads. In this proposed topology, the voltage source inverter (VSI) of DSTATCOM is connected to point of common coupling (point of interconnection of source, load, DSTATCOM) through interface inductor and series capacitance, unlike the conventional topology which consists of interface inductor alone. Load compensation with a lower value of input DC link voltage of VSI is possible in this modified topology compared to conventional topology. A comparative study on modified and conventional topologies in terms of voltage rating of inverter power switches, switching losses in VSI and power rating of input DC capacitor of VSI is presented. The detailed design aspects of DC link capacitor and interface series capacitor are also presented. The reference filter currents are generated using instantaneous symmetrical component theory and are tracked using hysteresis current control technique. A detailed simulation study is carried out, to compare the compensation performances of conventional, modified topologies using PSCAD simulator and experimental studies are done to validate the simulation results.
Self-generation and management of spin-electromagnetic wave solitons and chaos
Ustinov, Alexey B.; Kondrashov, Alexandr V.; Nikitin, Andrey A.; Kalinikos, Boris A.
2014-06-09
Self-generation of microwave spin-electromagnetic wave envelope solitons and chaos has been observed and studied. For the investigation, we used a feedback active ring oscillator based on artificial multiferroic, which served as a nonlinear waveguide. We show that by increasing the wave amplification in the feedback ring circuit, a transition from monochromatic auto-generation to soliton train waveform and then to dynamical chaos occurs in accordance with the Ruelle-Takens scenario. Management of spin-electromagnetic-wave solitons and chaos parameters by both dielectric permittivity and magnetic permeability of the multiferroic waveguiding structure is demonstrated.
Complexity: Order contra Chaos
California at Davis, University of
and typically impractical effort. Thus, mathematical techniques were developed to invert the equations of motion Berkeley, California 94720 USA Abstract A concise commentary on observing and modeling complexity within in deterministic chaos: the breakdown of predictability, observation of a complex process, and the mathematical
Nonlinear dynamics established in the ENSO
Elsner, J.B. (Florida State Univ., Tallahassee (United States)); Tsonis, A.A. (Univ. of Wisconsin, Milwaukee (United States))
1993-02-05
A time series describing the El-Nino-Southern Oscillation (ENSO) is analyzed using the latest techniques of chaos theory. The methods which rely on resampling statistics were developed to more finely distinguish between nonlinearity and linear correlated noise. From the results significant nonlinear structure arising from ENSO dynamics on the monthly time scale is established. 14 refs., 4 figs.
Quantum chaos meets coherent control.
Gong, Jiangbin; Brumer, Paul
2005-01-01
Coherent control of atomic and molecular processes has been a rapidly developing field. Applications of coherent control to large and complex molecular systems are expected to encounter the effects of chaos in the underlying classical dynamics, i.e., quantum chaos. Hence, recent work has focused on examining control in model chaotic systems. This work is reviewed, with an emphasis on a variety of new quantum phenomena that are of interest to both areas of quantum chaos and coherent control. PMID:15796694
Chaos, population biology, and epidemiology: some research implications.
Philippe, P
1993-08-01
In this article I aim to provide some feeling of the new paradigm of disease causation (chaos) as it applies to the field of population biology and epidemiology. A secondary objective is to show, with the aid of qualitative methods, how one can approach chaos in time-series data. The multifactorial stochastic paradigm of causation is contrasted with the new deterministic approach. This approach is embedded in the theory of nonlinear system dynamics. Chaos implies that randomness is intrinsic to a nonlinear deterministic system; this is true despite the extent of knowledge of the intervening causes and, ultimately, despite determinism. Three research avenues are discussed in depth from the standpoint of chaos theory. First, the topic of sporadic epidemics is dealt with. I argue that the space-time clustering of cases from a starting epidemic is due to a sudden and high increase of the contact rate beyond a threshold. Interaction rather than main effects and nonlinear rather than linear dynamics are involved. Second, the incubation period of disease is studied. I advocate that an individual-level deterministic process underlies Sartwell's model of the incubation period. This accounts for the robustness of the model vis-à-vis confounding variables. Third, monozygotic twinning is analyzed. Assumed by some to be a random process, monozygotic twinning proves to be dynamically different from dizygotic or single-maternity processes; its dynamics can actually be chaotic. Throughout the provided examples, the point is made that chancelike phenomena are primarily concerned with chaos theory. For biological problems showing recurrent inconsistencies by stochastic modeling, dynamic modeling should be envisaged. Inconsistencies can suggest that the relevant factors are out of the model and that they are related deterministically. Finally, spectral analysis and attractors in the phase space are presented; these tools can aid the population biologist in tracing out chaos from time-series data sets. Several time-series data sets are simulated according to a simple nonlinear difference equation that bears some relationship to the basics of the dynamics of infections in the population. I show how the series can be analyzed and interpreted. Much research remains to be carried out until the nonlinear effects of risk factors can be validated. The undertaking is worth the effort, as a new paradigm of causation is at stake. PMID:8406405
NASA Technical Reports Server (NTRS)
Hodges, D. H.
1976-01-01
Nonlinear equations of motion for a cantilever rotor blade are derived for the hovering flight condition. The blade is assumed to have twist, precone, droop, sweep, torque offset and blade root offset, and the elastic axis and the axes of center of mass, tension, and aerodynamic center coincident at the quarter chord. The blade is cantilevered in bending, but has a torsional root spring to simulate pitch link flexibility. Aerodynamic forces acting on the blade are derived from strip theory based on quasi-steady two-dimensional airfoil theory. The equations are hybrid, consisting of one integro-differential equation for root torsion and three integro-partial differential equations for flatwise and chordwise bending and elastic torsion. The equations are specialized for a uniform blade and reduced to nonlinear ordinary differential equations by Galerkin's method. They are linearized for small perturbation motions about the equilibrium operating condition. Modal analysis leads to formulation of a standard eigenvalue problem where the elements of the stability matrix depend on the solution of the equilibrium equations. Two different forms of the root torsion equation are derived that yield virtually identical numerical results. This provides a reasonable check for the accuracy of the equations.
Nonlinear waves: Dynamics and evolution
A. V. Gaponov-Grekhov; M. I. Rabinovich
1989-01-01
Papers on nonlinear waves are presented, covering topics such as the history of studies on nonlinear dynamics since Poincare, attractors, pattern formation and the dynamics of two-dimensional structures in nonequilibirum dissipative media, the onset of spatial chaos in one-dimensional systems, and self-organization phenomena in laser thermochemistry. Additional topics include criteria for the existence of moving structures in two-component reaction-diffusion systems,
Coherence properties of cycling chaos
T. A. Levanova; G. V. Osipov; A. Pikovsky
2013-10-11
Cycling chaos is a heteroclinic connection between several chaotic attractors, at which switching between the chaotic sets occur at growing time intervals. Here we characterize the coherence properties of these switchings, considering nearly periodic regimes that appear close to the cycling chaos due to imperfections or to instability. Using numerical simulations of coupled Lorenz, Roessler, and logistic map models, we show that the coherence is high in the case of imperfection (so that asymptotically the cycling chaos is very regular), while it is low close to instability of the cycling chaos.
Noise tolerant spatiotemporal chaos computing
Kia, Behnam; Kia, Sarvenaz; Ditto, William L. [Department of Physics and Astronomy, University of Hawaii at Manoa, Honolulu, Hawaii 96822 (United States); Lindner, John F. [Physics Department, The College of Wooster, Wooster, Ohio 44691 (United States); Sinha, Sudeshna [Indian Institute of Science Education and Research (IISER), Mohali, Punjab 140306 (India)
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.
Coherence properties of cycling chaos
NASA Astrophysics Data System (ADS)
Levanova, T. A.; Osipov, G. V.; Pikovsky, A.
2014-08-01
Cycling chaos is a heteroclinic connection between several chaotic attractors, at which switchings between the chaotic sets occur at growing time intervals. Here we characterize the coherence properties of these switchings, considering nearly periodic regimes that appear close to the cycling chaos due to imperfections or to instability. Using numerical simulations of coupled Lorenz, Roessler, and logistic map models, we show that the coherence is high in the case of imperfection (so that asymptotically the cycling chaos is very regular), while it is low close to instability of the cycling chaos.
Chaos supported stochastic resonance in a metal-ferroelectric-semiconductor heterostructure
NASA Astrophysics Data System (ADS)
Mereu, B.; Cristescu, C. P.; Alexe, M.
2005-04-01
An experimental study is presented on a complex nonlinear system showing a particular type of dynamics that can be interpreted as stochastic resonance. The system consists of a metal-ferroelectric-semiconductor structure, which plays the role of a nonlinear element in an electric circuit with linear resistance, inductance, and capacitance connected in series ( RLC series circuit) driven externally by a high-amplitude harmonic voltage source. The system presents various kinds of nonlinear behavior, of which the simplest, consisting of a period-doubling evolution to chaos, is of interest to this study. The broadband intrinsic chaos emerging after a period-doubling sequence exists for a large range of frequencies of the driving voltage. The appearance of the chaotic dynamics is associated with the promotion of a low-frequency harmonic spectral component. This is interpreted as stochastic resonance with intrinsic chaos replacing noise, the usual variable in regular SR.
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. PMID:24433364
Classical chaos and its correspondence in superconducting qubits
NASA Astrophysics Data System (ADS)
Neill, C.; Campbell, B.; Chen, Z.; Chiaro, B.; Dunsworth, A.; Fang, M.; Hoi, I.; Kelly, J.; Megrant, A.; O'Malley, P.; Quintana, C.; Vainsencher, A.; Wenner, J.; White, T.; Barends, R.; Chen, Yu; Fowler, A.; Jeffrey, E.; Mutus, J.; Roushan, P.; Sank, D.; Martinis, J. M.
2015-03-01
Advances in superconducting qubits have made it possible to experimentally investigate quantum-classical correspondence by constructing quantum systems with chaotic classical limits. We study the quantum equivalent of a classical spinning top using three fully coupled qubits that behave as a single spin-3/2 and subject the spin to a sequence of non-linear rotations. The resulting entanglement bears a striking resemblance to the classical phase space, including bifurcation, and suggests that classical chaos manifests itself as quantum entanglement. Studying the orientation of the spin-3/2 reveals that the rotations which generate chaos and entanglement are at the same time the source of disagreement between the quantum and classical trajectories. Our experiment highlights the correspondence between classical non-linear dynamics and interacting quantum systems.
Intrinsic chaos and external noise in population dynamics
J. A. Gonzalez; L. Trujillo; A. Escalante
2003-05-21
We address the problem of the relative importance of the intrinsic chaos and the external noise in determining the complexity of population dynamics. We use a recently proposed method for studying the complexity of nonlinear random dynamical systems. The new measure of complexity is defined in terms of the average number of bits per time-unit necessary to specify the sequence generated by the system. This measure coincides with the rate of divergence of nearby trajectories under two different realizations of the noise. In particular, we show that the complexity of a nonlinear time-series model constructed from sheep populations comes completely from the environmental variations. However, in other situations, intrinsic chaos can be the crucial factor. This method can be applied to many other systems in biology and physics.
Stochastic chaos: An analog of quantum chaos
Millonas, M.M.
1993-01-01
Some intriguing connections between the properties of nonlinear, noise driven systems and the nonlinear dynamics of a particular set of Hamilton's equation are discussed. A large class of Fokker-Planck Equations, like the Schroedinger equation, can exhibit a transition in their spectral statistics as a coupling parameter is varied. This transition is connected to the transition to non-integrability in the Hamilton's equations.
Stochastic chaos: An analog of quantum chaos
Millonas, M.M. Santa Fe Institute, Santa Fe )
1993-08-10
Some intriguing connections between the properties of nonlinear noise driven systems and the nonlinear dynamics of a particular set of Hamilton's equation are discussed. A large class of Fokker-Planck Equations, like the Schroedinger equation, can exhibit a transition in their spectral statistics as a coupling parameter is varied. This transition is connected to the transition to non-integrability in the Hamilton's equations.
Stochastic chaos: An analog of quantum chaos
Millonas, M.M.
1993-07-01
Some intriguing connections between the properties of nonlinear, noise driven systems and the nonlinear dynamics of a particular set of Hamilton`s equation are discussed. A large class of Fokker-Planck Equations, like the Schroedinger equation, can exhibit a transition in their spectral statistics as a coupling parameter is varied. This transition is connected to the transition to non-integrability in the Hamilton`s equations.
NASA Technical Reports Server (NTRS)
2002-01-01
(Released 11 June 2002) The Science This fractured surface belongs to a portion of a region called Gorgonum Chaos located in the southern hemisphere of Mars. Gorgonum Chaos is named after the Gorgons in ancient Greek mythology. The Gorgons were monstrous sisters with snakes for hair, tusks like boars and lolling tongues who lived in caves. As it turns out this is indeed a fitting name for this region of Mars because it contains a high density of gullies that 'snake' their way down the walls of the troughs located in this region of chaos. Upon closer examination one finds that these gullies and alluvial deposits, initially discovered by Mars Global Surveyor, are visible on the trough walls (best seen near the bottom of the image). These gullies appear to emanate from a specific layer in the walls. The gullies have been proposed to have formed by the subsurface release of water. The Story This fractured, almost spooky-looking surface belongs to a region called Gorgonum Chaos in the southern hemisphere of Mars. Chaos is a term used for regions of Mars with distinctive areas of broken terrain like the one seen above. This area of Martian chaos is named after the Gorgons in ancient Greek mythology. The Gorgons were monstrous sisters with snakes for hair, tusks like boars, and lolling tongues, who lived in caves. The Gorgons, including famous sister Medusa, could turn a person to stone, and their writhing, snakelike locks cause revulsion to this day. Given the afflicted nature of this contorted terrain, with all of its twisted, branching channels and hard, stony-looking hills in the top half of the image, this is indeed a fitting name for this region of Mars. The name also has great appeal, because the area contains a high density of gullies that 'snake' their way down the walls of the troughs located in this region of Martian chaos. Gullies are trenches cut into the land as accelerated streams of water (or another liquid) erode the surface. To see these, click on the above image to get a high-resolution view, and then focus on the trenches at the bottom. Running down the walls of the trough are the thin, dark lines of the gullies. Beneath the grooved, gully channels are faint, softer-looking fans of material. These are called alluvial deposits. Alluvial simply means all of the sand, gravel, and dirt that is carried and deposited by a liquid. On Earth, that liquid is typically water. As the liquid carves the gully, the eroded material from the channels get carried along and deposited below in fan-like shapes. These gully features were initially discovered by Odyssey's sister orbiter, Mars Global Surveyor, and caused quite a bit of emotional chaos in the scientific community when they were announced. Why? If you look closely, you can see that the gullies seem to form from a specific layer in the wall. That is, they all seem to begin at roughly the same point on the wall. That suggests that maybe, just maybe, there's a subsurface source of water at that layer that sometimes leaks out and runs down the walls to form both the gullies and the skirt-like fans of deposits beneath them. Other scientists, however, loudly assert that another liquid besides water could have carved the gullies. The debate sometimes gets so intense, you'd think that the opposing sides would want to turn each other's ideas to stone! But not for long. While the debate rages on, the neat thing is that everyone's really united. The goal is to find out, and the way to find out is to keep proposing different hypotheses and testing them out. That's the excitement of science, where everyone's solid research counts, and divergent views are appreciated for keeping science sound.
NASA Astrophysics Data System (ADS)
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.
Quantum chaos in quantum dots coupled to bosons
S. Ahadpour; N. Hematpour
2012-07-24
Chaos transition, as an important topic, has become an active research subject in non-linear science. By considering a Dicke Hamiltonian coupled to a bath of harmonic oscillator, we have been able to introduce a logistic map with quantum corrections. Some basic dynamical properties, such as Lyapunov exponents and bifurcation diagram of the model are studied. we show that in this model, the transition from integrable motion to periodic, chaotic and hyperchaotic as the control parameter $r$ is increased.
Wigner-function nonclassicality as indicator of quantum chaos.
Kowalewska-Kud?aszyk, A; Kalaga, J K; Leo?ski, W
2008-12-01
We propose a Wigner-function-based parameter that can be used as an indicator of quantum chaos. This parameter is defined as "entropy" from the time dependence of "nonclassicality" proposed by A. Kenfack and K. Zyczkowski [J. Opt. B 6, 394 (2004)]. We perform our considerations for the system of damped nonlinear (Kerr-like) oscillator excited by a series of ultrashort external pulses. PMID:19256937
Warshawsky, Nora E; Joseph, M Lindell; Fowler, Debra L; Edmonson, Cole; Nelson-Brantley, Heather V; Kowalski, Karren
2015-03-01
The 2014 International Nursing Administration Research Conference, "Pioneering Through Chaos: Leadership for a Changing World," was held at the Texas Woman's University in Dallas, Texas, in the fall of 2014. The program drew more than 100 attendees from 4 countries. The conference informed attendees from both academe and practice about the role of nursing administration in navigating the dynamic healthcare climate. This article will report on the insights from the conference presenters. PMID:25689497
NASA Technical Reports Server (NTRS)
2004-01-01
23 October 2004 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows light-toned rock outcrops, possibly sedimentary rocks, in the Arsinoes Chaos region east of the Valles Marineris trough system. These rocky materials were once below the martian surface. These features are located near 7.2oS, 27.9oW. The image covers an area about 3 km (1.9 mi) wide. Sunlight illuminates the scene from the upper left.
Route to chaos for combustion instability in ducted laminar premixed flames
NASA Astrophysics Data System (ADS)
Kabiraj, Lipika; Saurabh, Aditya; Wahi, Pankaj; Sujith, R. I.
2012-06-01
Complex thermoacoustic oscillations are observed experimentally in a simple laboratory combustor that burns lean premixed fuel-air mixture, as a result of nonlinear interaction between the acoustic field and the combustion processes. The application of nonlinear time series analysis, particularly techniques based on phase space reconstruction from acquired pressure data, reveals rich dynamical behavior and the existence of several complex states. A route to chaos for thermoacoustic instability is established experimentally for the first time. We show that, as the location of the heat source is gradually varied, self-excited periodic thermoacoustic oscillations undergo transition to chaos via the Ruelle-Takens scenario.
International Journal of Bifurcation Chaos, Vol. No.
Lai, Ying-Cheng
International Journal of Bifurcation Chaos, Vol. No. 6 (2000) 1471--1483 c World Scientific a heuristic theory numerical examples illustrate this route highdimensional chaos. Introduction this paper there formal definition lowdimensional versus highdimensional chaos, notion lowdimensional chaos is char
ONSET OF CHAOS IN A MODEL OF QUANTUM COMPUTATION
G. BERMAN; ET AL
2001-02-01
Recently, the question of a relevance of the so-called quantum chaos has been raised in applications to quantum computation [2,3]. Indeed, according to the general approach to closed systems of finite number of interacting Fermi-particles (see, e.g. [4,5]), with an increase of an interaction between qubits a kind of chaos is expected to emerge in the energy spectra and structure of many-body states. Specifically, the fluctuations of energy levels and components of the eigenstates turn out to be very strong and described by the Random Matrix Theory. Clearly, if this happens in a quantum computer, it may lead to a destruction of the coherence of quantum computations due to internal decoherence inside many-body states. It is important to stress that quantum chaos occurs not only in the systems with random interaction, but also for purely dynamical interaction. In the latter case, the mechanism of chaos is due to a complex (non-linear) form of a two-body interaction represented in the basis of non-interacting particles. Numerical analysis [2] of a simplest model of quantum computer (2D model of 1/2-spins with a random interqubit interaction J) shows that with an increase of the number L of qubits, the chaos threshold J{sub cr} decreases as J{sub cr} {infinity} 1/L. On this ground, it was claimed that the onset of quantum chaos could be dangerous for quantum computers, since their effectiveness requires L >> 1. On the other hand, in [3] it was argued that in order to treat this problem properly, one needs to distinguish between chaotic properties of stationary states, and the dynamical process of quantum computation.
Chaos Theory and Post Modernism
ERIC Educational Resources Information Center
Snell, Joel
2009-01-01
Chaos theory is often associated with post modernism. However, one may make the point that both terms are misunderstood. The point of this article is to define both terms and indicate their relationship. Description: Chaos theory is associated with a definition of a theory dealing with variables (butterflies) that are not directly related to a…
Counseling Chaos: Techniques for Practitioners
ERIC Educational Resources Information Center
Pryor, Robert G. L.; Bright, Jim E. H.
2006-01-01
The chaos theory of careers draws together a number of themes in current theory and research. This article applies some of these themes to career counseling. The chaos theory of careers is outlined, and a conceptual framework for understanding assessment and counseling issues that focuses on convergent and emergent qualities is presented. Three…
Complex chaos in the conditional dynamics of qubits
Kiss, T.; Jex, I.; Vymetal, S.; Alber, G.
2006-10-15
We analyze the consequences of iterative measurement-induced nonlinearity on the dynamical behavior of qubits. We present a one-qubit scheme where the equation governing the time evolution is a complex-valued nonlinear map with one complex parameter. In contrast to the usual notion of quantum chaos, exponential sensitivity to the initial state occurs here. We calculate analytically the Lyapunov exponent based on the overlap of quantum states, and find that it is positive. We present a few illustrative examples of the emerging dynamics.
Quantum Chaos1 The term Quantum Chaos designates a body of knowledge which has been estab-
Weigert, Stefan
Quantum Chaos1 The term Quantum Chaos designates a body of knowledge which has been estab- lished unreliable if not effectively impossible. A considerable amount of studies relevant to Quantum Chaos revolve
Multiple time scale chaos in a Schmitt trigger circuit
NASA Astrophysics Data System (ADS)
Carroll, Thomas L.
2005-09-01
It is known that stray radio frequency signals can produce nonlinear effects that disrupt the operation of circuits, but the mechanisms by which this disruption occurs are not well known. In this paper, an emitter coupled Schmitt trigger circuit is driven with a high-frequency signal to look for disruptive effects. As the circuit makes a transition between mode locked states (period 2 and period 3, for example), there is a region of chaos in which the largest peak in the power spectrum is in between the mode-locked frequencies, and is not related to the driving frequency by an integer multiple. This chaos resembles the chaos seen during a period adding sequence, except that it contains frequencies ranging over many orders of magnitude, from the driving frequencies on the order of megahertz, down to a few hertz. It is found that only a one-transistor circuit is necessary to produce this extremely broadband chaos, and true quasiperiodicity is not seen in this circuit. The single-transistor circuit is then simulated to confirm the frequency conversion effects.
Feigenbaum graphs at the onset of chaos
Bartolo Luque; Lucas Lacasa; Alberto Robledo
2012-10-31
We analyze the properties of the self-similar network obtained from the trajectories of unimodal maps at the transition to chaos via the horizontal visibility (HV) algorithm. We first show that this network is uniquely determined by the encoded sequence of positions in the dynamics within the Feigenbaum attractor and it is universal in that it is independent of the shape and nonlinearity of the maps in this class. We then find that the network degrees fluctuate at all scales with an amplitude that increases as the size of the network grows. This suggests the definition of a graph-theoretical Lyapunov exponent that measures the expansion rate of trajectories in network space. On good agreement with the map's counterpart, while at the onset of chaos this exponent vanishes, the subexponential expansion and contraction of network degrees can be fully described via a Tsallis-type scalar deformation of the expansion rate, that yields a discrete spectrum of non-null generalized exponents. We further explore the possibility of defining an entropy growth rate that describes the amount of information created along the trajectories in network space. Making use of the trajectory distributions in the map's accumulation point and the scaling properties of the associated network, we show that such entropic growth rate coincides with the spectrum of graph-theoretical exponents, what appears as a set of Pesin-like identities in the network.
Chaos in hydrodynamic BL Herculis models
NASA Astrophysics Data System (ADS)
Smolec, R.; Moskalik, P.
2014-06-01
We present non-linear, convective, BL Her-type hydrodynamic models that show complex variability characteristic for deterministic chaos. The bifurcation diagram reveals a rich structure, with many phenomena detected for the first time in hydrodynamic models of pulsating stars. The phenomena include not only period doubling cascades en route to chaos (detected in earlier studies) but also periodic windows within chaotic band, type-I and type-III intermittent behaviour, interior crisis bifurcation and others. Such phenomena are known in many textbook chaotic systems, from the simplest discrete logistic map, to more complex systems like Lorenz equations. We discuss the physical relevance of our models. Although except of period doubling such phenomena were not detected in any BL Her star, chaotic variability was claimed in several higher luminosity siblings of BL Her stars - RV Tau variables, and also in longer-period, luminous irregular pulsators. Our models may help to understand these poorly studied stars. Particularly interesting are periodic windows which are intrinsic property of chaotic systems and are not necessarily caused by resonances between pulsation modes, as sometimes claimed in the literature.
NASA Technical Reports Server (NTRS)
2004-01-01
15 May 2004 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows the results of a small landslide off of a hillslope in the Aureum Chaos region of Mars. Mass movement occurred from right (the slope) to left (the lobate feature pointed left). Small dark dots in the landslide area are large boulders. This feature is located near 2.6oS, 24.5oW. This picture covers an area approximately 3 km (1.9 mi) across and is illuminated by sunlight from the left/upper left.
Complex Gaussian multiplicative chaos
Hubert Lacoin; Rémi Rhodes; Vincent Vargas
2015-02-15
In this article, we study complex Gaussian multiplicative chaos. More precisely, we study the renormalization theory and the limit of the exponential of a complex log-correlated Gaussian field in all dimensions (including Gaussian Free Fields in dimension 2). Our main working assumption is that the real part and the imaginary part are independent. We also discuss applications in 2D string theory; in particular we give a rigorous mathematical definition of the so-called Tachyon fields, the conformally invariant operators in critical Liouville Quantum Gravity with a c=1 central charge, and derive the original KPZ formula for these fields.
Complex Gaussian Multiplicative Chaos
NASA Astrophysics Data System (ADS)
Lacoin, Hubert; Rhodes, Rémi; Vargas, Vincent
2015-07-01
In this article, we study complex Gaussian multiplicative chaos. More precisely, we study the renormalization theory and the limit of the exponential of a complex log-correlated Gaussian field in all dimensions (including Gaussian Free Fields in dimension 2). Our main working assumption is that the real part and the imaginary part are independent. We also discuss applications in 2 D string theory; in particular we give a rigorous mathematical definition of the so-called Tachyon fields, the conformally invariant operators in critical Liouville Quantum Gravity with a c = 1 central charge, and derive the original KPZ formula for these fields.
NASA Astrophysics Data System (ADS)
Gandomi, A. H.; Yang, X.-S.; Talatahari, S.; Alavi, A. H.
2013-01-01
A recently developed metaheuristic optimization algorithm, firefly algorithm (FA), mimics the social behavior of fireflies based on the flashing and attraction characteristics of fireflies. In the present study, we will introduce chaos into FA so as to increase its global search mobility for robust global optimization. Detailed studies are carried out on benchmark problems with different chaotic maps. Here, 12 different chaotic maps are utilized to tune the attractive movement of the fireflies in the algorithm. The results show that some chaotic FAs can clearly outperform the standard FA.
Shujun Li
2005-12-12
This paper focuses on an interesting phenomenon when chaos meets computers. It is found that digital computers are absolutely incapable of showing true long-time dynamics of some chaotic systems, including the tent map, the Bernoulli shift map and their analogues, even in a high-precision floating-point arithmetic. Although the results cannot directly generalized to most chaotic systems, the risk of using digital computers to numerically study continuous dynamical systems is shown clearly. As a result, we reach the old saying that "it is impossible to do everything with computers only".
Efetov, K.B.
1997-07-01
Quantum disordered problems with a direction (imaginary vector potential) are discussed and mapped onto a supermatrix {sigma} model. It is argued that the 0D version of the {sigma} model may describe a broad class of phenomena that can be called directed quantum chaos. It is demonstrated by explicit calculations that these problems are equivalent to those of random asymmetric or non-Hermitian matrices. A joint probability of complex eigenvalues is obtained. The fraction of states with real eigenvalues proves to be always finite for time reversal invariant systems. {copyright} {ital 1997} {ital The American Physical Society}
David Merritt
1995-10-17
Recent results on chaos in triaxial galaxy models are reviewed. Central mass concentrations like those observed in early-type galaxies -- either stellar cusps, or massive black holes -- render most of the box orbits in a triaxial potential stochastic. Typical Liapunov times are 3-5 crossing times, and ensembles of stochastic orbits undergo mixing on time scales that are roughly an order of magnitude longer. The replacement of the regular orbits by stochastic orbits reduces the freedom to construct self-consistent equilibria, and strong triaxiality can be ruled out for galaxies with sufficiently high central mass concentrations.
Virgil Baran; Aldo Bonasera
1998-04-13
The asymptotic distance between trajectories $d_{\\infty}$, is studied in detail to characterize the occurrence of chaos. We show that this quantity is quite distinct and complementary to the Lyapunov exponents, and it allows for a quantitave estimate for the folding mechanism which keeps the motion bounded in phase space. We study the behaviour of $d_{\\infty}$ in simple unidimensional maps. Near a critical point $d_{\\infty}$ has a power law dependence on the control parameter. Furthermore, at variance with the Lyapunov exponents, it shows jumps when there are sudden changes on the available phase-space.
Briesemeister, Linda
[1] A. G. Angel, T. Hanney, and M. R. Evans. Condensation transitions in a model for a directed network with weighted links. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 73 is introduced. Simulations indicate that the model exhibits two types of condensation: (i) a phase in which
Dissipative nonlinear dynamics in holography
NASA Astrophysics Data System (ADS)
Basu, Pallab; Ghosh, Archisman
2014-02-01
We look at the response of a nonlinearly coupled scalar field in an asymptotically AdS black brane geometry and find a behavior very similar to that of known dissipative nonlinear systems like the chaotic pendulum. Transition to chaos proceeds through a series of period-doubling bifurcations. The presence of dissipation, crucial to this behavior, arises naturally in a black hole background from the ingoing conditions imposed at the horizon. AdS/CFT translates our solution to a chaotic response of O, the operator dual to the scalar field. Our setup can also be used to study quenchlike behavior in strongly coupled nonlinear systems.
Explore the chaos behaviour of water quality variability: a case study at Huaihe River, China
NASA Astrophysics Data System (ADS)
Shi, Bi; Jiang, Jiping; Sivakumar, Bellie; Wang, Peng; Zhou, Weiwen
2015-04-01
Few studies investigated the nonlinear behaviour of water quality time series in natural surface waters. The work examines water quality time series in a Chinese River based on phase space reconstruction and optimal embedding dimension of chaos theories. It covers 3 regular water quality index (DO, CODMn, NH3-N) and 27 online monitoring stations. Through calculating and determining embedding dimension, m value, we analysis the chaotic characteristic of water quality variability in the river. Results shown the correlation dimension of typical water quality time series and the spatial variability. Reliability of dimension estimate and relationship between those chaos behaviours and impact factors were also discussed. It will improves the understanding of the nonlinear characteristics of water quality variation and chaos predication model.
NASA Astrophysics Data System (ADS)
Asif, Rameez; Shabbir, Ghulam; Akram, Adeel
2013-09-01
The hybrid mid-link spectral inversion (H-MLSI) and digital signal processing techniques to compensate for the optical Kerr effects in 224 Gbit/s DP-16QAM transmission over 640 km of single-mode fiber are numerically evaluated. Digital signal processing methods, i.e., electronic dispersion compensation (EDC) and digital backward propagation (DBP) techniques, are implemented. The system is evaluated for diverse signal input launch powers for both single-channel and multichannel transmission in which five channels are multiplexed with a channel spacing of 100 GHz with central wavelength at 1550 nm. The system performance is enumerated by monitoring the bit error ratio. From the results, it is clear that the nonlinear threshold point is improved by 2 and 3 dBm signal power by using H-MLSI and DBP, respectively, with 20 steps per fiber span as compared to EDC. Furthermore, we have also evaluated the DBP complexity as compared to H-MLSI and the resultant impact on maximum transmission distance. Moreover, the performance penalty coming from the span-offset of H-MLSI can be reduced by employing DBP to compensate for the residual Kerr effects.
Chaos in a neural network circuit
NASA Astrophysics Data System (ADS)
Kepler, Thomas B.; Datt, Sumeet; Meyer, Robert B.; Abott, L. F.
1990-12-01
We have constructed a neural network circuit of four clipped, high-grain, integrating operational amplifiers coupled to each other through an array of digitally programmable resistor ladders (MDACs). In addition to fixed-point and cyclic behavior, the circuit exhibits chaotic behavior with complex strange attractors which are approached through period doubling, intermittent attractor expansion and/or quasiperiodic pathways. Couplings between the nonlinear circuit elements are controlled by a computer which can automatically search through the space of couplings for interesting phenomena. We report some initial statistical results relating the behavior of the network to properties of its coupling matrix. Through these results and further research the circuit should help resolve fundamental issues concerning chaos in neural networks.
Quantifying chaos of curvilinear beams via exponents
NASA Astrophysics Data System (ADS)
Awrejcewicz, J.; Krysko, V. A.; Kutepov, I. E.; Vygodchikova, I. Yu.; Krysko, A. V.
2015-10-01
We propose a procedure for predicting the stability loss and transition into chaos of a network of oscillators lying on a curve, where each of the oscillators can move in two perpendicular directions. Dynamics of the coupled oscillators are governed by the sixth-order PDE, which is directly derived using the classical hypotheses of a curvilinear flexible beam movement theory. We apply FDM (Finite Difference Method) to reduce PDEs into ODEs, and the used number of spatial coordinate positions defines the number of involved oscillators approximating the dynamics of our continuous structural member (beam). Our procedure has a few advantages over the classical approaches, which has been illustrated and discussed. The proposed method has been validated for non-linear dynamical regimes by using the classical vibrational analysis (time histories, frequency power spectra and Poincaré maps).
Quantum Chaos in Compact Lattice QED
B. A. Berg; H. Markum; R. Pullirsch
1998-12-10
Complete eigenvalue spectra of the staggered Dirac operator in quenched $4d$ compact QED are studied on $8^3 \\times 4$ and $8^3 \\times 6$ lattices. We investigate the behavior of the nearest-neighbor spacing distribution $P(s)$ as a measure of the fluctuation properties of the eigenvalues in the strong coupling and the Coulomb phase. In both phases we find agreement with the Wigner surmise of the unitary ensemble of random-matrix theory indicating quantum chaos. Combining this with previous results on QCD, we conjecture that quite generally the non-linear couplings of quantum field theories lead to a chaotic behavior of the eigenvalues of the Dirac operator.
Quantum chaos in compact lattice QED
Berg, B.A.; Markum, H.; Pullirsch, R.
1999-05-01
Complete eigenvalue spectra of the staggered Dirac operator in quenched 4D compact QED are studied on 8{sup 3}{times}4 and 8{sup 3}{times}6 lattices. We investigate the behavior of the nearest-neighbor spacing distribution P(s) as a measure of the fluctuation properties of the eigenvalues in the strong coupling and the Coulomb phase. In both phases we find agreement with the Wigner surmise of the unitary ensemble of random-matrix theory indicating quantum chaos. Combining this with previous results on QCD, we conjecture that quite generally the non-linear couplings of quantum field theories lead to a chaotic behavior of the eigenvalues of the Dirac operator. {copyright} {ital 1999} {ital The American Physical Society}
Electrokinetic instability and hydrodynamic chaos near electrodes
NASA Astrophysics Data System (ADS)
Davidson, Scott M.; Andersen, Mathias B.; Mani, Ali
2013-11-01
It is known that ion-concentration-polarization (ICP) near ion-selective membranes can lead to electrokinetic instability of an aqueous solution. Consistent with experimental observations, recent DNS studies demonstrate these instabilities and even predict hydrodynamic chaos when ICP is subject to high voltage. Through direct numerical simulation (DNS) of the coupled Poisson-Nernst-Planck and Navier-Stokes equations in two dimensions, we demonstrate that this phenomena is not limited to membranes, but is much more general. Our DNS results predict sustained chaotic behavior between blocking parallel electrodes under applied AC forcing and at an ideally polarizable cylinder in a DC electric field. Comparison with asymptotic predictions in the linear, nonlinear, and chaotic regimes is performed as well as analysis of transport effects.
Dynamical properties and chaos synchronization of improved Colpitts oscillators
NASA Astrophysics Data System (ADS)
Kengne, J.; Chedjou, J. C.; Kenne, G.; Kyamakya, K.
2012-07-01
In this paper, the dynamics and synchronization of improved Colpitts oscillators designed to operate in ultrahigh frequency range are considered. The model is described by a continuous time four-dimensional autonomous system with an exponential nonlinearity. The system is integrated numerically and various bifurcation diagrams and corresponding graphs of largest 1D Lyapunov exponent are plotted to summarize different scenarios leading to chaos. It is found that the oscillator moves from the state of fixed point motion to chaos via the usual paths of period-doubling, intermittency and interior crisis routes when monitoring the bias (i.e. power supply) in tiny ranges. In order to promote chaos-based synchronization designs of this type of oscillators, a synchronization strategy based upon the design of a nonlinear state observer is successfully adapted. The suggested approach enables synchronization to be achieved via a scalar transmitted signal which represents a suitable feature for communication applications. Numerical simulations are performed to demonstrate the effectiveness and feasibility of the proposed technique.
Distinguishing Error from Chaos in Ecological Time Series
NASA Astrophysics Data System (ADS)
Sugihara, George; Grenfell, Bryan; May, Robert M.
1990-11-01
Over the years, there has been much discussion about the relative importance of environmental and biological factors in regulating natural populations. Often it is thought that environmental factors are associated with stochastic fluctuations in population density, and biological ones with deterministic regulation. We revisit these ideas in the light of recent work on chaos and nonlinear systems. We show that completely deterministic regulatory factors can lead to apparently random fluctuations in population density, and we then develop a new method (that can be applied to limited data sets) to make practical distinctions between apparently noisy dynamics produced by low-dimensional chaos and population variation that in fact derives from random (high-dimensional)noise, such as environmental stochasticity or sampling error. To show its practical use, the method is first applied to models where the dynamics are known. We then apply the method to several sets of real data, including newly analysed data on the incidence of measles in the United Kingdom. Here the additional problems of secular trends and spatial effects are explored. In particular, we find that on a city-by-city scale measles exhibits low-dimensional chaos (as has previously been found for measles in New York City), whereas on a larger, country-wide scale the dynamics appear as a noisy two-year cycle. In addition to shedding light on the basic dynamics of some nonlinear biological systems, this work dramatizes how the scale on which data is collected and analysed can affect the conclusions drawn.
1314 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 16, NO. 6, DECEMBER 2007 Chaos for a Microelectromechanical Oscillator Governed by the Nonlinear Mathieu Equation Barry E. DeMartini, Student Member, IEEE, ASME Abstract--A variety of microelectromechanical (MEM) oscilla- tors is governed by a version
Chaotic braided solutions via rigorous numerics: chaos in the Swift-Hohenberg equation
van den Berg, Jan Bouwe
also be used to rigorously extract coarse topological information from the systems, often revealing complicated dynamics. In particular, proving the existence of chaos in nonlinear dynamical systems that lead to fourth order ODEs. In particular, the well-known Swift-Hohenberg equation, one of standard
El Nino on the Devil's Staircase: Annual Subharmonic Steps to Chaos
Fei-Fei Jin; J. David Neelin; Michael Ghil
1994-01-01
The source of irregularity in El Nino, the large interannual climate variation of the Pacific ocean-atmosphere system, has remained elusive. Results from an El Nino model exhibit transition to chaos through a series of frequency-locked steps created by nonlinear resonance with the Earth's annual cycle. The overlapping of these resonances leads to the chaotic behavior. This transition scenario explains a
Developing Integrated Arts Curriculum in Hong Kong: Chaos Theory at Work?
ERIC Educational Resources Information Center
Wong, Marina
2013-01-01
This article reports the development of integrated arts curriculum in two Hong Kong secondary schools over a 9-year period. Initial findings display a range of individual responses to educational change that are both non-predictable and non-linear. Chaos theory is used to explain these varied responses in terms of bifurcations. The findings of…
Dissipative Quantum Chaos: Transition from Wave Packet Collapse to Explosion Gabriel G. Carlo,1
Shepelyansky, Dima
Dissipative Quantum Chaos: Transition from Wave Packet Collapse to Explosion Gabriel G. Carlo,1 and leads to wave packet explosion. The transition from collapse to explosion takes place when the dissipation time scale exceeds the Ehrenfest time. For integrable nonlinear dynamics the explosion practically
Spatiotemporal chaos in sine-Gordon systems subjected to wave fields: onset and suppression.
Chacón, R; Bellorín, A; Guerrero, L E; González, J A
2008-04-01
The onset of spatiotemporal chaos in a damped sine-Gordon system subjected to a plane wave field as well as its suppression by an additional small-amplitude plane wave field are proposed theoretically and confirmed numerically. The relevance of these findings in the context of nonlinear magnetization waves is discussed. PMID:18517715
Deterministic Chaos and Noise in Three In Vitro Hippocampal Models of Epilepsy
Cvitanovc', Predrag
Deterministic Chaos and Noise in Three In Vitro Hippocampal Models of Epilepsy MARC W. SLUTZKY,1. UPOs of multiple periods were highly prevalent in experiments from all three epilepsy models: 73, Epilepsy, Nonlinear, Un- stable periodic orbit, Lyapunov exponent, Determinism, Potas- sium, GABA
NASA Astrophysics Data System (ADS)
Sander, Evelyn; Yorke, James A.
There are many ways that a person can encounter chaos, such as through a time series from a lab experiment, a basin of attraction with fractal boundaries, a map with a crossing of stable and unstable manifolds, a fractal attractor, or in a system for which uncertainty doubles after some time period. These encounters appear so diverse, but the chaos is the same in all of the underlying systems; it is just observed in different ways. We describe these different types of chaos. We then give two conjectures about the types of dynamical behavior that is observable if one randomly picks out a dynamical system without searching for a specific property. In particular, we conjecture that from picking a system at random, one observes (1) only three types of basic invariant sets: periodic orbits, quasiperiodic orbits, and chaotic sets; and (2) that all the definitions of chaos are in agreement.
Quantum Instantons and Quantum Chaos
H. Jirari; H. Kröger; X. Q. Luo; K. J. M. Moriarty; S. G. Rubin
2001-02-05
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.
Quantum Chaos: Spectral Analysis of Floquet Operators
James Matthew McCaw
2005-03-23
The Floquet operator, defined as the time-evolution operator over one period, plays a central role in the work presented in this thesis on periodically perturbed quantum systems. Knowledge of the spectral nature of the Floquet operator gives us information on the dynamics of such systems. The work presented here on the spectrum of the Floquet operator gives further insight into the nature of chaos in quantum mechanics. After discussing the links between the spectrum, dynamics and chaos and pointing out an ambiguity in the physics literature, I present a number of new mathematical results on the existence of different types of spectra of the Floquet operator. I characterise the conditions for which the spectrum remains pure point and then, on relaxing these conditions, show the emergence of a continuous spectral component. The nature of the continuous spectrum is further analysed, and shown to be singularly continuous. Thus, the dynamics of these systems are a candidate for classification as chaotic. A conjecture on the emergence of a continuous spectral component is linked to a long standing number-theoretic conjecture on the estimation of finite exponential sums.
Observation of multiple-valued attractors and crises in a driven nonlinear circuit
NASA Astrophysics Data System (ADS)
Ikezi, H.; Degrassie, J. S.; Jensen, T. H.
1983-08-01
The attractor of the chaos in a driven nonlinear dissipative circuit is observed. The attractor is made of a curve imperfectly folded many times. The crisis effect, the sudden onset of chaos caused by the collision of the subband attractor with the unstable periodic orbit, is verified experimentally.
Chao Family Comprehensive Cancer Center
The University of California, Irvine (UCI) Cancer Center was established in 1989 as a university-based cancer center. In 1994, it became an NCI-designated cancer center, and it achieved comprehensive cancer center status in 1997. Soon after, it was renamed in honor of the Chao family as the Chao Family Comprehensive Cancer Center (CFCCC), operating fully integrated research, prevention, diagnostic, treatment, and rehabilitation programs.
Sub-Poissonian statistics in order-to-chaos transition
Kryuchkyan, Gagik Yu.; Manvelyan, Suren B.
2003-07-01
We study the phenomena at the overlap of quantum chaos and nonclassical statistics for the time-dependent model of nonlinear oscillator. It is shown in the framework of Mandel Q parameter and Wigner function that the statistics of oscillatory excitation numbers is drastically changed in the order-to-chaos transition. The essential improvement of sub-Poissonian statistics in comparison with an analogous one for the standard model of driven anharmonic oscillator is observed for the regular operational regime. It is shown that in the chaotic regime, the system exhibits the range of sub-Poissonian and super-Poissonian statistics which alternate one to other depending on time intervals. Unusual dependence of the variance of oscillatory number on the external noise level for the chaotic dynamics is observed. The scaling invariance of the quantum statistics is demonstrated and its relation to dissipation and decoherence is studied.
Pattern dynamics and spatiotemporal chaos in the quantum Zakharov equations
Misra, A. P.; Shukla, P. K.
2009-05-15
The dynamical behavior of the nonlinear interaction of quantum Langmuir waves (QLWs) and quantum ion-acoustic waves (QIAWs) is studied in the one-dimensional quantum Zakharov equations. Numerical simulations of coupled QLWs and QIAWs reveal that many coherent solitary patterns can be excited and saturated via the modulational instability of unstable harmonic modes excited by a modulation wave number of monoenergetic QLWs. The evolution of such solitary patterns may undergo the states of spatially partial coherence (SPC), coexistence of temporal chaos and spatiotemporal chaos (STC), as well as STC. The SPC state is essentially due to ion-acoustic wave emission and due to quantum diffraction, while the STC is caused by the combined effects of SPC and quantum diffraction, as well as by collisions and fusions among patterns in stochastic motion. The energy in the system is strongly redistributed, which may switch on the onset of weak turbulence in dense quantum plasmas.
NASA Astrophysics Data System (ADS)
Schmidt, Britney E.
2013-10-01
A critical question for the habitability of Europa remains: how does the ice shell work? The detection of shallow subsurface lenses below Europa’s chaos implies that the ice shell is recycled rapidly and that Europa may be currently active. While this is not the first time liquid water has been implicated for Europa, the location of these features combined with new perspective on their dynamics frames the question in a new way. Melt lenses are intriguing potential habitats. Moreover, their formation requires the existence of impurities within the upper ice shell that may be sources of energy for microorganisms. Geomorphic evidence also exists for hydraulic redistribution of fluids both vertically and horizontally through pores and fractures. This process, observed in terrestrial ice shelves, may preserve liquid water within the ice matrix over many kilometers from the source. Horizontal transport of material may produce interconnectivity between distinct regions of Europa, thus preserving habitable conditions within the ice over a longer duration. At a surface age of 40-90 Myr, with 25-50% covered by chaos terrain, Europa's resurfacing rate is very high and water likely plays a significant role. Because of the vigor of overturn implied by this new work, it is likely that surface and subsurface materials are well-mixed within the largest and deepest lenses, providing a mechanism for bringing oxidants and other surface contaminants to the deeper ice shell where it can reach the ocean by convective or compositional effects. The timescales over which large lenses refreeze are large compared to the timescales for vertical transport, while the timescales for smaller lenses are comparable to or shorter than convective timescales. Moreover, marine ice accretion at the bottom of the ice shell may be contributing to a compositional buoyancy engine that would change the makeup of the ice shell. From this point of view, we evaluate the habitability of Europa’s ice and ocean in light of active processes that may form a “chaos conveyor belt” that drives material exchange on Europa.
Category:Quantum chaos Quantum Chaos emerged as a new field of physics from the
Shepelyansky, Dima
Category:Quantum chaos Quantum Chaos emerged as a new field of physics from the efforts in number theory, fractal and complex spectra, atomic and molecular physics, clusters and nuclei, quantum billiards and quantum chaos Categories: Chaos Physics Quantum Mechanics Dynamical Systems Category:Quantum
Strong and Weak Chaos in Networks of Semiconductor Lasers with Time-delayed Couplings
Sven Heiligenthal; Thomas Jüngling; Otti D'Huys; Diana A. Arroyo-Almanza; Miguel C. Soriano; Ingo Fischer; Ido Kanter; Wolfgang Kinzel
2012-10-05
Nonlinear networks with time-delayed couplings may show strong and weak chaos, depending on the scaling of their Lyapunov exponent with the delay time. We study strong and weak chaos for semiconductor lasers, either with time-delayed self-feedback or for small networks. We examine the dependence on the pump current and consider the question whether strong and weak chaos can be identified from the shape of the intensity trace, the auto-correlations and the external cavity modes. The concept of the sub-Lyapunov exponent $\\lambda_0$ is generalized to the case of two time-scale separated delays in the system. We give the first experimental evidence of strong and weak chaos in a network of lasers which supports the sequence 'weak to strong to weak chaos' upon monotonically increasing the coupling strength. Finally, we discuss strong and weak chaos for networks with several distinct sub-Lyapunov exponents and comment on the dependence of the sub-Lyapunov exponent on the number of a laser's inputs in a network.
Strong and weak chaos in networks of semiconductor lasers with time-delayed couplings.
Heiligenthal, Sven; Jüngling, Thomas; D'Huys, Otti; Arroyo-Almanza, Diana A; Soriano, Miguel C; Fischer, Ingo; Kanter, Ido; Kinzel, Wolfgang
2013-07-01
Nonlinear networks with time-delayed couplings may show strong and weak chaos, depending on the scaling of their Lyapunov exponent with the delay time. We study strong and weak chaos for semiconductor lasers, either with time-delayed self-feedback or for small networks. We examine the dependence on the pump current and consider the question of whether strong and weak chaos can be identified from the shape of the intensity trace, the autocorrelations, and the external cavity modes. The concept of the sub-Lyapunov exponent ?(0) is generalized to the case of two time-scale-separated delays in the system. We give experimental evidence of strong and weak chaos in a network of lasers, which supports the sequence of weak to strong to weak chaos upon monotonically increasing the coupling strength. Finally, we discuss strong and weak chaos for networks with several distinct sub-Lyapunov exponents and comment on the dependence of the sub-Lyapunov exponent on the number of a laser's inputs in a network. PMID:23944533
Ercsey-Ravasz, Mária; Toroczkai, Zoltán
2012-01-01
The mathematical structure of Sudoku puzzles is akin to hard constraint satisfaction problems lying at the basis of many applications, including protein folding and the ground-state problem of glassy spin systems. Via an exact mapping of Sudoku into a deterministic, continuous-time dynamical system, here we show that the difficulty of Sudoku translates into transient chaotic behavior exhibited by this system. We also show that the escape rate ?, an invariant of transient chaos, provides a scalar measure of the puzzle's hardness that correlates well with human difficulty ratings. Accordingly, ? = ?log10 ? can be used to define a “Richter”-type scale for puzzle hardness, with easy puzzles having 0 < ? ? 1, medium ones 1 < ? ? 2, hard with 2 < ? ? 3 and ultra-hard with ? > 3. To our best knowledge, there are no known puzzles with ? > 4. PMID:23061008
NASA Technical Reports Server (NTRS)
2006-01-01
11 January 2006 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows light-toned, layered rock outcrops in Eos Chaos, located near the east end of the Valles Marineris trough system. The outcrops occur in the form of a distinct, circular butte (upper half of image) and a high slope (lower half of image). The rocks might be sedimentary rocks, similar to those found elsewhere exposed in the Valles Marineris system and the chaotic terrain to the east of the region.
Location near: 12.9oS, 49.5oW Image width: 3 km (1.9 mi) Illumination from: lower left Season: Southern Summer
Overview of nonlinear dynamical systems and complexity theory
Herbert, D.E.
1996-06-01
A brief overview is presented of the principal elements of {open_quote}{open_quote}nonlinear dynamics{close_quote}{close_quote}: catastrophes, fractals, chaos, solitary waves, and coherent and dissipative structures. The text is followed by a set of 10 portraits of the strange and violent world of nonlinear dynamics. {copyright} {ital 1996 American Institute of Physics.}
Nonlinear modeling and bifurcations in the boost converter
Soumitro Banerjee; Krishnendu Chakrabarty
1998-01-01
The occurrence of nonlinear phenomena like subharmonics and chaos in power electronic circuits has been reported recently. In this paper, the authors investigate these phenomena in the current-mode-controlled boost power converter. A nonlinear model in the form of a mapping from one point of observation to the next has been derived. The map has a closed form even when the
Classical Chaos and its Quantum Manifestations
Shepelyansky, Dima
Classical Chaos and its Quantum Manifestations Sputnik Conference of STATPHYS 20 In honor of Boris of classical chaos have also become important in quantum systems due to a rapid technological progress in nanostructures and laser physics. The quantum and classical theory of chaos is developing rapidly
QUANTUM CHAOS, CLASSICAL RANDOMNESS, AND BOHMIAN MECHANICS
Goldstein, Sheldon
QUANTUM CHAOS, CLASSICAL RANDOMNESS, AND BOHMIAN MECHANICS Detlef DË? urr* ,+ , Sheldon Goldstein of quantum theory, Bohmian mechanics, in which ``quantum chaos'' also arises solely from the dynamical law. Moreover, this occurs in a manner far simpler than in the classical case. KEY WORDS: Quantum chaos; quantum
Finite Models for Arithmetical Quantum Chaos
Terras, Audrey
Finite Models for Arithmetical Quantum Chaos Audrey Terras Math. Dept., U.C.S.D., San Diego, Ca termed by Sarnak "arithmetic quantum chaos" when the manifolds are quotients of a symmet- ric space have been evident to physicists for some time. Here we survey what may be called "finite quantum chaos
UNIVERSALITIES: FROM ANDERSON LOCALIZATION TO QUANTUM CHAOS
Simons, Ben
COURSE 1 UNIVERSALITIES: FROM ANDERSON LOCALIZATION TO QUANTUM CHAOS BORIS L. ALTSHULER AND B. D, and Quantum Chaos 73 8.1. Quantum Billiards 74 8.2. Numerics 75 8.3. Hard and Soft Chaos 77 8.4. Periodic
Invited review Nonlinear dynamical analysis of EEG and MEG: Review of an emerging field
C. J. Stam
Many complex and interesting phenomena in nature are due to nonlinear phenomena. The theory of nonlinear dynamical systems, also called 'chaos theory', has now progressed to a stage, where it becomes possible to study self-organization and pattern formation in the complex neuronal networks of the brain. One approach to nonlinear time series analysis consists of reconstructing, from time series of
Nonlinear dynamical analysis of EEG and MEG: Review of an emerging field
C. J. Stam
2005-01-01
Many complex and interesting phenomena in nature are due to nonlinear phenomena. The theory of nonlinear dynamical systems, also called ‘chaos theory’, has now progressed to a stage, where it becomes possible to study self-organization and pattern formation in the complex neuronal networks of the brain. One approach to nonlinear time series analysis consists of reconstructing, from time series of
The Nonlinear Schrodinger Equation as Both a PDE and a Dynamical System
Cai, David
The Nonlinear SchrÂ¨odinger Equation as Both a PDE and a Dynamical System David Cai \\Lambda systems, dispersive turbulence and the propagation of spatiotemporal chaos. Nonlinear dispersive wavesÂ98Â1Â0256, and Sloan Foundation Grant #96Â3Â1. i #12; Abstract Nonlinear dispersive wave equations provide excellent
Nonlinear dynamics, fractals, cardiac physiology and sudden death
NASA Technical Reports Server (NTRS)
Goldberger, Ary L.
1987-01-01
The authors propose a diametrically opposite viewpoint to the generally accepted tendency of equating healthy function with order and disease with chaos. With regard to the question of sudden cardiac death and chaos, it is suggested that certain features of dynamical chaos related to fractal structure and fractal dynamics may be important organizing principles in normal physiology and that certain pathologies, including ventricular fibrillation, represent a class of 'pathological periodicities'. Some laboratory work bearing on the relation of nonlinear analysis to physiological and pathophysiological data is briefly reviewed, with tentative theories and models described in reference to the mechanism of ventricular fibrillation.
New Features about Chaos in Bianchi I non-Abelian Born-Infeld cosmology
Dyadichev, Vladimir V.; Gal'tsov, Dmitri V. [Theoretical Physics, Moscow State University, 119899, Moscow (Russian Federation); Moniz, Paulo Vargas [Astronomy Unit, Mathematical Sciences, University of London, Mile End Road, London E1 4NS (United Kingdom)
2006-11-03
When the action is replaced by the Born-Infeld-type non-Abelian action (NBI), a chaos-order transition is observed in the high energy region for a Bianchi I cosmology with the homogeneous SU(2) Yang-Mills field. This is interpreted as a smothering effect due to (non-perturbative in {alpha}') string corrections to the classical EYM action. We give a numerical evidence for the chaos-order transition and present an analytical proof of regularity of color oscillations in the limit of strong Born-Infeld non-linearity.
Evidence for bifurcation and universal chaotic behavior in nonlinear semiconducting devices
Testa, J.; Perez, J.; Jeffries, C.
1982-01-01
Bifurcations, chaos, and extensive periodic windows in the chaotic regime are observed for a driven LRC circuit, the capacitive element being a nonlinear varactor diode. Measurements include power spectral analysis; real time amplitude data; phase portraits; and a bifurcation diagram, obtained by sampling methods. The effects of added external noise are studied. These data yield experimental determinations of several of the universal numbers predicted to characterize nonlinear systems having this route to chaos.
Nonlinear dynamics in meso and nano scales: fundamental aspects and applications.
da Luz, Marcos G E; Anteneodo, Celia
2011-01-28
This introduction to the special issue, Nonlinear dynamics in meso and nano scales: fundamental aspects and applications, gives a short overview about different contexts and current challenges posed by the emergence of nonlinearities at meso and nano characteristic sizes. It also addresses different aspects related to classical and quantum chaos. Moreover, it comments on the articles in this thematic publication, briefly summarizing their relevance in helping to understand the uprise of chaos and complex behaviour at those small scales. PMID:21149369
Magnetospheric Dynamics and Chaos Theory
G. P. Pavlos
2012-03-26
The results of this study were announced and published in Greek in the Fifth Panhellenic Conference Proceedings of the Hellenic Physical Society. It is the sequel of a previous study (Pavlos, 1988), in which it was introduced the hypothesis of magnetospheric chaos for the interpretation of magnetic substorms. In this study it is described the possibility of tracing magnetospheric chaos through Grassberger and Procassia method for the estimation of correlation dimension. In addition, it is proposed, the estimation of chaoticity through the computation of Lyapunov exponents. This study and its previous one constitute the first studies ever concerning the hypothesis of magnetospheric chaos for the interpretation and understanding the magnetospheric substorms. A series of publications of G.P.Pavlos followed the initial two studies in scientific journals and conference proceedings (www.gpavlos.gr). The publication of this study in English version has a historical importance and interest regarding the history of evolution of the concept of magnetospheric chaos. For an extended discussion concerning magnetospheric chaos, see, Pavlos 2012 ArXiv.
Bistability and chaos at low levels of quanta.
Gevorgyan, T V; Shahinyan, A R; Chew, Lock Yue; Kryuchkyan, G Yu
2013-08-01
We study nonlinear phenomena of bistability and chaos at a level of few quanta. For this purpose, we consider a single-mode dissipative oscillator with strong Kerr nonlinearity with respect to the dissipation rate driven by a monochromatic force as well as by a train of Gaussian pulses. The quantum effects and decoherence in the oscillatory mode are investigated in the framework of the purity of states and the Wigner functions calculated from the master equation. We demonstrate the quantum chaotic regime by means of a comparison between the contour plots of the Wigner functions and the strange attractors on the classical Poincaré section. Considering bistability at a low limit of quanta, we analyze the minimal level of excitation numbers at which the bistable regime of the system is displayed. We also discuss the formation of an oscillatory chaotic regime by varying oscillatory excitation numbers at ranges of a few quanta. We demonstrate quantum-interference phenomena that are assisted hysteresis-cycle behavior and quantum chaos for the oscillator driven by a train of Gaussian pulses. We establish the border of quantum-classical correspondence for chaotic regimes in the case of strong nonlinearities. PMID:24032904
Chaos control in passive walking dynamics of a compass-gait model
NASA Astrophysics Data System (ADS)
Gritli, Hassène; Khraief, Nahla; Belghith, Safya
2013-08-01
The compass-gait walker is a two-degree-of-freedom biped that can walk passively and steadily down an incline without any actuation. The mathematical model of the walking dynamics is represented by an impulsive hybrid nonlinear model. It is capable of displaying cyclic motions and chaos. In this paper, we propose a new approach to controlling chaos cropped up from the passive dynamic walking of the compass-gait model. The proposed technique is to linearize the nonlinear model around a desired passive hybrid limit cycle. Then, we show that the nonlinear model is transformed to an impulsive hybrid linear model with a controlled jump. Basing on the linearized model, we derive an analytical expression of a constrained controlled Poincaré map. We present a method for the numerical simulation of this constrained map where bifurcation diagrams are plotted. Relying on these diagrams, we show that the linear model is fairly close to the nonlinear one. Using the linearized controlled Poincaré map, we design a state feedback controller in order to stabilize the fixed point of the Poincaré map. We show that this controller is very efficient for the control of chaos for the original nonlinear model.
Chaos in a three-species food chain
Hastings, A.; Powell, T. (University of California, Davis (United States))
1991-06-01
A continuous time model of a food chain incorporating nonlinear functional (and numerical) responses exhibits chaotic dynamics in long-term behavior when biologically reasonable parameter values are chosen. The appearance of chaos in this model suggests the chaotic dynamics may be common in natural food webs. One approach to the study of an ecological community begins with an important object: its food web. Theoretical studies of food webs must contend with the question of how to couple the large number of interacting species.
Quantum chaos and order based on classically moving reference frames
Hai Wenhua; Xie Qiongtao; Fang Jianshu
2005-07-15
We develop a mathematically consistent approach for treating the quantum systems based on moving classical reference frames. The classical and quantum exact solutions show excellently classical-quantum correspondence, in which the quantum chaotic coherent states correspond to the classically chaotic motions. Applying the approach to the periodically driven linear and nonlinear oscillators, the regular and chaotic quantum states and quantum levels, and the quantum chaotic regions are evidenced. The results indicate that chaos may cause the collapse of matter wave packets and suppress the quantum effect of energy.
More memory under evolutionary learning may lead to chaos
NASA Astrophysics Data System (ADS)
Diks, Cees; Hommes, Cars; Zeppini, Paolo
2013-02-01
We show that an increase of memory of past strategy performance in a simple agent-based innovation model, with agents switching between costly innovation and cheap imitation, can be quantitatively stabilising while at the same time qualitatively destabilising. As memory in the fitness measure increases, the amplitude of price fluctuations decreases, but at the same time a bifurcation route to chaos may arise. The core mechanism leading to the chaotic behaviour in this model with strategy switching is that the map obtained for the system with memory is a convex combination of an increasing linear function and a decreasing non-linear function.
When chaos meets hyperchaos: 4D Rössler model
NASA Astrophysics Data System (ADS)
Barrio, Roberto; Angeles Martínez, M.; Serrano, Sergio; Wilczak, Daniel
2015-10-01
Chaotic behavior is a common feature of nonlinear dynamics, as well as hyperchaos in high-dimensional systems. In numerical simulations of these systems it is quite difficult to distinguish one from another behavior in some situations, as the results are frequently quite "noisy". We show that in such systems a global hyperchaotic invariant set is present giving rise to long hyperchaotic transient behaviors. This fact provides a mechanism for these noisy results. The coexistence of chaos and hyperchaos is proved via Computer-Assisted Proofs techniques.
Exploration of Order in Chaos with Replica Exchange Monte Carlo
Tatsuo Yanagita; Yukito Iba
2008-11-20
A method for exploring unstable structures generated by nonlinear dynamical systems is introduced. It is based on the sampling of initial conditions and parameters by Replica Exchange Monte Carlo (REM), and efficient both for the search of rare initial conditions and for the combined search of rare initial conditions and parameters. Examples discussed here include the sampling of unstable periodic orbits in chaos and search for the stable manifold of unstable fixed points, as well as construction of the global bifurcation diagram of a map.
Chaos, decoherence and quantum cosmology
Esteban Calzetta
2012-05-08
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 Wave function 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.
Global Superdiffusion of Weak Chaos
Itzhack Dana
2003-10-20
A class of kicked rotors is introduced, exhibiting accelerator-mode islands (AIs) and {\\em global} superdiffusion for {\\em arbitrarily weak} chaos. The corresponding standard maps are shown to be exactly related to generalized web maps taken modulo an ``oblique cylinder''. Then, in a case that the web-map orbit structure is periodic in the phase plane, the AIs are essentially {\\em normal} web islands folded back into the cylinder. As a consequence, chaotic orbits sticking around the AI boundary are accelerated {\\em only} when they traverse tiny {\\em ``acceleration spots''}. This leads to chaotic flights having a quasiregular {\\em steplike} structure. The global weak-chaos superdiffusion is thus basically different in nature from the strong-chaos one in the usual standard and web maps.
Nuclear spectroscopy and quantum chaos
NASA Astrophysics Data System (ADS)
Sakata, Fumihiko; Marumori, Toshio; Hashimoto, Yukio; Yamamoto, Yoshifumi; Tsukuma, Hidehiko; Iwasawa, Kazuo
1990-12-01
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 a 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.
Quantum Correlations, Chaos and Information
Vaibhav Madhok
2012-12-19
Quantum chaos is the study of quantum systems whose classical description is chaotic. How does chaos manifest itself in the quantum world? In this spirit, we study the dynamical generation of entanglement as a signature of chaos in a system of periodically kicked coupled-tops, where chaos and entanglement arise from the same physical mechanism. The long-time entanglement as a function of the position of an initially localized wave packet very closely correlates with the classical phase space surface of section - it is nearly uniform in the chaotic sea, and reproduces the detailed structure of the regular islands. The uniform value in the chaotic sea is explained by the random state conjecture. As classically chaotic dynamics take localized distributions in phase space to random distributions, quantized versions take localized coherent states to pseudo-random states in Hilbert space. Such random states are highly entangled, with an average value near that of the maximally entangled state. Continuing on our journey to find the footprints of chaos in the quantum world, we explore quantum signatures of classical chaos by studying the rate of information gain in quantum tomography. We find an increase in the rate of information gain and hence higher fidelities in the process when the Floquet maps employed increase in chaoticity. We make predictions for the information gain using random matrix theory in the fully chaotic regime and show a remarkable agreement between the two. The last part of this thesis is devoted to the study of the nature of quantum correlations themselves. We present an operational interpretation of quantum discord based on the quantum state merging protocol. Quantum discord is the markup in the cost of quantum communication in the process of quantum state merging, if one discards relevant prior information.
Observing chaos for quantum-dot microlasers with external feedback.
Albert, Ferdinand; Hopfmann, Caspar; Reitzenstein, Stephan; Schneider, Christian; Höfling, Sven; Worschech, Lukas; Kamp, Martin; Kinzel, Wolfgang; Forchel, Alfred; Kanter, Ido
2011-01-01
Chaos presents a striking and fascinating phenomenon of nonlinear systems. A common aspect of such systems is the presence of feedback that couples the output signal partially back to the input. Feedback coupling can be well controlled in optoelectronic devices such as conventional semiconductor lasers that provide bench-top platforms for the study of chaotic behaviour and high bit rate random number generation. Here we experimentally demonstrate that chaos can be observed for quantum-dot microlasers operating close to the quantum limit at nW output powers. Applying self-feedback to a quantum-dot microlaser results in a dramatic change in the photon statistics wherein strong, super-thermal photon bunching is indicative of random-intensity fluctuations associated with the spiked emission of light. Our experiments reveal that gain competition of few quantum dots in the active layer enhances the influence of self-feedback and will open up new avenues for the study of chaos in quantum systems. PMID:21694714
NASA Astrophysics Data System (ADS)
Lugiato, Luigi; Prati, Franco; Brambilla, Massimo
2015-03-01
Preface; Part I. Models, Propagation, Steady-State Phenomena: 1. Rate equation model for the laser; 2. Interaction of a system of two-level atoms with the electromagnetic field; 3. The Maxwell–Bloch equations; 4. Inclusion of the irreversible processes in the atomic equations; 5. Linear and nonlinear propagation in irreversible Maxwell–Bloch equations; 6. Optical nonlinearities: materials with quadratic nonlinearities; 7. Optical nonlinearities: materials with cubic nonlinearities; 8. Optical resonators: the planar ring cavity, empty cavity, linear cavity; 9. Nonlinear active ring cavity: the ring laser, stationary states; 10. The adiabatic elimination principle; 11. Nonlinear passive ring cavity: optical bistability; 12. Modal equations for the ring cavity: the single-mode model; 13. Single- and two-mode models; 14. Nonlinear dynamics in Fabry–Perot cavities; 15. Inhomogeneous broadening; 16. The semiconductor laser; 17. Laser without inversion and the effects of atomic coherence; Part II. Dynamical Phenomena, Instabilities, Chaos: 18. Some general aspects in nonlinear dissipative dynamical systems; 19. Special limits in the single-mode model; 20. The linear stability analysis of Maxwell–Bloch equations; 21. Adiabatic elimination in the complete Maxwell–Bloch equations; 22. Dynamical aspects in the laser; 23. Single- and multi-mode operation in inhomogeneously broadened lasers; 24. Dynamical aspects in optical bistability; 25. Self-pulsing in other optical systems; Part III. Transverse Optical Patterns: 26. Gaussian beams and modes of cavities with spherical mirrors; 27. General features about optical pattern formation in planar cavities; 28. The LL model; 29. Spatial patterns in cavities with spherical mirrors; 30. Cavity solitons; Appendixes; References; Index.
Controlling chaos with simple limiters
Corron; Pethel; Hopper
2000-04-24
New experimental results demonstrate that chaos control can be accomplished using controllers that are very simple relative to the system being controlled. Chaotic dynamics in a driven pendulum and a double scroll circuit are controlled using an adjustable, passive limiter-a weight for the pendulum and a diode for the circuit. For both experiments, multiple unstable periodic orbits are selectively controlled using minimal perturbations. These physical examples suggest that chaos control can be practically applied to a much wider array of important problems than initially thought possible. PMID:11019218
Hyperbolic Chaos of Turing Patterns
NASA Astrophysics Data System (ADS)
Kuptsov, Pavel V.; Kuznetsov, Sergey P.; Pikovsky, Arkady
2012-05-01
We consider time evolution of Turing patterns in an extended system governed by an equation of the Swift-Hohenberg type, where due to an external periodic parameter modulation longwave and shortwave patterns with length scales related as 1?3 emerge in succession. We show theoretically and demonstrate numerically that the spatial phases of the patterns, being observed stroboscopically, are governed by an expanding circle map, so that the corresponding chaos of Turing patterns is hyperbolic, associated with a strange attractor of the Smale-Williams solenoid type. This chaos is shown to be robust with respect to variations of parameters and boundary conditions.
Hyperbolic chaos of Turing patterns.
Kuptsov, Pavel V; Kuznetsov, Sergey P; Pikovsky, Arkady
2012-05-11
We consider time evolution of Turing patterns in an extended system governed by an equation of the Swift-Hohenberg type, where due to an external periodic parameter modulation longwave and shortwave patterns with length scales related as 1:3 emerge in succession. We show theoretically and demonstrate numerically that the spatial phases of the patterns, being observed stroboscopically, are governed by an expanding circle map, so that the corresponding chaos of Turing patterns is hyperbolic, associated with a strange attractor of the Smale-Williams solenoid type. This chaos is shown to be robust with respect to variations of parameters and boundary conditions. PMID:23003043
Hyperbolic Chaos of Turing Patterns
Pavel V. Kuptsov; Sergey P. Kuznetsov; Arkady Pikovsky
2012-05-10
We consider time evolution of Turing patterns in an extended system governed by an equation of the Swift-Hohenberg type, where due to an external periodic parameter modulation long-wave and short-wave patterns with length scales related as 1:3 emerge in succession. We show theoretically and demonstrate numerically that the spatial phases of the patterns, being observed stroboscopically, are governed by an expanding circle map, so that the corresponding chaos of Turing patterns is hyperbolic, associated with a strange attractor of the Smale-Williams solenoid type. This chaos is shown to be robust with respect to variations of parameters and boundary conditions.
Quantum Chaos and Quantum Algorithms
Daniel Braun
2001-10-05
It was recently shown (quant-ph/9909074) that parasitic random interactions between the qubits in a quantum computer can induce quantum chaos and put into question the operability of a quantum computer. In this work I investigate whether already the interactions between the qubits introduced with the intention to operate the quantum computer may lead to quantum chaos. The analysis focuses on two well--known quantum algorithms, namely Grover's search algorithm and the quantum Fourier transform. I show that in both cases the same very unusual combination of signatures from chaotic and from integrable dynamics arises.
Changes in Routes to Chaos with Increasing Number of Degrees of Freedom
NASA Astrophysics Data System (ADS)
Musielak, Zdzislaw
2006-10-01
There are at least five basic routes to chaos discovered in low-dimensional dynamical systems. To investigate routes to chaos in higher-dimensional systems, generalized Lorenz models and coupled Duffing oscillators were considered. The generalized Lorenz models with dimensions ranging from four to nine were constructed by taking into account higher-order modes in doubled Fourier expansions of a stream function and temperature variations. Degrees of freedom were added to the original Duffing system by coupling two, three, four, five and six non-linear oscillators together. The obtained results show that routes to chaos in these systems significantly change when the number of degrees of freedom is increased. Physical implications of these result will be discussed.
NASA Technical Reports Server (NTRS)
Smyrlis, Yiorgos S.; Papageorgiou, Demetrios T.
1991-01-01
The results of extensive computations are presented in order to accurately characterize transitions to chaos for the Kuramoto-Sivashinsky equation. In particular, the oscillatory dynamics in a window that supports a complete sequence of period doubling bifurcations preceding chaos is followed. As many as thirteen period doublings are followed and used to compute the Feigenbaum number for the cascade and so enable, for the first time, an accurate numerical evaluation of the theory of universal behavior of nonlinear systems, for an infinite dimensional dynamical system. Furthermore, the dynamics at the threshold of chaos exhibit a fractal behavior which is demonstrated and used to compute a universal scaling factor that enables the self-similar continuation of the solution into a chaotic regime.
Kullback-Leibler quantum divergence as an indicator of quantum chaos
Kowalewska-Kud?aszyk, A; Leo?ski, W; Long, V Cao; 10.1016/j.physleta.2012.02.049
2012-01-01
We discuss a system of a nonlinear Kerr-like oscillator externally pumped by ultra-short, external, coherent pulses. For such a system, we analyse the application of the Kullback-Leibler quantum divergence $K[\\rho||\\sigma]$ to the detection of quantum chaotic behaviour. Defining linear and nonlinear quantum divergences, and calculating their power spectra, we show that these parameters are more suitable indicators of quantum chaos than the fidelity commonly discussed in the literature, and are useful for dealing with short time series. Moreover, the nonlinear divergence is more sensitive to chaotic bands and to boundaries of chaotic regions, compared to its linear counterpart.
The Promise of Chaos... Chaos Article. . . continued from front cover
Chen, Guanrong "Ron"
, and biomedical science. Chaos control refers to the situation where chaotic dynam- ics is weakened or eliminated regulate dynamical re- sponses of mechanical and electronic devices (e.g., diodes, laser machines in the multi-planetary space system.A suitable modification of cha- otic dynamics such as stability conversion
Hill, Nick
2003-11-01
A waste revolution, potentially greater in impact than the changes in clinical waste disposal practices in the 1990s, is just over the horizon. There are many new initiatives and regulations relating to waste, its production, recycling and disposal. This article focuses on hazardous waste, a new category of waste with a much broader scope than the current special waste category. The volume of waste to be categorised as hazardous is expected to triple. One of the major reasons for change has occurred due to a long-running battle between the UK and other EU members about whether co-disposal of inert, biodegradable and hazardous waste in landfill sites is environmentally acceptable. The UK argued that co-disposal was acceptable but lost the argument. Consequently from July 2004 the EU Landfill Directive banning co-disposal will come into effect. According to the Government, this will mean that only 14 of the 182 commercial landfills that currently accept hazardous waste will continue to do so after July 2004. The expectation is that hazardous waste, such as electronic equipment, will require pre-treatment before landfilling. Meanwhile the landfill tax is expected to rise from 13 Pounds per tonne in 2002-03 to approximately 35 Pounds per tonne by 2007. In the near future, more waste will be classified as hazardous, it will cost much more to dispose of, waste management practices will need to change and the risk of breaking the law will increase. This article explains the actions that should be considered now to avoid chaos as the revolution takes place. PMID:14655415
A Simple Circuit for Demonstrating Regular and Synchronized Chaos.
ERIC Educational Resources Information Center
Carroll, Thomas L.
1995-01-01
Discusses the physics behind the synchronization of chaos. Describes an easy to build an electronic circuit which can be used to demonstrate chaos and the synchronization of chaos. Contains 19 references. (JRH)
Meaning Finds a Way: Chaos (Theory) and Composition
ERIC Educational Resources Information Center
Kyburz, Bonnie Lenore
2004-01-01
The explanatory power provided by the chaos theory is explored. A dynamic and reciprocal relationship between culture and chaos theory indicates that the progressive cultural work may be formed by the cross-disciplinary resonance of chaos theory.
NASA Astrophysics Data System (ADS)
Lafranceschina, Jacopo
Transient spatiotemporal chaos was reported in models for chemical reactions and in experiments for turbulence in shear flow. This study shows that transient spatiotemporal chaos also exists in a diffusively coupled Morris-Lecar (ML) neuronal network, with a collapse to either a global rest state or to a state of pulse propagation. Adding synaptic coupling to this network reduces the average lifetime of spatiotemporal chaos for small to intermediate coupling strengths and almost all numbers of synapses. For large coupling strengths, close to the threshold of excitation, the average lifetime increases beyond the value for only diffusive coupling, and the collapse to the rest state dominates over the collapse to a traveling pulse state. The regime of spatiotemporal chaos is characterized by a slightly increasing Lyapunov exponent and degree of phase coherence as the number of synaptic links increases. In contrast to the diffusive network, the pulse solution must not be asymptotic in the presence of synapses. The fact that chaos could be transient in higher dimensional systems, such as the one being explored in this study, point to its presence in every day life. Transient spatiotemporal chaos in a network of coupled neurons and the associated chaotic saddle provide a possibility for switching between metastable states observed in information processing and brain function. Such transient dynamics have been observed experimentally by Mazor, when stimulating projection neurons in the locust antennal lobe with different odors.
ERIC Educational Resources Information Center
Berthoff, Ann E.
This paper addresses the issue of learning to write and the need for defining a means of teaching the process of composing. Following a description of what kind of process writing is not, the composing process is presented as a continuum of making meaning out of a chaos of images, half-truths, remembrances, and syntactic fragments. The discovery…
Random matrices and quantum chaos
Kriecherbauer, Thomas; Marklof, Jens; Soshnikov, Alexander
2001-01-01
The theory of random matrices has far-reaching applications in many different areas of mathematics and physics. In this note, we briefly describe the state of the theory and two of the perhaps most surprising appearances of random matrices, namely in the theory of quantum chaos and in the theory of prime numbers. PMID:11553804
NASA Technical Reports Server (NTRS)
Lecar, Myron; Franklin, Fred A.; Holman, Matthew J.; Murray, Norman J.
2001-01-01
The physical basis of chaos in the solar system is now better understood: In all cases investigated so far, chaotic orbits result from overlapping resonances. Perhaps the clearest examples are found in the asteroid belt. Overlapping resonances account for its kirkwood gaps and were used to predict and find evidence for very narrow gaps in the outer belt. Further afield, about one new "short-peroid" comet is discovered each year. They are believed to come from the "Kuiper Belt" (at 40 AU or more) via chaotic orbits produced by mean-motion and secular resonances with Neptune. Finally, the planetary system itself is not immune from chaos. In the inner solar system, overlapping secular resonances have been identified as the possible source of chaos. For example, Mercury in 1012 years, may suffer a close encounter with Venus or plunge into the Sun. In the outer solar system, three-body resonances have been identified as a source of chaos, but on an even longer time scale of 109 times the age of the solar system. On the human time scale, the planets do follow their orbits in a stately procession, and we can predict their trajectories for hundreds of thousands of years. That is because the mavericks, with shorter instability times, have long since been ejected. The solar system is not stable; it is just old!
ERIC Educational Resources Information Center
Bright, Jim E. H.; Pryor, Robert G. L.
2011-01-01
The Chaos Theory of Careers (CTC; Pryor & Bright, 2011) construes both individuals and the contexts in which they develop their careers in terms of complex dynamical systems. Such systems perpetually operate under influences of stability and change both internally and in relation to each other. The CTC introduces new concepts to account for…
BOOK REVIEW: Chaos: A Very Short Introduction
NASA Astrophysics Data System (ADS)
Klages, R.
2007-07-01
This book is a new volume of a series designed to introduce the curious reader to anything from ancient Egypt and Indian philosophy to conceptual art and cosmology. Very handy in pocket size, Chaos promises an introduction to fundamental concepts of nonlinear science by using mathematics that is `no more complicated than X=2. Anyone who ever tried to give a popular science account of research knows that this is a more challenging task than writing an ordinary research article. Lenny Smith brilliantly succeeds to explain in words, in pictures and by using intuitive models the essence of mathematical dynamical systems theory and time series analysis as it applies to the modern world. In a more technical part he introduces the basic terms of nonlinear theory by means of simple mappings. He masterly embeds this analysis into the social, historical and cultural context by using numerous examples, from poems and paintings over chess and rabbits to Olbers' paradox, card games and `phynance'. Fundamental problems of the modelling of nonlinear systems like the weather, sun spots or golf balls falling through an array of nails are discussed from the point of view of mathematics, physics and statistics by touching upon philosophical issues. At variance with Laplace's demon, Smith's 21st century demon makes `real world' observations only with limited precision. This poses a severe problem to predictions derived from complex chaotic models, where small variations of initial conditions typically yield totally different outcomes. As Smith argues, this difficulty has direct implications on decision-making in everyday modern life. However, it also asks for an inherently probabilistic theory, which somewhat reminds us of what we are used to in the microworld. There is little to criticise in this nice little book except that some figures are of poor quality thus not really reflecting the beauty of fractals and other wonderful objects in this field. I feel that occasionally the book is also getting a bit too intricate for the complete layman, and experts may not agree on all details of the more conceptual discussions. Altogether I thoroughly enjoyed reading this book. It was a happy companion while travelling and a nice bedtime literature. It is furthermore an excellent reminder of the `big picture' underlying nonlinear science as it applies to the real world. I will gladly recommend this book as background literature for students in my introductory course on dynamical systems. However, the book will be of interest to anyone who is looking for a very short account on fundamental problems and principles in modern nonlinear science.
Chaos in high-dimensional dissipative dynamical systems
Ispolatov, Iaroslav; Madhok, Vaibhav; Allende, Sebastian; Doebeli, Michael
2015-01-01
For dissipative dynamical systems described by a system of ordinary differential equations, we address the question of how the probability of chaotic dynamics increases with the dimensionality of the phase space. We find that for a system of d globally coupled ODE’s with quadratic and cubic non-linearities with randomly chosen coefficients and initial conditions, the probability of a trajectory to be chaotic increases universally from ~10?5???10?4 for d?=?3 to essentially one for d?~?50. In the limit of large d, the invariant measure of the dynamical systems exhibits universal scaling that depends on the degree of non-linearity, but not on the choice of coefficients, and the largest Lyapunov exponent converges to a universal scaling limit. Using statistical arguments, we provide analytical explanations for the observed scaling, universality, and for the probability of chaos. PMID:26224119
Kravtsov, Nikolai V; Firsov, V V; Chekina, S N [D.V. Skobel'tsyn Institute of Nuclear Physics, M.V. Lomonosov Moscow State University, Moscow (Russian Federation); Sidorov, S S; Pashinin, Pavel P [A.M. Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow (Russian Federation)
2004-04-30
The peculiarities of nonlinear dynamics of solid-state bidirectional ring Nd:YAG chip lasers are studied theoretically and experimentally during periodic modulation of mechanical stresses in the active element. It is shown that modulation of mechanical stresses is an effective method for exciting dynamic chaos in a monolithic chip laser. (control of laser radiation parameters)
The Dynamics of Deterministic Chaos in Numerical Weather Prediction Models
A. Mary Selvam
2003-10-07
Atmospheric weather systems are coherent structures consisting of discrete cloud cells forming patterns of rows/streets, mesoscale clusters and spiral bands which maintain their identity for the duration of their appreciable life times in the turbulent shear flow of the planetary Atmospheric Boundary Layer. The existence of coherent structures (seemingly systematic motion) in turbulent flows has been well established during the last 20 years of research in turbulence. Numerical weather prediction models based on the inherently non-linear Navier-Stokes equations do not give realistic forecasts because of the following inherent limitations: (1) the non-linear governing equations for atmospheric flows do not have exact analytic solutions and being sensitive to initial conditions give chaotic solutions characteristic of deterministic chaos (2) the governing equations do not incorporate the dynamical interactions and co-existence of the complete spectrum of turbulent fluctuations which form an integral part of the large coherent weather systems (3) limitations of available computer capacity necessitates severe truncation of the governing equations, thereby generating errors of approximations (4) the computer precision related roundoff errors magnify the earlier mentioned uncertainties exponentially with time and the model predictions become unrealistic. The accurate modelling of weather phenomena therefore requires alternative concepts and computational techniques. In this paper a universal theory of deterministic chaos applicable to the formation of coherent weather structures in the ABL is presented.
ERIC Educational Resources Information Center
McKay, Hannah; Bright, Jim E. H.; Pryor, Robert G. L.
2005-01-01
Chaos career counseling, based on the Chaos Theory of Careers (R. G. L. Pryor & J. E. H. Bright, 2003a, 2003b), was compared with trait matching career counseling and a wait list control. Sixty university students who attended the Careers Research and Assessment Service seeking career advice were randomly assigned to the chaos intervention, the…
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. PMID:25554034
NASA Astrophysics Data System (ADS)
Porta, G.; Tamellini, L.; Lever, V.; Riva, M.
2014-12-01
We present an inverse modeling procedure for the estimation of model parameters of sedimentary basins subject to compaction driven by mechanical and geochemical processes. We consider a sandstone basin whose dynamics are governed by a set of unknown key quantities. These include geophysical and geochemical system attributes as well as pressure and temperature boundary conditions. We derive a reduced (or surrogate) model of the system behavior based on generalized Polynomial Chaos Expansion (gPCE) approximations, which are directly linked to the variance-based Sobol indices associated with the selected uncertain model parameters. Parameter estimation is then performed within a Maximum Likelihood (ML) framework. We then study the way the ML inversion procedure can benefit from the adoption of anisotropic polynomial approximations (a-gPCE) in which the surrogate model is refined only with respect to selected parameters according to an analysis of the nonlinearity of the input-output mapping, as quantified through the Sobol sensitivity indices. Results are illustrated for a one-dimensional setting involving quartz cementation and mechanical compaction in sandstones. The reliability of gPCE and a-gPCE approximations in the context of the inverse modeling framework is assessed. The effects of (a) the strategy employed to build the surrogate model, leading either to a gPCE or a-gPCE representation, and (b) the type and quality of calibration data on the goodness of the parameter estimates is then explored.
Subharmonics, Chaos, and Beyond
NASA Technical Reports Server (NTRS)
Adler, Laszlo; Yost, William T.; Cantrell, John H.
2011-01-01
While studying finite amplitude ultrasonic wave resonance in a one dimensional liquid-filled cavity, which is formed by a narrow band transducer and a plane reflector, subharmonics of the driver's frequency were observed in addition to the expected harmonic structure. Subsequently it was realized that the system was one of the many examples where parametric resonance takes place and in which the observed subharmonics are parametrically generated. Parametric resonance occurs in any physical system which has a periodically modulated natural frequency. The generation mechanism also requires a sufficiently high threshold value of the driving amplitude so that the system becomes increasingly nonlinear in response. The nonlinear features were recently investigated and are the objective of this presentation. An ultrasonic interferometer with optical precision was built. The transducers were compressional undamped quartz and Lithium Niobate crystals ranging from 1-10 Mhz, and driven by a high power amplifier. Both an optical diffraction system and a receive transducer attached to an aligned reflector with lapped flat and parallel surfaces were used to observe the generated frequency components in the cavity.
Bifurcation and Chaos in a Rub-Impact Jeffcott Rotor System
NASA Astrophysics Data System (ADS)
Chu, F.; Zhang, Z.
1998-02-01
Non-linear vibration characteristics of a rub-impact Jeffcott rotor are investigated. The system is two-dimensional, non-linear and periodic. Fourier series analysis and the Floquet theory are used to perform qualitative global analysis on bifurcation and stability. The governing ordinary differential equations are also integrated using a numerical method to give the quantitative result. This preliminary study reveals the chaotic feature of the system. After the rub-impact, as the rotating speed is increased, three kinds of routes to chaos are found, that is, from a stable periodic motion through period doubling bifurcation, grazing bifurcation and a sudden transition from periodic motion to chaos. Quasi-periodic motions are also found.
Control design and robustness analysis of a ball and plate system by using polynomial chaos
NASA Astrophysics Data System (ADS)
Colón, Diego; Balthazar, José M.; dos Reis, Célia A.; Bueno, Átila M.; Diniz, Ivando S.; de S. R. F. Rosa, Suelia
2014-12-01
In this paper, we present a mathematical model of a ball and plate system, a control law and analyze its robustness properties by using the polynomial chaos method. The ball rolls without slipping. There is an auxiliary robot vision system that determines the bodies' positions and velocities, and is used for control purposes. The actuators are to orthogonal DC motors, that changes the plate's angles with the ground. The model is a extension of the ball and beam system and is highly nonlinear. The system is decoupled in two independent equations for coordinates x and y. Finally, the resulting nonlinear closed loop systems are analyzed by the polynomial chaos methodology, which considers that some system parameters are random variables, and generates statistical data that can be used in the robustness analysis.
Spatiotemporal chaos from bursting dynamics
NASA Astrophysics Data System (ADS)
Berenstein, Igal; De Decker, Yannick
2015-08-01
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.
Boris Chirikov
2005-03-09
In this short report the first attempt of a new approach to the still mysterious phenomenon of the life, and its peak, the human being, is presented from the view point of the natural sciences, i.e. of the physics in the broad sense of the word. This idea has come to my mind about 10 years ago when doing a completely different problem I suddenly have noticed to my surprise (see [1], p.20) a wonderful relation between a very complicated human (physical) conception {\\it creation} and the relatively simple mathematical theorem due to Alekseev - Brudno (see for instance [2]) in an almost unknown for physicists field of the so-called {\\it symbolic dynamics} and {\\it algorithmic chaos}, which one I have immediately christen {\\it the creating chaos}.
Route to chaos in optomechanics.
Bakemeier, L; Alvermann, A; Fehske, H
2015-01-01
We establish the emergence of chaotic motion in optomechanical systems. Chaos appears at negative detuning for experimentally accessible values of the pump power and other system parameters. We describe the sequence of period-doubling bifurcations that leads to chaos and state the experimentally observable signatures in the optical spectrum. In addition to the semiclassical dynamics, we analyze the possibility of chaotic motion in the quantum regime. We find that quantum mechanics protects the optomechanical system against irregular dynamics, such that simple periodic orbits reappear and replace the classically chaotic motion. In this way observation of the dynamical signatures makes it possible to pin down the crossover from quantum to classical mechanics. PMID:25615468
Design, implementation and analysis of fully digital 1-D controllable multiscroll chaos
A. S. Mansingka; A. G. Radwan; K. N. Salama
2011-01-01
This paper introduces the fully digital implementation of a 1-D multiscroll chaos generator based on a staircase nonlinearity in the 3rd-order jerk system using the Euler approximation. For the first time, digital design is exploited to provide real-time controllability of (i) number of scrolls, (ii) position in 1-D space, (iii) Euler step size and (iv) system parameter. The effect of
Quantum Chaos at Finite Temperature
L. A. Caron; H. Jirari; H. Kröger; X. Q. Luo; G. Melkonyan; K. J. M. Moriarty
2001-06-23
We use the quantum action to study quantum chaos at finite temperature. We present a numerical study of a classically chaotic 2-D Hamiltonian system - harmonic oscillators with anharmonic coupling. We construct the quantum action non-perturbatively and find temperature dependent quantum corrections in the action parameters. We compare Poincar\\'{e} sections of the quantum action at finite temperature with those of the classical action.
Understanding of Arab Spring with Chaos Theory - Uprising or Revolution
NASA Astrophysics Data System (ADS)
Aç?kal?n, ?uay Nilhan; Bölücek, Cemal Alpgiray
`Arab Spring' can be considered as one of the most remarkable events in the history of world politics. On December 18, 2010, a Tunisian young protestor burned himself in a public square of the city. This event triggered probably one of the most chaotic and long term uprisings in the Middle East. From the day of its initiation until the present, `Arab Spring' in the Middle East created unstable political situation and several uprisings. In this chapter, we will first give general information about chaos theory, and then we will examine the `butterfly effect' created by the Tunisian young protestor and process of Arab Spring in the Middle East regarding its extend and form in those countries within the framework of chaos theory. For the first part of this chapter, the spark created by the Tunisian young protestor and its effects can be analyzed under `butterfly effect' perspective within chaos theory, arguing whether the events followed each other consecutively or randomly. The question is whether the incidents following each other have reasonable links of causality to one another, or the events defining the phenomena known as `Arab Spring' have no predictable reasons and outcomes regardless of the regional, social and political differences. The events caused the collapse of the regimes in Tunisia, Egypt and Libya; they had very serious outcomes.
Chaos Theory and James Joyce's "ulysses": Leopold Bloom as a Human COMPLEX@SYSTEM^
NASA Astrophysics Data System (ADS)
Mackey, Peter Francis
1995-01-01
These four ideas apply as much to our lives as to the life of Leopold Bloom: (1) A trivial decision can wholly change a life. (2) A chance encounter can dramatically alter life's course. (3) A contingent nexus exists between consciousness and environment. (4) A structure of meaning helps us interpret life's chaos. These ideas also relate to a contemporary science called by some "chaos theory." The connection between Ulysses and chaos theory enhances our understanding of Bloom's day; it also suggests that this novel may be about the real process of life itself. The first chapter explains how Joyce's own essays and comments to friends compel attention to the links between Ulysses and chaos theory. His scientific contemporaries anticipated chaos theory, and their ideas seem to have rubbed off on him. We see this in his sense of trivial things and chance, his modernistic organizational impulses, and the contingent nature of Bloom's experience. The second chapter studies what chaos theory and Joyce's ideas tell us about "Ithaca," the episode which particularly implicates our processes of interpreting this text as well as life itself as we face their chaos. The third chapter examines Bloom's close feel for the aboriginal world, a contingency that clarifies his vulnerability to trivial changes. The fourth chapter studies how Bloom's stream of consciousness unfolds--from his chance encounters with trivial things. Beneath this stream's seeming chaos, Bloom's distinct personality endures, similar to how Joyce's schemas give Ulysses an imbedded, underlying order. The fifth chapter examines how trivial perturbations, such as Lyons' misunderstanding about "Throwaway," produce small crises for Bloom, exacerbating his seeming impotence before his lonely "fate.". The final chapter analyzes Bloom's views that fate and chance dictate his life. His views provide an opportunity to explore the implications chaos theory has for our understanding of free will and determinism. Ultimately, despite ungovernable fate and chance, Bloom asserts his will with Stephen and Molly, proving that he will live on, attempting to create his own destiny, wresting hope from the "chaos" of his experience.
?W H A T I S . . . Quantum Chaos?
Marcolli, Matilde
?W H A T I S . . . Quantum Chaos? Ze'ev Rudnick A referee of one of my grant proposals com- plained recently that the text did not explain "what is quantum chaos"; the desire for an an- swer to that question and provide such an explanation. Quantum chaos began as an attempt to find chaos, in the sense of extreme
Chaos crisis and bistability of self-pulsing dynamics in a laser diode with phase-conjugate feedback
Virte, Martin; Karsaklian Dal Bosco, Andreas; Wolfersberger, Delphine; Sciamanna, Marc [Supelec, OPTEL Research Group, Laboratoire Materiaux Optiques, Photonique et Systemes, EA-4423, 2 rue Edouard Belin, F-57070 Metz (France)
2011-10-15
A laser diode subject to a phase-conjugate optical feedback can exhibit rich nonlinear dynamics and chaos. We report here on two bifurcation mechanisms that appear when increasing the amount of light being fed back to the laser. First, we report on a full suppression of chaos from a crisis induced by a saddle-node bifurcation on self-pulsing, so-called external-cavity-mode solutions (ECMs). Second, the feedback-dependent torus and saddle-node bifurcations on ECMs may be responsible for large regions of bistability between ECMs of different and high (beyond gigahertz) frequencies.
Modification of epileptiform bursting using chaos control
M. W. Slutzky; David J. Mogul
2000-01-01
Recently, attempts have been made to apply chaos control techniques to manipulate the electrical discharges in the brain (interictal bursts) that are characteristic of epilepsy. These techniques would offer the advantage of using small and relatively infrequent stimuli to revert a seizure. However, questions have since arisen as to whether these results were truly chaos control or simply demand pacing.
Quantum Chaos, Degeneracies and Exceptional Points
W. Dieter Heiss; Stefanel Radu
1995-07-11
It is argued that, if a regular Hamiltonian is perturbed by a term that produces chaos, the onset of chaos is shifted towards larger values of the perturbation parameter if the unperturbed spectrum is degenerate and the lifting of the degeneracy is of second order in this parameter. The argument is based on the behaviour of the exceptional points of the full problem.
Quantum chaos viewed from quantum action
D. Huard; H. Kröger; G. Melkonyan; L. P. Nadeau; K. J. M. Moriarty
2004-06-18
We consider a mixed chaotic Hamiltonian system and compare classical with quantum chaos. As alternative to the methods of enegy level spacing statistics and trace formulas, we construct a quantum action and a quantum analogue phase space to analyse quantum chaos.
Advising Undecided Students: Lessons from Chaos Theory.
ERIC Educational Resources Information Center
Beck, Amy
1999-01-01
Uses chaos theory as a metaphor for advising undecided college students. Applies chaos theory concepts of dependence on initial conditions, strange attractors, emergent behavior in complex systems, and fractals to the advising relationship. Suggests the paradigm reinforces the basics of advising, such as the importance of accepting the student's…
Hung, Yu-Han; Chu, Cheng-Hao; Hwang, Sheng-Kwang
2013-05-01
To distribute microwaves over fibers, optical single-sideband (SSB) modulation signals are preferred to optical double-sideband (DSB) modulation signals. This study investigates an optically injected semiconductor laser at period-one nonlinear dynamics for optical DSB-to-SSB conversion. For the operating microwave frequencies up to 40 GHz investigated in this study, the proposed system regenerates or even enhances the microwave features of an optical DSB input while converting its optical feature into SSB with an intensity difference of at least 20 dB. The bit-error ratio at 622 Mb/s is down to 10(-9) with a sensitivity improvement of up to 3 dB. The proposed system can be self-adapted to certain changes in the operating microwave frequency and can operate stably under certain fluctuations in the input optical power and frequency. PMID:23632525
New Chaotic PSO-Based Neural Network Predictive Control for Nonlinear Process
Ying Song; Zengqiang Chen; Zhuzhi Yuan
2007-01-01
In this letter, a novel nonlinear neural network (NN) predictive control strategy based on the new tent-map chaotic particle swarm optimization (TCPSO) is presented. The TCPSO incorporating tent-map chaos, which can avoid trapping to local minima and improve the searching performance of standard particle swarm optimization (PSO), is applied to perform the nonlinear optimization to enhance the convergence and accuracy.
A Teaching and Learning Sequence about the Interplay of Chance and Determinism in Nonlinear Systems
ERIC Educational Resources Information Center
Stavrou, D.; Duit, R.; Komorek, M.
2008-01-01
A teaching and learning sequence aimed at introducing upper secondary school students to the interplay between chance and determinism in nonlinear systems is presented. Three experiments concerning nonlinear systems (deterministic chaos, self-organization and fractals) and one experiment concerning linear systems are introduced. Thirty upper…
NASA Astrophysics Data System (ADS)
Bouloufa, R.; Cacciani, P.; Delsart, C.; Luc-Koenig, E.; Pinard, J.
1993-10-01
How does the existence of chaos in classical dynamics affect the quantum spectrum of the system? The atom in a magnetic field is a prototype of systems where complete classical and quantal calculations are possible. Transition from regular to chaotic trajectories are linked quantally to the progressive breaking of some peculiar symmetries of the system. We propose a method and its experimental realization on lithium atom to clearly see a transition between regularity and chaos on a quantum spectrum by selecting the starting state of the excitation. In addition, experimental and calculated spectra on hydrogen shows a remarkably good agreement.
Robust chaos in a model of the electroencephalogram: Implications for brain dynamics
NASA Astrophysics Data System (ADS)
Dafilis, Mathew P.; Liley, David T. J.; Cadusch, Peter J.
2001-09-01
Various techniques designed to extract nonlinear characteristics from experimental time series have provided no clear evidence as to whether the electroencephalogram (EEG) is chaotic. Compounding the lack of firm experimental evidence is the paucity of physiologically plausible theories of EEG that are capable of supporting nonlinear and chaotic dynamics. Here we provide evidence for the existence of chaotic dynamics in a neurophysiologically plausible continuum theory of electrocortical activity and show that the set of parameter values supporting chaos within parameter space has positive measure and exhibits fat fractal scaling.
Melnikov chaos in a modified Rayleigh-Duffing oscillator with $ ?^6$ potential
C. H. Miwadinou; A. V. Monwanou; L. A. Hinvi; A. A. Koukpemedji; C. Ainamon; J. B. Chabi Orou
2015-08-23
The chaotic behavior of the modified Rayleigh-Duffing oscillator with $ \\phi^6$ potential and external excitation which modeles ship rolling motions are investigated both analytically and numerically. Melnikov method is applied and the conditions for the existence of homoclinic and heteroclinic chaos are obtained. The effects of nonlinear damping on roll motion of ships are analyzed in detail. As it is known, nonlinear roll damping is a very important parameter in estimating ship reponses. The predictions are tested numerical simulations based on the basin of attraction. We conclude that certains quadratic damping effects are contrary to cubic damping effect.
The route to chaos for the Kuramoto-Sivashinsky equation
NASA Technical Reports Server (NTRS)
Papageorgiou, Demetrios T.; Smyrlis, Yiorgos
1990-01-01
The results of extensive numerical experiments of the spatially periodic initial value problem for the Kuramoto-Sivashinsky equation. This paper is concerned with the asymptotic nonlinear dynamics at the dissipation parameter decreases and spatio-temporal chaos sets in. To this end the initial condition is taken to be the same for all numerical experiments (a single sine wave is used) and the large time evolution of the system is followed numerically. Numerous computations were performed to establish the existence of windows, in parameter space, in which the solution has the following characteristics as the viscosity is decreased: a steady fully modal attractor to a steady bimodal attractor to another steady fully modal attractor to a steady trimodal attractor to a periodic attractor, to another steady fully modal attractor, to another periodic attractor, to a steady tetramodal attractor, to another periodic attractor having a full sequence of period-doublings (in parameter space) to chaos. Numerous solutions are presented which provide conclusive evidence of the period-doubling cascades which precede chaos for this infinite-dimensional dynamical system. These results permit a computation of the length of subwindows which in turn provide an estimate for their successive ratios as the cascade develops. A calculation based on the numerical results is also presented to show that the period doubling sequences found here for the Kuramoto-Sivashinsky equation, are in complete agreement with Feigenbaum's universal constant of 4,669201609... . Some preliminary work shows several other windows following the first chaotic one including periodic, chaotic, and a steady octamodal window; however, the windows shrink significantly in size to enable concrete quantitative conclusions to be made.
Discretization chaos - Feedback control and transition to chaos
NASA Technical Reports Server (NTRS)
Grantham, Walter J.; Athalye, Amit M.
1990-01-01
Problems in the design of feedback controllers for chaotic dynamical systems are considered theoretically, focusing on two cases where chaos arises only when a nonchaotic continuous-time system is discretized into a simpler discrete-time systems (exponential discretization and pseudo-Euler integration applied to Lotka-Volterra competition and prey-predator systems). Numerical simulation results are presented in extensive graphs and discussed in detail. It is concluded that care must be taken in applying standard dynamical-systems methods to control systems that may be discontinuous or nondifferentiable.
The Application of Nonlinear Dynamics in Nursing Research
Patti Hamilton; Jane Englebright Pollock; De Ann F. Mitchell; Angela E. Vicenzi; Bruce J. West
1997-01-01
In this article, the authors present an overview of the applications of chaos theory and nonlinear dynamics to problems of relevance not only to nurses, but to anyone dealing with human functioning and interaction. These applications have been in the areas of epidemiology, nursing management and physiological functioning. In some cases, the applications were successful in identifying information that would
Evidence for universal chaotic behavior of a driven nonlinear oscillator
James Testa; José Pérez; Carson Jeffries
1982-01-01
A bifurcation diagram for a driven nonlinear semiconductor oscillator is measured directly, showing successive subharmonic bifurcations to f\\/32, onset of chaos, noise band merging, and extensive noise-free windows. The overall diagram closely resembles that computed for the logistic model. Measured values of universal numbers are reported, including effects of added noise.
ATTRACTOR AND PATTERN CONTROL IN NONLINEAR MEDIA BY LOCALIZED DEFECTS
S. Vakulenko; B. Kazmierczak
2004-01-01
Summary We consider pattern and attractor control in nonlinear dissipative systems. We develop an analytic approach to attractor control for neural, genetic networks systems of coupled oscillators and spatially extended systems. In particular, we apply this method for some systems of Ginzburg-Landau's type and others. 1. Introduction. In the last decade, a great attention has been given to chaos existence
Control mechanisms for a nonlinear model of international relations
Pentek, A.; Kadtke, J. [Univ. of California, San Diego, La Jolla, CA (United States). Inst. for Pure and Applied Physical Sciences; Lenhart, S. [Univ. of Tennessee, Knoxville, TN (United States). Mathematics Dept.; Protopopescu, V. [Oak Ridge National Lab., TN (United States). Computer Science and Mathematics Div.
1997-07-15
Some issues of control in complex dynamical systems are considered. The authors discuss two control mechanisms, namely: a short range, reactive control based on the chaos control idea and a long-term strategic control based on an optimal control algorithm. They apply these control ideas to simple examples in a discrete nonlinear model of a multi-nation arms race.
Lee, Hae June
Parametrization of nonlinear and chaotic oscillations in driven beam-plasma diodes Min Sup Hur, Hae instability and a perturbation grows to exhibit nonlinear oscillations including chaos. Two standard routes 790-784, South Korea Received 20 January 1998 Nonlinear phenomena in a driven plasma diode are studied
Emergence of nonlinear behavior in the dynamics of ultracold bosons
NASA Astrophysics Data System (ADS)
Vermersch, Benoît; Garreau, Jean Claude
2015-04-01
We study the evolution of a system of interacting ultracold bosons which presents nonlinear, chaotic behaviors in the limit of a very large number of particles. Using the spectral entropy as an indicator of chaos and three different numerical approaches—exact diagonalization, the truncated Husimi method, and the mean-field (Gross-Pitaevskii) approximation—we put into evidence the destructive impact of quantum noise on the emergence of nonlinear dynamics.
Emergence of nonlinear behavior in the dynamics of ultracold bosons
Benoit Vermersch; Jean Claude Garreau
2015-01-28
We study the evolution of a system of interacting ultracold bosons, which presents nonlinear, chaotic, behaviors in the limit of very large number of particles. Using the spectral entropy as an indicator of chaos and three different numerical approaches : Exact diagonalization, truncated Husimi method and mean-field (Gross-Pitaevskii) approximation, we put into evidence the destructive impact of quantum noise on the emergence of the nonlinear dynamics.
Four dimensional chaos and intermittency in a mesoscopic model of the electroencephalogram
NASA Astrophysics Data System (ADS)
Dafilis, Mathew P.; Frascoli, Federico; Cadusch, Peter J.; Liley, David T. J.
2013-06-01
The occurrence of so-called four dimensional chaos in dynamical systems represented by coupled, nonlinear, ordinary differential equations is rarely reported in the literature. In this paper, we present evidence that Liley's mesoscopic theory of the electroencephalogram (EEG), which has been used to describe brain activity in a variety of clinically relevant contexts, possesses a chaotic attractor with a Kaplan-Yorke dimension significantly larger than three. This accounts for simple, high order chaos for a physiologically admissible parameter set. Whilst the Lyapunov spectrum of the attractor has only one positive exponent, the contracting dimensions are such that the integer part of the Kaplan-Yorke dimension is three, thus giving rise to four dimensional chaos. A one-parameter bifurcation analysis with respect to the parameter corresponding to extracortical input is conducted, with results indicating that the origin of chaos is due to an inverse period doubling cascade. Hence, in the vicinity of the high order, strange attractor, the model is shown to display intermittent behavior, with random alternations between oscillatory and chaotic regimes. This phenomenon represents a possible dynamical justification of some of the typical features of clinically established EEG traces, which can arise in the case of burst suppression in anesthesia and epileptic encephalopathies in early infancy.
Subtleties of arithmetical quantum chaos
NASA Astrophysics Data System (ADS)
Aurich, R.; Scheffler, F.; Steiner, F.
1995-05-01
The spectral statistics of two closely related strongly chaotic quantum billiards are studied. Both are defined on the same triangular domain on the hyperbolic plane and differ only in the choice of the boundary conditions on the edges of the billiards. The fundamental domain is generated by the action of the reflection group T*(2,3,8), which is an arithmetical group leading to an exponentially degenerate length spectrum of the classical periodic orbits. The boundary conditions on one billiard, called billard scrA, are chosen such that it does not belong to a representation of the reflection group, whereas for billiard scrB the boundary conditions correspond to an irreducible symmetry representation. The crucial property of arithmetical chaos, i.e., the exponential degeneracy of periodic orbits having the same length, is not affected by the choice of the boundary conditions. For both billiards our analysis of the spectral statistics is based on the first 1050 quantal energy levels, which we have computed using the boundary element method. It is found that the quantal level statistics for billiard scrB show the peculiar properties typical for arithmetical quantum chaos, as discovered previously for other arithmetical systems. Billiard scrA, however, behaves generically in that it shows at short- and mdeium-range correlations a behavior in agreement with the random-matrix theory. The periodic-orbit theory is scrutinized to shed some light on the mysterious differences between these two almost identical quantum billiards. The trace of the cosine-modulated heat kernel and the spectral form factor are studied. It is demonstrated that subtle properties of the characters attached to the classical periodic orbits are very important ingredients in the phenomenon of arithmetical quantum chaos.
Persistent Chaos in High Dimensions
D. J. Albers; J. C. Sprott; J. P. Crutchfield
2005-10-26
An extensive statistical survey of universal approximators shows that as the dimension of a typical dissipative dynamical system is increased, the number of positive Lyapunov exponents increases monotonically and the number of parameter windows with periodic behavior decreases. A subset of parameter space remains in which topological change induced by small parameter variation is very common. It turns out, however, that if the system's dimension is sufficiently high, this inevitable, and expected, topological change is never catastrophic, in the sense chaotic behavior is preserved. One concludes that deterministic chaos is persistent in high dimensions.
Quantum chaos on discrete graphs
Uzy Smilansky
2007-04-26
Adapting a method developed for the study of quantum chaos on {\\it quantum (metric)} graphs \\cite {KS}, spectral $\\zeta$ functions and trace formulae for {\\it 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 belongs to the class of $\\zeta$ functions proposed originally by Ihara \\cite {Ihara}, and expanded by subsequent authors \\cite {Stark,Sunada}. Finally, a model of "classical dynamics" on the discrete graph is proposed. It is analogous to the corresponding classical dynamics derived for quantum graphs \\cite {KS}.
Quantum chaos and effective thermalization
Altland, Alexander
2011-01-01
We demonstrate effective equilibration for unitary quantum dynamics under conditions of classical chaos. Focusing on the paradigmatic example of the Dicke model, we show how a constructive description of the thermalization process is facilitated by the Glauber $Q$ or Husimi function, for which the evolution equation turns out to be of Fokker-Planck type. The equation describes a competition of classical drift and quantum diffusion in contractive and expansive directions. By this mechanism the system follows a 'quantum smoothened' approach to equilibrium, which avoids the notorious singularities inherent to classical chaotic flows.
Quantum chaos and effective thermalization.
Altland, Alexander; Haake, Fritz
2012-02-17
We demonstrate effective equilibration for unitary quantum dynamics under conditions of classical chaos. Focusing on the paradigmatic example of the Dicke model, we show how a constructive description of the thermalization process is facilitated by the Glauber Q or Husimi function, for which the evolution equation turns out to be of Fokker-Planck type. The equation describes a competition of classical drift and quantum diffusion in contractive and expansive directions. By this mechanism the system follows a "quantum smoothened" approach to equilibrium, which avoids the notorious singularities inherent to classical chaotic flows. PMID:22401203
Titration of chaos with added noise
Poon, Chi-Sang; Barahona, Mauricio
2001-01-01
Deterministic chaos has been implicated in numerous natural and man-made complex phenomena ranging from quantum to astronomical scales and in disciplines as diverse as meteorology, physiology, ecology, and economics. However, the lack of a definitive test of chaos vs. random noise in experimental time series has led to considerable controversy in many fields. Here we propose a numerical titration procedure as a simple “litmus test” for highly sensitive, specific, and robust detection of chaos in short noisy data without the need for intensive surrogate data testing. We show that the controlled addition of white or colored noise to a signal with a preexisting noise floor results in a titration index that: (i) faithfully tracks the onset of deterministic chaos in all standard bifurcation routes to chaos; and (ii) gives a relative measure of chaos intensity. Such reliable detection and quantification of chaos under severe conditions of relatively low signal-to-noise ratio is of great interest, as it may open potential practical ways of identifying, forecasting, and controlling complex behaviors in a wide variety of physical, biomedical, and socioeconomic systems. PMID:11416195
Markov transitions and the propagation of chaos
Gottlieb, A.
1998-12-01
The propagation of chaos is a central concept of kinetic theory that serves to relate the equations of Boltzmann and Vlasov to the dynamics of many-particle systems. Propagation of chaos means that molecular chaos, i.e., the stochastic independence of two random particles in a many-particle system, persists in time, as the number of particles tends to infinity. We establish a necessary and sufficient condition for a family of general n-particle Markov processes to propagate chaos. This condition is expressed in terms of the Markov transition functions associated to the n-particle processes, and it amounts to saying that chaos of random initial states propagates if it propagates for pure initial states. Our proof of this result relies on the weak convergence approach to the study of chaos due to Sztitman and Tanaka. We assume that the space in which the particles live is homomorphic to a complete and separable metric space so that we may invoke Prohorov's theorem in our proof. We also s how that, if the particles can be in only finitely many states, then molecular chaos implies that the specific entropies in the n-particle distributions converge to the entropy of the limiting single-particle distribution.
NASA Astrophysics Data System (ADS)
Shevtsov, Maxim A.; Nikolaev, Boris P.; Ryzhov, Vyacheslav A.; Yakovleva, Ludmila Y.; Dobrodumov, Anatolii V.; Marchenko, Yaroslav Y.; Margulis, Boris A.; Pitkin, Emil; Guzhova, Irina V.
2015-08-01
Brain tumor targeting efficiency and biodistribution of the superparamagnetic nanoparticles conjugated with heat shock protein Hsp70 (SPION-Hsp70) were evaluated in experimental glioma model. Synthesized conjugates were characterized using the method of longitudinal nonlinear response of magnetic nanoparticles to a weak ac magnetic field with measurements of second harmonic of magnetization (NLR-M2). Cellular interaction of magnetic conjugates was analyzed in 9L glioma cell culture. The biodistribution of the nanoparticles and their accumulation in tumors was assessed by the latter approach as well. The efficacy of Hsp70-conjugates for contrast enhancement in the orthotopic model of 9L glioma was assessed by MR imaging (11 T). Magnetic nanoparticles conjugated with Hsp70 had the relaxivity properties of the MR-negative contrast agents. Morphological observation and cell viability test demonstrated good biocompatibility of Hsp70-conjugates. Analysis of the T2-weighted MR scans in tumor-bearing rats demonstrated the high efficacy of Hsp70-conjugates in contrast enhancement of the glioma in comparison to non-conjugated nanoparticles. High contrast enhancement of the glioma was provided by the accumulation of the SPION-Hsp70 particles in the glioma tissue (as shown by the histological assay). Biodistribution analysis by NLR-M2 measurements evidenced the many-fold increase (~40) in the tumor-to-normal brain uptake ratio in the Hsp70-conjugates treated animals. Biodistribution pattern of Hsp70-decorated nanoparticles differed from that of non-conjugated SPIONs. Coating of the magnetic nanoparticles with Hsp70 protein enhances the tumor-targeting ability of the conjugates that could be applied in the MR imaging of the malignant brain tumors.
Nonlinear Dynamics of Fluid Motion
NASA Astrophysics Data System (ADS)
Gollub, Jerry
2003-11-01
More than 30 years ago, the notion that deterministic chaos might "explain" fluid turbulence was proposed. While that hope did not produce much practical insight into the complex phenomenology of turbulence, it is now widely accepted that chaos and the collection of ideas known as "nonlinear dynamics" contribute to understanding a variety of phenomena in fluid dynamics. Examples include the onset of non-periodic motion in confined geometries, the mixing of fluids in some laminar flows, the evolution of patterns formed by flowing films and nonlinear waves, and the interactions between particles that are moving or sedimenting in a fluid. In this talk, I first review from a personal point of view some of the connections between fluid and nonlinear dynamics. Then, I will discuss two recent examples related to mixing in fluids and interacting particles. (a) Concepts of nonlinear dynamics such as fixed points and invariant manifolds of flow maps are important in understanding mixing; they can now be measured using precise particle tracking, thus providing new insights into the origin of mixing, especially its extremely localized or inhomogeneous nature. (b) Particles that oscillate with respect to a background fluid experience hydrodynamic forces that give rise to clustering at a preferred separation. Particle motions within these clusters are often chaotic, and the resulting dynamics poses interesting questions about the hydrodynamic forces acting on the particles. For large clusters, the particles diffuse over large distances. How can we best think about these complex phenomena involving both particles and fluids? In the various examples discussed in this lecture, I will illustrate how ideas from nonlinear dynamics can contribute productively to understanding fluid phenomena.
NASA Astrophysics Data System (ADS)
Kengne, J.
In this paper, the dynamics of the paradigmatic hyperchaotic oscillator with gyrators introduced by Tamasevicius and co-workers (referred to as the TCMNL oscillator hereafter) is considered. This well known hyperchaotic oscillator with active RC realization of inductors is suitable for integrated circuit implementation. Unlike previous literature based on piecewise-linear approximation methods, I derive a new (smooth) mathematical model based on the Shockley diode equation to explore the dynamics of the oscillator. Various tools for detecting chaos including bifurcation diagrams, Lyapunov exponents, frequency spectra, phase portraits and Poincaré sections are exploited to establish the connection between the system parameters and various complex dynamic regimes (e.g. hyperchaos, period-3 doubling bifurcation, coexistence of attractors, transient chaos) of the hyperchaotic oscillator. One of the most interesting and striking features of this oscillator discovered/revealed in this work is the coexistence of a hyperchaotic attractor with a chaotic one over a broad range of system parameters. This phenomenon was not reported previously and therefore represents a meaningful contribution to the understanding of the behavior of nonlinear dynamical systems in general. A close agreement is observed between theoretical and experimental analyses.
Bifurcations and Chaos in Simple Dynamical Systems
Mrs. T. Theivasanthi
2009-07-16
Chaos is an active research subject in the fields of science in recent years. it is a complex and an erratic behavior that is possible in very simple systems. in the present day, the chaotic behavior can be observed in experiments. Many studies have been made in chaotic dynamics during the past three decades and many simple chaotic systems have been discovered. in this work-bifurcations and chaos in simple dynamical systems - the behavior of some simple dynamical systems is studied by constructing mathematical models. investigations are made on the periodic orbits for continuous maps and idea of sensitive dependence on initial conditions,which is the hallmark of chaos, is obtained.
From Deterministic Chaos to Anomalous Diffusion
R. Klages
2009-07-20
This is an easy-to-read introduction to foundations of deterministic chaos, deterministic diffusion and anomalous diffusion. The first part introduces to deterministic chaos in one-dimensional maps in form of Ljapunov exponents and dynamical entropies. The second part outlines the concept of deterministic diffusion. Then the escape rate formalism for deterministic diffusion, which expresses the diffusion coefficient in terms of the above two chaos quantities, is worked out for a simple map. Part three explains basics of anomalous diffusion by demonstrating the stochastic approach of continuous time random walk theory for an intermittent map. As an example of experimental applications, the anomalous dynamics of biological cell migration is discussed.
Detection of "noisy" chaos in a time series
NASA Technical Reports Server (NTRS)
Chon, K. H.; Kanters, J. K.; Cohen, R. J.; Holstein-Rathlou, N. H.
1997-01-01
Time series from biological system often displays fluctuations in the measured variables. Much effort has been directed at determining whether this variability reflects deterministic chaos, or whether it is merely "noise". The output from most biological systems is probably the result of both the internal dynamics of the systems, and the input to the system from the surroundings. This implies that the system should be viewed as a mixed system with both stochastic and deterministic components. We present a method that appears to be useful in deciding whether determinism is present in a time series, and if this determinism has chaotic attributes. The method relies on fitting a nonlinear autoregressive model to the time series followed by an estimation of the characteristic exponents of the model over the observed probability distribution of states for the system. The method is tested by computer simulations, and applied to heart rate variability data.
Transition to Chaos in a Shell Model of Turbulence
L. Biferale; A. Lambert; R. Lima; G. Paladin
1994-02-22
We study a shell model for the energy cascade in three dimensional turbulence at varying the coefficients of the non-linear terms in such a way that the fundamental symmetries of Navier-Stokes are conserved. When a control parameter $\\epsilon$ related to the strength of backward energy transfer is enough small, the dynamical system has a stable fixed point corresponding to the Kolmogorov scaling. This point becomes unstable at $\\epsilon=0.3843...$ where a stable limit cycle appears via a Hopf bifurcation. By using the bi-orthogonal decomposition, the transition to chaos is shown to follow the Ruelle-Takens scenario. For $\\epsilon > 0.3953..$ the dynamical evolution is intermittent with a positive Lyapunov exponent. In this regime, there exists a strange attractor which remains close to the Kolmogorov (now unstable) fixed point, and a local scaling invariance which can be described via a intermittent one-dimensional map.
Classical and Quantum Chaos and Control of Heat Flow
Giulio Casati; Carlos Mejia-Monasterio
2006-10-10
We discuss the problem of heat conduction in classical and quantum low dimensional systems from a microscopic point of view. At the classical level we provide convincing numerical evidence for the validity of Fourier law of heat conduction in linear mixing systems, i.e. in systems without exponential instability. At the quantum level, where motion is characterized by the lack of exponential dynamical instability, we show that the validity of Fourier law is in direct relation with the onset of quantum chaos. We then study the phenomenon of thermal rectification and briefly discuss the different types of microscopic mechanisms that lead to the rectification of heat flow. The control of heat conduction by nonlinearity opens the possibility to propose new devices such as a thermal rectifier.
Different routes to chaos in the Ti:sapphire laser
Kovalsky, Marcelo G.; Hnilo, Alejandro A. [Centro de Investigaciones en Laseres y Aplicaciones (CEILAP), Instituto de Investigaciones Cientificas y Tecnicas de las Fuerzas Armadas (CITEFA), Consejo Nacional de Investigaciones Cientificas y Tecnicas - CONICET, Universidad Nacional de San Martin - UNSAM, San Martin (Argentina)
2004-10-01
Kerr-lens mode-locked, femtosecond Ti:sapphire lasers can operate in two coexistent pulsed modes of operation, named P1 (transform limited output pulses) and P2 (chirped output pulses). We study, both theoretically and experimentally, the transition to chaotic behavior for each of these two modes of operation as the net intracavity group velocity dispersion parameter approaches to zero. We find that P1 reaches chaos through a quasiperiodic route, while P2 does it through intermittency. The modulation frequencies involved, the size of the transition regions in the parameter's space, and the embedding and correlation dimensions of the attractors (and also the kurtosis for the intermittent regime) are theoretically predicted and also measured, showing a satisfactory agreement. We consider that this finding of a low-dimensional system of widespread practical use with (at least) two coexistent chaotic scenarios will have a broad impact on the studies on nonlinear dynamics.
Nonlinear Dynamics of a Diffusing Interface
NASA Technical Reports Server (NTRS)
Duval, Walter M. B.
2001-01-01
Excitation of two miscible-viscous liquids inside a bounded enclosure in a microgravity environment has shown the evolution of quasi-stationary waves of various modes for a range of parameters. We examine computationally the nonlinear dynamics of the system as the interface breakup and bifurcates to resonance structures typified by the Rayleigh-Taylor instability mechanism. Results show that when the mean steady field is much smaller than the amplitude of the sinusoidal excitation, the system behaves linearly, and growth of quasi-stationary waves occurs through the Kelvin-Helmholtz instability mechanism. However, as the amplitude of excitation increases, nonlinearity occurs through subharmonic bifurcation prior to broadband chaos.
Semiclassical limit and quantum chaos
NASA Astrophysics Data System (ADS)
Lecheminant, P.
1993-02-01
In this paper we present the field on which R. Rammal was working in the last moments of his life : quantum chaos. The behavior of various distributions is investigated numerically for different planar billiards in presence of a magnetic field or not. We find exponential laws for the distributions of the trajectory lengths, of the algebraic areas, and of the number of boundary reflections. These results support the conjecture that the signature of the classical chaotic scattering in the quantum description is the appearance of fluctuations of the S-matrix (or conductance for ballistic conductors) in the semiclassical limit. Dans cet article, nous présentons le domaine sur lequel R. Rammal travaillait dans les derniers moments de sa vie : le chaos quantique. Nous étudions numériquement le comportement de plusieurs distributions pour des billards avec ou sans champ magnétique. Nous trouvons des lois exponentielles pour la distribution des longueurs des trajectoires, pour celle de la surface balayée par la particule et ainsi que pour la distribution du nombre de réflections sur les parois du billard. Ces résultats confortent l'hypothèse que la signature de la diffusion classiquement chaotique dans le domaine quantique est l'apparition de fluctuations de la matrice S (ou de conductance pour des conducteurs ballistiques) dans la limite semiclassique.
Chaos and microbial systems. Progress report, July 1989--July 1990
Kot, M.
1990-07-01
A recurrent theme of much recent research is that seemingly random fluctuations often occur as the result of simple deterministic mechanisms. Hence, much of the recent work in nonlinear dynamics has centered on new techniques for identifying order in seemingly chaotic systems. To determine the robustness of these techniques, chaos must, to some extent, be brought into the laboratory. Preliminary investigations of the forced double-Monod equations, a model for a predator and a prey in a chemostat with periodic variation in inflowing substrate concentration, suggest that simple microbial systems may provide the perfect framework for determining the efficacy and relevance of the new nonlinear dynamics in dealing with complex population dynamics. This research has two main goals, that is the mathematical analysis and computer simulation of the periodically forced double-Monod equations and of related models; and experimental (chemostat) population studies that evaluate the accuracy and generality of the models, and that judge the usefulness of various new techniques of nonlinear dynamics to the study of populations.
Topological approximation of the nonlinear Anderson model
NASA Astrophysics Data System (ADS)
Milovanov, Alexander V.; Iomin, Alexander
2014-06-01
We study the phenomena of Anderson localization in the presence of nonlinear interaction on a lattice. A class of nonlinear Schrödinger models with arbitrary power nonlinearity is analyzed. We conceive the various regimes of behavior, depending on the topology of resonance overlap in phase space, ranging from a fully developed chaos involving Lévy flights to pseudochaotic dynamics at the onset of delocalization. It is demonstrated that the quadratic nonlinearity plays a dynamically very distinguished role in that it is the only type of power nonlinearity permitting an abrupt localization-delocalization transition with unlimited spreading already at the delocalization border. We describe this localization-delocalization transition as a percolation transition on the infinite Cayley tree (Bethe lattice). It is found in the vicinity of the criticality that the spreading of the wave field is subdiffusive in the limit t ?+?. The second moment of the associated probability distribution grows with time as a power law ? t?, with the exponent ? =1/3 exactly. Also we find for superquadratic nonlinearity that the analog pseudochaotic regime at the edge of chaos is self-controlling in that it has feedback on the topology of the structure on which the transport processes concentrate. Then the system automatically (without tuning of parameters) develops its percolation point. We classify this type of behavior in terms of self-organized criticality dynamics in Hilbert space. For subquadratic nonlinearities, the behavior is shown to be sensitive to the details of definition of the nonlinear term. A transport model is proposed based on modified nonlinearity, using the idea of "stripes" propagating the wave process to large distances. Theoretical investigations, presented here, are the basis for consistency analysis of the different localization-delocalization patterns in systems with many coupled degrees of freedom in association with the asymptotic properties of the transport.
Chaos in Nonlinear Dynamical Systems Helicopter Flight-data Analysis
Taylor, James H.
been identified are complex chemical reactions, pendula with periodic forcing functions [2], NMR laser. In most real-life situations, system behaviour is characterized by time series data sequences available [16], in which state-space reconstruction of time series data was proposed for the first time
Parameter identification using experimental nonlinear dynamics and chaos
Chancellor, Roy Scott
1993-01-01
data from accelerometer signals mounted on the test specimens. Data acquisition software samples velocity and displacement signals and displays a phase portrait or Poincare map on a computer screen. Experimental data show the chaotic nature...
Lagrangian chaos in an ABC-forced nonlinear dynamo
NASA Astrophysics Data System (ADS)
Rempel, Erico L.; C-L Chian, Abraham; Brandenburg, Axel
2012-07-01
The Lagrangian properties of the velocity field in a magnetized fluid are studied using three-dimensional simulations of a helical magnetohydrodynamic dynamo. We compute the attracting and repelling Lagrangian coherent structures (LCS), which are dynamic lines and surfaces in the velocity field that delineate particle transport in flows with chaotic streamlines and act as transport barriers. Two dynamo regimes are explored, one with a robust coherent mean magnetic field and the other with intermittent bursts of magnetic energy. The LCS and the statistics of the finite-time Lyapunov exponents indicate that the stirring/mixing properties of the velocity field decay as a linear function of magnetic energy. The relevance of this study to the solar dynamo problem is also discussed.
Chaos, fractals and nonlinear dynamics in evolution and phylogeny.
Green, D M
1991-10-01
Biological evolution is a dynamic system that can be modelled using physical-time-evolution equations, Even simple iterative models can have complex dynamics, and replication, the fundamental evolutionary property of living things, is an iterative process. All living things can be conceived in abstract geometric terms as elements comprising an infinite fractal set in n-dimensional euclidian space. Phylogeny, the ancestral-descendant time series connecting individuals through successive generations, is also fractal. This article shows how dynamic models and fractal geometry can be applied to phylogeny and evolutionary theory, providing a basis for refuting linnaean categorical ranks in taxonomy, for recognizing limits to the naturalness of any classification and for understanding the physics of the evolutionary process. PMID:21232500
Lagrangian chaos in an ABC--forced nonlinear dynamo
Erico L. Rempel; Abraham C. -L. Chian; Axel Brandenburg
2012-01-20
The Lagrangian properties of the velocity field in a magnetized fluid are studied using three-dimensional simulations of a helical magnetohydrodynamic dynamo. We compute the attracting and repelling Lagrangian coherent structures, which are dynamic lines and surfaces in the velocity field that delineate particle transport in flows with chaotic streamlines and act as transport barriers. Two dynamo regimes are explored, one with a robust coherent mean magnetic field and one with intermittent bursts of magnetic energy. The Lagrangian coherent structures and the statistics of finite--time Lyapunov exponents indicate that the stirring/mixing properties of the velocity field decay as a linear function of the magnetic energy. The relevance of this study for the solar dynamo problem is discussed.
Wang, Yuan-Fang
these partial models are registered together. We propose to use a nonlinear optimization method, the Double DogUniscale Multi-view Registration Using Double Dog-Leg Method Chao-I Chena, Dusty Sargentb, Chang Barbara, CA, USA 93106 bSTI Medical Systems, 733 Bishop Street, Honolulu, HI, USA 96813 ABSTRACT 3D
Relation of Origins of Primitive Chaos
Yoshihito Ogasawara
2014-10-29
A new concept, primitive chaos, was proposed, as a concept closely related to the fundamental problems of sciences themselves such as determinism, causality, free will, predictability, and time asymmetry [{\\em J. Phys. Soc. Jpn.} {\\bf 2014}, {\\em 83}, 1401]. This concept is literally a primitive chaos in such a sense that it leads to the characteristic properties of the conventional chaos under natural conditions. Then, two contrast concepts, nondegenerate Peano continuum and Cantor set, are known as the origins of the primitive chaos. In this study, the relation of these origins is investigated with the aid of a mathematical method, topology. Then, we can see the emergence of interesting concepts such as the relation of whole and part, and coarse graining, which imply the essence of our intrinsic recognition for phenomena.
Chaos and Fractals in Human Physiology.
ERIC Educational Resources Information Center
Goldberger, Ary L.; And Others
1990-01-01
Discusses the irregularity and unpredictability of the human body. Presented are pictures showing the fractallike structures and research findings on the mechanism for chaos in the human body. Lists four further reading materials. (YP)
Quantum Chaos and Symmetries in Nuclear Spectroscopy
NASA Astrophysics Data System (ADS)
Tambergs, J.; Krasta, T.; Dumbr?js, O.
2003-06-01
There is no generally acceptable quantum chaos definition in physics yet, hence we believe that the application of existing approaches to various specific physical systems would help to solve this problem. In our approach to quantum chaos problem we employ the dynamical quantum chaos criterion ?k = ?spr (k)/D0, introduced by V.Bunakov, where ?spr (k) - fragmentation width of the unperturbed quantum state, D0 - averaged distance between the levels of unperturbed system. This criterion is associated with physical system symmetries via the conservation laws for corresponding quantum numbers. We consider the application of Bunakov's criterion ?k both to the traditional (Nilson single-particle) nuclear model as well as to the algebraic microscopic strictly restricted dynamics nuclear model (SRDM). In the case of SRDM dynamical criterion ?k seems to be more sensitive indicator of quantum chaos, in comparision with the statistical one, associated with level spacing distributions.
Adapted polynomial chaos expansion for failure detection
NASA Astrophysics Data System (ADS)
Paffrath, M.; Wever, U.
2007-09-01
In this paper, we consider two methods of computation of failure probabilities by adapted polynomial chaos expansions. The performance of the two methods is demonstrated by a predator-prey model and a chemical reaction problem.
Entanglement across a transition to quantum chaos
Mejia-Monasterio, Carlos; Benenti, Guliano; Casati, Giulio; Carlo, Gabriel G.
2005-06-15
We study the relation between entanglement and quantum chaos in one- and two-dimensional spin-1/2 lattice models, which exhibit mixing of the noninteracting eigenfunctions and transition from integrability to quantum chaos. Contrary to what occurs in a quantum phase transition, the onset of quantum chaos is not a property of the ground state but takes place for any typical many-spin quantum state. We study bipartite and pairwise entanglement measures--namely, the reduced von Neumann entropy and the concurrence--and discuss quantum entanglement sharing. Our results suggest that the behavior of the entanglement is related to the mixing of the eigenfunctions rather than to the transition to chaos.
International Journal of Bifurcation Chaos, Vol. No.
Lai, Ying-Cheng
Publishing Company ENCODING DIGITAL INFORMATION USING TRANSIENT CHAOS YINGCHENG LAI # Department Physics Astronomy, Department Mathematics, University Kansas, Lawrence, Kansas 66045, USA Received May 1999; Revised August 1999 Recent work has demonstrated symbolic representations of controlled chaotic orbits utilized
Adapted polynomial chaos expansion for failure detection
Paffrath, M. [Siemens AG, Corporate Technology, Otto-Hahn-Ring 6, D81730 Munich (Germany)], E-mail: meinhard.paffrath@siemens.com; Wever, U. [Siemens AG, Corporate Technology, Otto-Hahn-Ring 6, D81730 Munich (Germany)], E-mail: utz.wever@siemens.com
2007-09-10
In this paper, we consider two methods of computation of failure probabilities by adapted polynomial chaos expansions. The performance of the two methods is demonstrated by a predator-prey model and a chemical reaction problem.
CHAOS FROM MAPS Lecture 7: 1-dimensional
Read, Peter L.
CHAOS FROM MAPS Lecture 7: 1-dimensional Maps #12;7. Chaos from Maps Now we turn to a new class of period 8, 16, 32... occur as r increases. Computer experiments show that r1 = 3 (period 2 is born) r2 = 3.449... (period 4 is born) r3 = 3.54409... (period 8 is born) r4 = 3.5644... (period 16 is born) . . . r = 3
Wave chaos in rapidly rotating stars
F. Lignieres; B. Georgeot
2008-05-12
Effects of rapid stellar rotation on acoustic oscillation modes are poorly understood. We study the dynamics of acoustic rays in rotating polytropic stars and show using quantum chaos concepts that the eigenfrequency spectrum is a superposition of regular frequency patterns and an irregular frequency subset respectively associated with near-integrable and chaotic phase space regions. This opens new perspectives for rapidly rotating star seismology and also provides a new and potentially observable manifestation of wave chaos in a large scale natural system.
Observation and Control of Hamiltonian Chaos in Wave-particle Interaction
Doveil, F.; Ruzzon, A.; Elskens, Y.
2010-11-23
Wave-particle interactions are central in plasma physics. The paradigm beam-plasma system can be advantageously replaced by a traveling wave tube (TWT) to allow their study in a much less noisy environment. This led to detailed analysis of the self-consistent interaction between unstable waves and an either cold or warm electron beam. More recently a test cold beam has been used to observe its interaction with externally excited wave(s). This allowed observing the main features of Hamiltonian chaos and testing a new method to efficiently channel chaotic transport in phase space. To simulate accurately and efficiently the particle dynamics in the TWT and other 1D particle-wave systems, a new symplectic, symmetric, second order numerical algorithm is developed, using particle position as the independent variable, with a fixed spatial step.This contribution reviews: presentation of the TWT and its connection to plasma physics, resonant interaction of a charged particle in electrostatic waves, observation of particle trapping and transition to chaos, test of control of chaos, and description of the simulation algorithm.The velocity distribution function of the electron beam is recorded with a trochoidal energy analyzer at the output of the TWT. An arbitrary waveform generator is used to launch a prescribed spectrum of waves along the 4m long helix of the TWT. The nonlinear synchronization of particles by a single wave, responsible for Landau damping, is observed. We explore the resonant velocity domain associated with a single wave as well as the transition to large scale chaos when the resonant domains of two waves and their secondary resonances overlap. This transition exhibits a devil's staircase behavior when increasing the excitation level in agreement with numerical simulation.A new strategy for control of chaos by building barriers of transport in phase space as well as its robustness is successfully tested. The underlying concepts extend far beyond the field of electron devices and plasma physics.
Controlling Chaos Via Knowledge of Initial Condition for a Curved Structure
NASA Technical Reports Server (NTRS)
Maestrello, L.
2000-01-01
Nonlinear response of a flexible curved panel exhibiting bifurcation to fully developed chaos is demonstrated along with the sensitivity to small perturbation from the initial conditions. The response is determined from the measured time series at two fixed points. The panel is forced by an external nonharmonic multifrequency and monofrequency sound field. Using a low power time-continuous feedback control, carefully tuned at each initial condition, produces large long-term effects on the dynamics toward taming chaos. Without the knowledge of the initial conditions, control may be achieved by destructive interference. In this case, the control power is proportional to the loading power. Calculation of the correlation dimension and the estimation of positive Lyapunov exponents, in practice, are the proof of chaotic response.
NASA Astrophysics Data System (ADS)
Takougang Kingni, Sifeu; Hervé Talla Mbé, Jimmi; Woafo, Paul
2012-09-01
In this work, we numerically study the dynamics of vertical cavity surface emitting laser (VCSEL) firstly when it is driven by Chua's oscillator, secondly in case where it is driven by a broad frequency spectral bandwidth chaotic oscillator developed by Nana et al. [Commun. Nonlinear Sci. Numer. Simul. 14, 2266 (2009)]. We demonstrated that the VCSEL generated robust chaotic dynamics compared to the ones found in VCSEL subject to a sinusoidally modulated current and therefore it is more suitable for chaos encryption techniques. The synchronization characteristics and the communication performances of unidirectional coupled VCSEL driven by the broad frequency spectral bandwidth chaotic oscillators are investigated numerically. The results show that high-quality synchronization and transmission of messages can be realized for suitable system parameters. Chaos shift keying method is successfully applied to encrypt a message at a high bitrate.
Loss of 'complexity' and aging. Potential applications of fractals and chaos theory to senescence
NASA Technical Reports Server (NTRS)
Lipsitz, L. A.; Goldberger, A. L.
1992-01-01
The concept of "complexity," derived from the field of nonlinear dynamics, can be adapted to measure the output of physiologic processes that generate highly variable fluctuations resembling "chaos." We review data suggesting that physiologic aging is associated with a generalized loss of such complexity in the dynamics of healthy organ system function and hypothesize that such loss of complexity leads to an impaired ability to adapt to physiologic stress. This hypothesis is supported by observations showing an age-related loss of complex variability in multiple physiologic processes including cardiovascular control, pulsatile hormone release, and electroencephalographic potentials. If further research supports this hypothesis, measures of complexity based on chaos theory and the related geometric concept of fractals may provide new ways to monitor senescence and test the efficacy of specific interventions to modify the age-related decline in adaptive capacity.
NASA Astrophysics Data System (ADS)
Gekelman, W. N.; DeHaas, T.; Van Compernolle, B.
2013-12-01
Magnetic Flux Ropes Immersed in a uniform magnetoplasma are observed to twist about themselves, writhe about each other and rotate about a central axis. They are kink unstable and smash into one another as they move. Full three dimensional magnetic field and flows are measured at thousands of time steps. Each collision results in magnetic field line generation and the generation of a quasi-seperatrix layer and induced electric fields. Three dimensional magnetic field lines are computed by conditionally averaging the data using correlation techniques. The permutation entropy1 ,which is related to the Lyapunov exponent, can be calculated from the the time series of the magnetic field data (this is also done with flows) and used to calculate the positions of the data on a Jensen Shannon complexity map2. The location of data on this map indicates if the magnetic fields are stochastic, or fall into regions of minimal or maximal complexity. The complexity is a function of space and time. The complexity map, and analysis will be explained in the course of the talk. Other types of chaotic dynamical models such as the Lorentz, Gissinger and Henon process also fall on the map and can give a clue to the nature of the flux rope turbulence. The ropes fall in the region of the C-H plane where chaotic systems lie. The entropy and complexity change in space and time which reflects the change and possibly type of chaos associated with the ropes. The maps give insight as to the type of chaos (deterministic chaos, fractional diffusion , Levi flights..) and underlying dynamical process. The power spectra of much of the magnetic and flow data is exponential and Lorentzian structures in the time domain are embedded in them. Other quantities such as the Hurst exponent are evaluated for both magnetic fields and plasma flow. Work Supported by a UC-LANL Lab fund and the Basic Plasma Science Facility which is funded by DOE and NSF. 1) C. Bandt, B. Pompe, Phys. Rev. Lett., 88,174102 (2007) 2) O. Russo et al., Phys. Rev. Lett., 99, 154102 (2007), J. Maggs, G.Morales, 55, 085015 (2013)
Chaos, Boltzmann, Shannon and Electroencephalography
NASA Astrophysics Data System (ADS)
Albano, A. M.; Duckrow, R. B.
2008-06-01
Nonlinear dynamics has made possible the development of new tools for the quantitative analysis of electroencephalographic (EEG) signals. Some of the tools used in the initial applications required large quantities of noise-free, stationary data which are usually not available from biological systems. Information theoretic measures calculated using coarsegrained data are more appropriate for the analysis of these data. We review Nonlinear Dynamics and some nonlinear dynamical tools, introduce some Information Theoretic notions and use Mutual Information and Transfer Entropy to probe relationships among data streams in 19-channel scalp EEG recorded during three sleep stages-wakefulness, slow-wave sleep, and REM sleep.
CHAOS: An Active Security Mediation System 1 CHAOS: An Active Security Mediation System
Wiederhold, Gio
according to the patients in a hospital rather than according to doctors and staff on whom securityCHAOS: An Active Security Mediation System 1 CHAOS: An Active Security Mediation System David Liu1 security issues that arise when information is shared among collaborating enterprises. It provides
Rey Juan Carlos, Universidad
Effect of nonlinear dissipation on the basin boundaries of a driven two-well RayleighDuffing oscillator M. Siewe Siewe a , Hongjun Cao b,c , Miguel A.F. Sanjua´n c,* a Laboratoire de Me´canique, De Nonlinear Dynamics and Chaos Group, Departamento de Fi´sica, Universidad Rey Juan Carlos, Tulipa´n s
Schaffer, William M.
Nonlinear Dynamics of the Peroxidase-Oxidase Reaction: I. Bistability and Bursting Oscillations range of nonlinear dynamical behaviors. Many of these regimes have proved to be predictable in the Belousov- Zhabotinskyi reaction. I. Introduction The first indications of chaos in a chemical oscillator
Nonlinear problems in flight dynamics
NASA Technical Reports Server (NTRS)
Chapman, G. T.; Tobak, M.
1984-01-01
A comprehensive framework is proposed for the description and analysis of nonlinear problems in flight dynamics. Emphasis is placed on the aerodynamic component as the major source of nonlinearities in the flight dynamic system. Four aerodynamic flows are examined to illustrate the richness and regularity of the flow structures and the nature of the flow structures and the nature of the resulting nonlinear aerodynamic forces and moments. A framework to facilitate the study of the aerodynamic system is proposed having parallel observational and mathematical components. The observational component, structure is described in the language of topology. Changes in flow structure are described via bifurcation theory. Chaos or turbulence is related to the analogous chaotic behavior of nonlinear dynamical systems characterized by the existence of strange attractors having fractal dimensionality. Scales of the flow are considered in the light of ideas from group theory. Several one and two degree of freedom dynamical systems with various mathematical models of the nonlinear aerodynamic forces and moments are examined to illustrate the resulting types of dynamical behavior. The mathematical ideas that proved useful in the description of fluid flows are shown to be similarly useful in the description of flight dynamic behavior.
The effect of Lagrangian chaos on locking bifurcations in shear flows.
Finn, John M.
2002-06-01
The effect of an externally imposed perturbation on an unstable or weakly stable shear flow is investigated, with a focus on the role of Lagrangian chaos in the bifurcations that occur. The external perturbation is at rest in the laboratory frame and can form a chain of resonances or cat's eyes where the initial velocity v(x0)(y) vanishes. If in addition the shear profile is unstable or weakly stable to a Kelvin-Helmholtz instability, for a certain amplitude of the external perturbation there can be an unlocking bifurcation to a nonlinear wave resonant around a different value of y, with nonzero phase velocity. The interaction of the propagating nonlinear wave with the external perturbation leads to Lagrangian chaos. We discuss results based on numerical simulations for different amplitudes of the external perturbation. The response to the external perturbation is strong, apparently because of non-normality of the linear operator, and the unlocking bifurcation is hysteretic. The results indicate that the observed Lagrangian chaos is responsible for a second bifurcation occurring at larger external perturbation, locking the wave to the wall. This bifurcation is nonhysteretic. The mechanism by which the chaos leads to locking in this second bifurcation is by means of chaotic advective transport of momentum from one chain of resonances to the other (Reynolds stress) and momentum transport to the vicinity of the wall via chaotic scattering. These results suggest that locking of waves in rotating tank experiments in the presence of two unstable modes is due to a similar process. (c) 2002 American Institute of Physics. PMID:12779581
Control of collective network chaos
Wagemakers, Alexandre Sanjuán, Miguel A. F.
2014-06-01
Under certain conditions, the collective behavior of a large globally-coupled heterogeneous network of coupled oscillators, as quantified by the macroscopic mean field or order parameter, can exhibit low-dimensional chaotic behavior. Recent advances describe how a small set of “reduced” ordinary differential equations can be derived that captures this mean field behavior. Here, we show that chaos control algorithms designed using the reduced equations can be successfully applied to imperfect realizations of the full network. To systematically study the effectiveness of this technique, we measure the quality of control as we relax conditions that are required for the strict accuracy of the reduced equations, and hence, the controller. Although the effects are network-dependent, we show that the method is effective for surprisingly small networks, for modest departures from global coupling, and even with mild inaccuracy in the estimate of network heterogeneity.
NASA Astrophysics Data System (ADS)
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).
Sándor, Bulcsú; Járai-Szabó, Ferenc; Tél, Tamás; Néda, Zoltán
2013-04-01
The dynamics of a spring-block train placed on a moving conveyor belt is investigated both by simple experiments and computer simulations. The first block is connected by a spring to an external static point and, due to the dragging effect of the belt, the blocks undergo complex stick-slip dynamics. A qualitative agreement with the experimental results can be achieved only by taking into account the spatial inhomogeneity of the friction force on the belt's surface, modeled as noise. As a function of the velocity of the conveyor belt and the noise strength, the system exhibits complex, self-organized critical, sometimes chaotic, dynamics and phase transition-like behavior. Noise-induced chaos and intermittency is also observed. Simulations suggest that the maximum complexity of the dynamical states is achieved for a relatively small number of blocks (around five). PMID:23679502
Chaos Theory and Protein Dynamics
NASA Astrophysics Data System (ADS)
Bui, James; Clarage, James
2010-10-01
Chaos theory, commonly known as the butterfly effect, states that a small change in a complex system may cause large changes in the system as time moves forward. This phenomenon was first discovered by Henri Poincare in the 1880's. The computer programs NAMD, VMD (Visual Molecular Dynamics) and Mathematica were used to calculate the movements and graphically analyze the trajectories of the protein ubiquitin. A small change was applied to a single atom's initial position in the x-coordinate to see how it would affect the future dynamics and trajectory of the protein. Our findings indicate an exponential divergence from the controlled trajectory with a Lyapunov exponent = 10.5 [1/ps]. In other words after less than a picosecond (trillionth of a second) the dynamics of a small biophysical system is no longer predictable, even though the underlying Newtonian physical laws are completely deterministic.
Quantum chaos: a decoherent definition.
W. H. Zurek; J. P. Paz
1995-02-28
We show that the rate of increase of von Neumann entropy computed from the reduced density matrix of an open quantum system is an excellent indicator of the dynamical behavior of its classical hamiltonian counterpart. In decohering quantum analogs of systems which exhibit classical hamiltonian chaos entropy production rate quickly tends to a constant which is given by the sum of the positive Lyapunov exponents, and falls off only as the system approaches equilibrium. By contrast, integrable systems tend to have entropy production rate which decreases as $t^{-1}$ well before equilibrium is attained. Thus, behavior of quantum systems in contact with the environment can be used as a test to determine the nature of their hamiltonian evolution.
Electrical resistivity as quantum chaos
Laughlin, R.B.
1987-08-01
The physics of quantum transport is re-examined as a problem in quantum chaos. It is proposed that the ''random potential'' in which electrons in dirty metals move is not random at all, but rather any potential inducing the electron motion to be chaotic. The Liapunov characteristic exponent of classical electron motion in this potential is identified with the collision rate l/tau appearing in Ohm's law. A field theory for chaotic systems, analogous to that used to describe dirty metals, is developed and used to investigate the quantum Sinai billiard problem. It is shown that a noninteracting degenerate electron gas moving in this potential exhibits Drude conductivity in the limit h-bar ..-->.. 0. 15 refs., 4 figs.
NASA Technical Reports Server (NTRS)
2008-01-01
[figure removed for brevity, see original site] Click on image for animation of 3-dimensional model with 5x vertical exaggeration
This image of chaotic terrain in the Aureum Chaos region of Mars was taken by the Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) at 0858UTC (3:58 a.m. EST) on January 24, 2008, near 3.66 degrees south latitude, 26.5 degrees west longitude. The image was taken in 544 colors covering 0.36-3.92 micrometers, and shows features as small as 18 meters (60 feet) across. The image is about 10 kilometers (6.2 miles) wide at its narrowest point.
Aureum Chaos is a 368 kilometer (229 mile) wide area of chaotic terrain in the eastern part of Valles Marineris. The chaotic terrain is thought to have formed by collapse of the surrounding Margaritifer Terra highland region. Aureum Chaos contains heavily eroded, randomly oriented mesas, plateaus, and knobs many revealing distinct layered deposits along their slopes. These deposits may be formed from remnants of the collapsed highlands, sand carried by Martian winds, dust or volcanic ash that settled out of the atmosphere, or sediments laid down on the floor of an ancient lake.
The top panel in the montage above shows the location of the CRISM image on a mosaic taken by the Mars Odyssey spacecraft's Thermal Emission Imaging System (THEMIS). The CRISM data cover a narrow plateau near the edge of the chaotic terrain, that stretches across from the southwest to the northeast.
The lower left image, an infrared false color image, reveals the plateau and several eroded knobs of varying sizes. The plateau's layer-cake structure is similar to that of other layered outcrops in Valles Marineris.
The lower right image reveals the strengths of mineral spectral features overlain on a black-and-white version of the infrared image. Areas shaded in red hold more of the mineral pyroxene, a primary component of basaltic rocks that are prevalent in the highlands. Spots of green indicate monohydrated sulfate minerals (sulfates with one water molecule incorporated into each molecule of the mineral), while blue indicates polyhydrated sulfate minerals (sulfates with multiple waters per mineral molecule).
Although the plateau's dark cap rock is somewhat mineralogically non-descript, the bright, white swath of underlying material cascading down the plateau's flanks appears to hold polyhydrated sulfates. Dark eolian or wind deposited sediments in the south-central part of the plateau are also rich in polyhydrated sulfates.
Surrounding the plateau are small greenish spots of monoyhydrated sulfates. These are erosional remnants of an even lower part of the layered deposits that is compositionally distinct from the main part of the plateau.
The deepest layer visible is preexisting 'basement' rock that forms the floor of Aureum Chaos around the plateau. It is comprised of basaltic rock exposed by collapse of the crust and the debris derived from that collapse.
The animation (see above) of a 3-dimensional topographic model illustrates the relationship of these materials. It was made using the lower right CRISM image, draped over MOLA topography with 5X vertical exaggeration.
CRISM is one of six science instruments on NASA's Mars Reconnaissance Orbiter. Led by The Johns Hopkins University Applied Physics Laboratory, Laurel, Md., the CRISM team includes expertise from universities, government agencies and small businesses in the United States and abroad. NASA's Jet Propulsion Laboratory, a division of the California Institute of Technology in Pasadena, manages the Mars Reconnaissance Orbiter and the Mars Science Laboratory for NASA's Science Mission Directorate, Washington. Lockheed Martin Space Systems, Denver, built the orbiter.
Quantum chaos and perturbation theory: from the analysis of wavefunctions
Cohen, Doron
Quantum chaos and perturbation theory: from the analysis of wavefunctions to the implications? Quantum chaos! How to use this expression? The bare Kubo formula gives no dissipation! To define an energy
A note on chaos via Furstenberg family couple
Risong Li
2010-01-01
The concepts of the first type of distributional chaos in the Tan–Xiong sense (Abbrev. DC1 in the Tan–Xiong sense), the second type of strong-distributional chaos (Abbrev. strong DC2) and the third type of strong-distributional chaos (Abbrev. strong DC3) were introduced by Tan et al. [F. Tan, J. Xiong. Chaos via Furstenberg family couple, Topology Appl. (2008), doi:10.1016\\/j.topol.2008.08.006] for continuous maps of
Chaos theory in hydrology: important issues and interpretations
B. Sivakumar
2000-01-01
The application of the concept of chaos theory in hydrology has been gaining considerable interest in recent times. However, studies reporting the existence of chaos in hydrological processes are often criticized due to the fundamental assumptions with which the chaos identification methods have been developed, i.e. infinite and noise-free time series, and the inherent limitations of the hydrological time series,
Chaos and Relaxation in Classical and Quantum Spin Systems
Gertz, Michael
Chaos and Relaxation in Classical and Quantum Spin Systems Dissertation submitted to the Combined Zusammenfassung Probleme im Kontext von Chaos und Relaxation haben eine fundamentale Bedeutung fÃ¼r die in Feststoffen. #12;ii Abstract The problems of chaos and relaxation have a fundamental importance in the study
The Nature (and Nurture) of Children's Perceptions of Family Chaos
ERIC Educational Resources Information Center
Hanscombe, Ken B.; Haworth, Claire M. A.; Davis, Oliver S. P.; Jaffee, Sara R.; Plomin, Robert
2010-01-01
Chaos in the home is a key environment in cognitive and behavioural development. However, we show that children's experience of home chaos is partly genetically mediated. We assessed children's perceptions of household chaos at ages 9 and 12 in 2337 pairs of twins. Using child-specific reports allowed us to use structural equation modelling to…
On an example of genuine quantum chaos Department of Physics
On an example of genuine quantum chaos M. Kuna Department of Physics Pedagogical College of S@halina.univ.gda.pl Abstract: The first example of a quantum system with the genuine quantum chaos is presented. PACS numbers the definition of ``quantum chaos''. Several defiÂ nitions exist and their interconnections have not been fully
Contemporary Mathematics Quantum chaos: a brief rst visit
Contemporary Mathematics Quantum chaos: a brief #28;rst visit Stephan De BiÃ¨vre Abstract to some aspects of quantum chaos that is adapted #21; it is hoped #21; to the audience of the school of the Schnirelman theorem is given in this context. 1. Introduction Quantum chaos, or quantum chaology, as Michael
QUANTUM CHAOS USING DELTA KICKED SYSTEMS VIJAYASHANKAR RAMAREDDY
Summy, Gil
QUANTUM CHAOS USING DELTA KICKED SYSTEMS By VIJAYASHANKAR RAMAREDDY Bachelor of Science Bangalore December, 2008 #12;QUANTUM CHAOS USING DELTA KICKED SYSTEMS Dissertation Approved: iii #12;ACKNOWLEDGMENTS a memorable experi- ence. v #12;TABLE OF CONTENTS Chapter Page 1 Introduction 1 1.1 Quantum Chaos
From the Academy Random matrices and quantum chaos
Marklof, Jens
From the Academy Random matrices and quantum chaos Thomas Kriecherbauer*, Jens Marklof appearances of random matrices, namely in the theory of quantum chaos and in the theory of prime numbers, in fact, are not only used to describe statistical properties of physical systems (e.g., in quantum chaos
MAT656 --Topics in Dynamical Systems: Introduction to Quantum Chaos
Sutherland, Scott
MAT656 -- Topics in Dynamical Systems: Introduction to Quantum Chaos Spring 2011 Shimon Brooks MWF mainly on simpler "toy models" of quantum chaos, that capture many of the ideas, without much conventions and notations! Â· Quantum Chaos: a Brief First Visit, by Stephan De Bi`evre. Good intro- ductory
God's Stuff: The Constructive Powers of Chaos for Teaching Religion
ERIC Educational Resources Information Center
Willhauck, Susan
2010-01-01
Order and organization are valued in the classroom, and there is a prevailing understanding that chaos should be avoided. Yet chaos can also be potent space or a source from which new things spring forth. This article investigates biblical, scientific, and cultural understandings of chaos to discover how these contribute to a revelatory metaphor…
REGULAR ARTICLES Food chain chaos due to Shilnikov's orbit
Deng, Bo
REGULAR ARTICLES Food chain chaos due to Shilnikov's orbit Bo Denga) and Gwendolen Hinesb of the predator over the prey is sufficiently small in a basic tri-trophic food chain model. This assumption not be properly understood without understanding the role chaos plays in food chains. Yet chaos generating
Effects of RF Stimulus and Negative Feedback on Nonlinear Circuits
Renato Mariz de Moraes; Steven M. Anlage
2002-08-27
We investigate the combined effect of rectification and nonlinear dynamics on the behavior of several simple nonlinear circuits. We consider the classic Resistor-Inductor-Diode (RLD) circuit driven by a low frequency source when an operational amplifier with negative feedback is added to the circuit. Radio frequency signals are applied to the circuit, causing significant changes in the onset of period-doubling and chaos. Measurements indicate that this effect is associated with a DC voltage induced by rectification of the RF signal in the circuit. The combination of rectification and nonlinear circuit dynamics produce qualitatively new behavior, which opens up a new channel of RF interference in circuits.
Amplifier similariton fiber laser with nonlinear spectral compression.
Boscolo, Sonia; Turitsyn, Sergei K; Finot, Christophe
2012-11-01
We propose a new concept of a fiber laser architecture supporting self-similar pulse evolution in the amplifier and nonlinear spectral pulse compression in the passive fiber. The latter process allows for transform-limited picosecond pulse generation, and improves the laser's power efficiency by preventing strong spectral filtering from being highly dissipative. Aside from laser technology, the proposed scheme opens new possibilities for studying nonlinear dynamical processes. As an example, we demonstrate a clear period-doubling route to chaos in such a nonlinear laser system. PMID:23114353
Nonlinear Lattice Waves in Random Potentials
Sergej Flach
2014-09-10
Localization of waves by disorder is a fundamental physical problem encompassing a diverse spectrum of theoretical, experimental and numerical studies in the context of metal-insulator transition, quantum Hall effect, light propagation in photonic crystals, and dynamics of ultra-cold atoms in optical arrays. Large intensity light can induce nonlinear response, ultracold atomic gases can be tuned into an interacting regime, which leads again to nonlinear wave equations on a mean field level. The interplay between disorder and nonlinearity, their localizing and delocalizing effects is currently an intriguing and challenging issue in the field. We will discuss recent advances in the dynamics of nonlinear lattice waves in random potentials. In the absence of nonlinear terms in the wave equations, Anderson localization is leading to a halt of wave packet spreading. Nonlinearity couples localized eigenstates and, potentially, enables spreading and destruction of Anderson localization due to nonintegrability, chaos and decoherence. The spreading process is characterized by universal subdiffusive laws due to nonlinear diffusion. We review extensive computational studies for one- and two-dimensional systems with tunable nonlinearity power. We also briefly discuss extensions to other cases where the linear wave equation features localization: Aubry-Andre localization with quasiperiodic potentials, Wannier-Stark localization with dc fields, and dynamical localization in momentum space with kicked rotors.
Bifurcations and chaos in register transitions of excised larynx experiments.
Tokuda, Isao T; Horácek, Jaromir; Svec, Jan G; Herzel, Hanspeter
2008-03-01
Experimental data from an excised larynx are analyzed in the light of nonlinear dynamics. The excised larynx provides an experimental framework that enables artificial control and direct observation of the vocal fold vibrations. Of particular interest in this experiment is the coexistence of two distinct vibration patterns, which closely resemble chest and falsetto registers of the human voice. Abrupt transitions between the two registers are typically accompanied by irregular vibrations. Two approaches are presented for the modeling of the excised larynx experiment; one is the nonlinear predictive modeling of the experimental time series and the other is the biomechanical modeling (three-mass model) that takes into account basic mechanisms of the vocal fold vibrations. The two approaches show that the chest and falsetto vibrations correspond to two coexisting limit cycles, which jump to each other with a change in the bifurcation parameter. Irregular vibrations observed at the register jumps are due to chaos that exists near the two limit cycles. This provides an alternative mechanism to generate chaotic vibrations in excised larynx experiment, which is different from the conventionally known mechanisms such as strong asymmetry between the left and right vocal folds or excessively high subglottal pressure. PMID:18377053
Deterministic chaos in the X-Ray sources
Grzedzielski, M; Janiuk, A
2015-01-01
Hardly any of the observed black hole accretion disks in X-Ray binaries and active galaxies shows constant flux. When the local stochastic variations of the disk occur at specific regions where a resonant behaviour takes place, there appear the Quasi-Periodic Oscillations (QPOs). If the global structure of the flow and its non-linear hydrodynamics affects the fluctuations, the variability is chaotic in the sense of deterministic chaos. Our aim is to solve a problem of the stochastic versus deterministic nature of the black hole binaries vari- ability. We use both observational and analytic methods. We use the recurrence analysis and we study the occurence of long diagonal lines in the recurrence plot of observed data series and compare it to the sur- rogate series. We analyze here the data of two X-Ray binaries - XTE J1550-564, and GX 339-4 observed by Rossi X-ray Timing Explorer. In these sources, the non-linear variability is expected because of the global conditions (such as the mean accretion rate) leadin...
Feigenbaum graphs: a complex network perspective of chaos
Bartolo Luque; Lucas Lacasa; Fernando J. Ballesteros; Alberto Robledo
2011-09-06
The recently formulated theory of horizontal visibility graphs transforms time series into graphs and allows the possibility of studying dynamical systems through the characterization of their associated networks. This method leads to a natural graph-theoretical description of nonlinear systems with qualities in the spirit of symbolic dynamics. We support our claim via the case study of the period-doubling and band-splitting attractor cascades that characterize unimodal maps. We provide a universal analytical description of this classic scenario in terms of the horizontal visibility graphs associated with the dynamics within the attractors, that we call Feigenbaum graphs, independent of map nonlinearity or other particulars. We derive exact results for their degree distribution and related quantities, recast them in the context of the renormalization group and find that its fixed points coincide with those of network entropy optimization. Furthermore, we show that the network entropy mimics the Lyapunov exponent of the map independently of its sign, hinting at a Pesin-like relation equally valid out of chaos.
Bifurcations and chaos in register transitions of excised larynx experiments
NASA Astrophysics Data System (ADS)
Tokuda, Isao T.; Horá?ek, Jaromir; Švec, Jan G.; Herzel, Hanspeter
2008-03-01
Experimental data from an excised larynx are analyzed in the light of nonlinear dynamics. The excised larynx provides an experimental framework that enables artificial control and direct observation of the vocal fold vibrations. Of particular interest in this experiment is the coexistence of two distinct vibration patterns, which closely resemble chest and falsetto registers of the human voice. Abrupt transitions between the two registers are typically accompanied by irregular vibrations. Two approaches are presented for the modeling of the excised larynx experiment; one is the nonlinear predictive modeling of the experimental time series and the other is the biomechanical modeling (three-mass model) that takes into account basic mechanisms of the vocal fold vibrations. The two approaches show that the chest and falsetto vibrations correspond to two coexisting limit cycles, which jump to each other with a change in the bifurcation parameter. Irregular vibrations observed at the register jumps are due to chaos that exists near the two limit cycles. This provides an alternative mechanism to generate chaotic vibrations in excised larynx experiment, which is different from the conventionally known mechanisms such as strong asymmetry between the left and right vocal folds or excessively high subglottal pressure.
NASA Astrophysics Data System (ADS)
Gekelman, Walter; Dehaas, Tim; van Compernolle, Bart
2013-10-01
Magnetic Flux Ropes Immersed in a uniform magnetoplasma are observed to twist about themselves, writhe about each other and rotate about a central axis. They are kink unstable and smash into one another as they move. Full three dimensional magnetic field and flows are measured at thousands of time steps. Each collision results in magnetic field line generation and the generation of a quasi-seperatrix layer and induced electric fields. Three dimensional magnetic field lines are computed by conditionally averaging the data. The permutation entropy can be calculated from the time series of the magnetic field data or flows is used to calculate the positions of the data on a Jensen Shannon complexity map. The location of data on this map indicates if the magnetic fields are stochastic, or fall into regions of minimal or maximal complexity. Other types of chaotic dynamical models (Gissinger , Lorentz and Henon) also fall on the map and can give a clue to the nature of the turbulence. The ropes fall in the region of the C-H plane where chaotic systems lie. The entropy and complexity change in space and time, which reflects the change and possibly type of chaos associated with the ropes. Magnetic Flux Ropes Immersed in a uniform magnetoplasma are observed to twist about themselves, writhe about each other and rotate about a central axis. They are kink unstable and smash into one another as they move. Full three dimensional magnetic field and flows are measured at thousands of time steps. Each collision results in magnetic field line generation and the generation of a quasi-seperatrix layer and induced electric fields. Three dimensional magnetic field lines are computed by conditionally averaging the data. The permutation entropy can be calculated from the time series of the magnetic field data or flows is used to calculate the positions of the data on a Jensen Shannon complexity map. The location of data on this map indicates if the magnetic fields are stochastic, or fall into regions of minimal or maximal complexity. Other types of chaotic dynamical models (Gissinger , Lorentz and Henon) also fall on the map and can give a clue to the nature of the turbulence. The ropes fall in the region of the C-H plane where chaotic systems lie. The entropy and complexity change in space and time, which reflects the change and possibly type of chaos associated with the ropes. Work sponsoerd by a LANL-UC grant and done at the Basic Plasma Science Facility (supported by DOE and NSF).
Simultaneous bidirectional message transmission in a chaos-based communication scheme.
Vicente, Raúl; Mirasso, Claudio R; Fischer, Ingo
2007-02-15
We introduce a chaos-based communication scheme allowing for bidirectional exchange of information. Coupling [corrected] two semiconductor lasers through a partially transparent optical mirror, placed in the pathway connecting the lasers [corrected] delay dynamics is induced in both lasers. We numerically demonstrate that this dynamics can be identically synchronized, and moreover, information introduced on both ends of the link can be simultaneously transmitted. This scheme allows one to negotiate a key through a public channel. PMID:17356667
Nonlinear Control of Heart Rate Variability in Human Infants
NASA Astrophysics Data System (ADS)
Sugihara, George; Allan, Walter; Sobel, Daniel; Allan, Kenneth D.
1996-03-01
Nonlinear analyses of infant heart rhythms reveal a marked rise in the complexity of the electrocardiogram with maturation. We find that normal mature infants (gestation >= 35 weeks) have complex and distinctly nonlinear heart rhythms (consistent with recent reports for healthy adults) but that such nonlinearity is lacking in preterm infants (gestation <= 27 weeks) where parasympathetic-sympathetic interaction and function are presumed to be less well developed. Our study further shows that infants with clinical brain death and those treated with atropine exhibit a similar lack of nonlinear feedback control. These three lines of evidence support the hypothesis championed by Goldberger et al. [Goldberger, A. L., Rigney, D. R. & West, B. J. (1990) Sci. Am. 262, 43-49] that autonomic nervous system control underlies the nonlinearity and possible chaos of normal heart rhythms. This report demonstrates the acquisition of nonlinear heart rate dynamics and possible chaos in developing human infants and its loss in brain death and with the administration of atropine. It parallels earlier work documenting changes in the variability of heart rhythms in each of these cases and suggests that nonlinearity may provide additional power in characterizing physiological states.
Universal learning network and its application to chaos control.
Hirasawa, K; Wang, X; Murata, J; Hu, J; Jin, C
2000-03-01
Universal Learning Networks (ULNs) are proposed and their application to chaos control is discussed. ULNs provide a generalized framework to model and control complex systems. They consist of a number of inter-connected nodes where the nodes may have any continuously differentiable nonlinear functions in them and each pair of nodes can be connected by multiple branches with arbitrary time delays. Therefore, physical systems, which can be described by differential or difference equations and also their controllers, can be modeled in a unified way, and so ULNs may form a super set of neural networks and fuzzy neural networks. In order to optimize the ULNs, a generalized learning algorithm is derived, in which both the first order derivatives (gradients) and the higher order derivatives are incorporated. The derivatives are calculated by using forward or backward propagation schemes. These algorithms for calculating the derivatives are extended versions of Back Propagation Through Time (BPTT) and Real Time Recurrent Learning (RTRL) of Williams in the sense that generalized node functions, generalized network connections with multi-branch of arbitrary time delays, generalized criterion functions and higher order derivatives can be deal with. As an application of ULNs, a chaos control method using maximum Lyapunov exponent of ULNs is proposed. Maximum Lyapunov exponent of ULNs can be formulated by using higher order derivatives of ULNs, and the parameters of ULNs can be adjusted so that the maximum Lyapunov exponent approaches the target value. From the simulation results, it has been shown that a fully connected ULN with three nodes is able to display chaotic behaviors. PMID:10935763
Order-to-chaos transition in the model of a quantum pendulum subjected to noisy perturbation
Denis Makarov; Leonid Kon'kov
2015-02-06
Motion of randomly-driven quantum nonlinear pendulum is considered. Utilizing one-step Poincar\\'e map, we demonstrate that classical phase space corresponding to a single realization of the random perturbation involves domains of finite-time stability. Statistical analysis of the finite-time evolution operator (FTEO) is carried out in order to study influence of finite-time stability on quantum dynamics. It is shown that domains of finite-time stability give rise to ordered patterns in distributions of FTEO eigenfunctions. Transition to global chaos is accompanied by smearing of these patterns; however, some of their traces survive on relatively long timescales.
Order-to-chaos transition in the model of a quantum pendulum subjected to noisy perturbation
NASA Astrophysics Data System (ADS)
Makarov, D. V.; Kon’kov, L. E.
2015-03-01
The motion of a randomly driven quantum nonlinear pendulum is considered. Utilizing a one-step Poincaré map, we demonstrate that the classical phase space corresponding to a single realization of the random perturbation can involve domains of finite-time stability. Statistical analysis of the finite-time evolution operator (FTEO) is carried out in order to study the influence of finite-time stability on quantum dynamics. It is shown that domains of finite-time stability give rise to ordered patterns in distributions of FTEO eigenfunctions. The transition to global chaos is accompanied by smearing of these patterns; however, some of their traces survive on relatively long timescales.
Electronic circuits manifesting hyperbolic chaos and their simulation with software package Multisim
Sergey P. Kuznetsov
2011-11-24
We consider several electronic circuits, which represent dynamical systems with hyperbolic chaotic attractors of Smale-Williams type, and demonstrate results of their simulation using the software package NI Multisim 10. The developed approach is useful as an intermediate step of constructing real electronic devices manifesting structurally stable hyperbolic chaos applicable e.g. in systems of secure communication, noise radar, for cryptographic systems and random number generators. This is also of methodological interest for training students who specialize in radio-physics and nonlinear dynamics in the design and analysis of systems with complex dynamics using examples close to practical applications.
Transition to chaos of a vertical collapsible tube conveying air flow
NASA Astrophysics Data System (ADS)
Castillo Flores, F.; Cros, A.
2009-05-01
"Sky dancers", the large collapsible tubes used as advertising, are studied in this work through a simple experimental device. Our study is devoted to the nonlinear dynamics of this system and to its transition to chaos. Firstly, we have shown that after a collapse occurs, the air fills the tube at a different speed rate from the flow velocity. Secondly, the temporal intermittency is studied as the flow rate is increased. A statistical analysis shows that the chaotic times maintain roughly the same value by increasing air speed. On the other hand, laminar times become shorter, until the system reaches a completely chaotic state.
Entanglement measures in quantum and classical chaos
Arul Lakshminarayan; Jayendra N. Bandyopadhyay; M. S. Santhanam; V. B. Sheorey
2005-09-05
Entanglement is a Hilbert-space based measure of nonseparability of states that leads to unique quantum possibilities such as teleportation. It has been at the center of intense activity in the area of quantum information theory and computation. In this paper we discuss the implications of quantum chaos on entanglement, showing how chaos can lead to large entanglement that is universal and describable using random matrix theory. We also indicate how this measure can be used in the Hilbert space formulation of classical mechanics. This leads us to consider purely Hilbert-space based measures of classical chaos, rather than the usual phase-space based ones such as the Lyapunov exponents, and can possibly lead to understanding of partial differential equations and nonintegrable classical field theories.
Controlling chaos in wave-particle interactions.
de Sousa, M C; Caldas, I L; Rizzato, F B; Pakter, R; Steffens, F M
2012-07-01
We analyze the behavior of a relativistic particle moving under the influence of a uniform magnetic field and a stationary electrostatic wave. We work with a set of pulsed waves that allows us to obtain an exact map for the system. We also use a method of control for near-integrable Hamiltonians that consists of the addition of a small and simple control term to the system. This control term creates invariant tori in phase space that prevent chaos from spreading to large regions, making the controlled dynamics more regular. We show numerically that the control term just slightly modifies the system but is able to drastically reduce chaos with a low additional cost of energy. Moreover, we discuss how the control of chaos and the consequent recovery of regular trajectories in phase space are useful to improve regular particle acceleration. PMID:23005517
Avoiding Quantum Chaos in Quantum Computation
G. P. Berman; F. Borgonovi; F. M. Izrailev; V. I. Tsifrinovich
2000-12-19
We study a one-dimensional chain of nuclear $1/2-$spins in an external time-dependent magnetic field. This model is considered as a possible candidate for experimental realization of quantum computation. According to the general theory of interacting particles, one of the most dangerous effects is quantum chaos which can destroy the stability of quantum operations. According to the standard viewpoint, the threshold for the onset of quantum chaos due to an interaction between spins (qubits) strongly decreases with an increase of the number of qubits. Contrary to this opinion, we show that the presence of a magnetic field gradient helps to avoid quantum chaos which turns out to disappear with an increase of the number of qubits. We give analytical estimates which explain this effect, together with numerical data supporting
From Hamiltonian chaos to Maxwell's Demon.
Zaslavsky, George M.
1995-12-01
The problem of the existence of Maxwell's Demon (MD) is formulated for systems with dynamical chaos. Property of stickiness of individual trajectories, anomalous distribution of the Poincare recurrence time, and anomalous (non-Gaussian) transport for a typical system with Hamiltonian chaos results in a possibility to design a situation equivalent to the MD operation. A numerical example demonstrates a possibility to set without expenditure of work a thermodynamically non-equilibrium state between two contacted domains of the phase space lasting for an arbitrarily long time. This result offers a new view of the Hamiltonian chaos and its role in the foundation of statistical mechanics. (c) 1995 American Institute of Physics. PMID:12780222
Chaos in orbits due to disk crossings.
Hunter, C
2005-06-01
We study orbits of halo stars in simple models of galaxies with disks and halos to see if the cumulative effects of the sudden changes in acceleration that occur at disk crossings can induce chaos. We find that they can, although not in all orbits and not in all potentials. Most of the orbits that become chaotic stay relatively close to the disk and range widely in the radial direction. Heavier disks and increased halo flattening both enhance the extent of the chaos. A limited range of experiments with a three-component model of the Milky Way with an added central bulge finds that many chaotic disk-crossing orbits can be expected in the central regions, and that prolateness of the halo is much more effective than oblateness in generating chaos. PMID:15980309
Irreversible evolution of quantum chaos.
Ugulava, A; Chotorlishvili, L; Nickoladze, K
2005-05-01
The pendulum is the simplest system having all the basic properties inherent in dynamic stochastic systems. In the present paper we investigate the pendulum with the aim to reveal the properties of a quantum analogue of dynamic stochasticity or, in other words, to obtain the basic properties of quantum chaos. It is shown that a periodic perturbation of the quantum pendulum (similarly to the classical one) in the neighborhood of the separatrix can bring about irreversible phenomena. As a result of recurrent passages between degenerate states, the system gets self-chaotized and passes from the pure state to the mixed one. Chaotization involves the states, the branch points of whose levels participate in a slow "drift" of the system along the Mathieu characteristics this "drift" being caused by a slowly changing variable field. Recurrent relations are obtained for populations of levels participating in the irreversible evolution process. It is shown that the entropy of the system first grows and, after reaching the equilibrium state, acquires a constant value. PMID:16089638
Resurvey of order and chaos in spinning compact binaries
Wu, Xin; 10.1103/PhysRevD.77.103012
2010-01-01
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.
Resurvey of order and chaos in spinning compact binaries
Xin Wu; Yi Xie
2010-04-29
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.
Resurvey of order and chaos in spinning compact binaries
Wu Xin [Department of Physics, Nanchang University, Nanchang 330031 (China); Xie Yi [Department of Astronomy, Nanjing University, Nanjing 210093 (China)
2008-05-15
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.
Boyd, R.W. (Rochester Univ., NY (United States). Inst. of Optics)
1992-01-01
Nonlinear optics is the study of the interaction of intense laser light with matter. This book is a textbook on nonlinear optics at the level of a beginning graduate student. The intent of the book is to provide an introduction to the field of nonlinear optics that stresses fundamental concepts and that enables the student to go on to perform independent research in this field. This book covers the areas of nonlinear optics, quantum optics, quantum electronics, laser physics, electrooptics, and modern optics.
Chaos-induced intensification of wave scattering.
Smirnov, I P; Virovlyansky, A L; Edelman, M; Zaslavsky, G M
2005-08-01
Sound-wave propagation in a strongly idealized model of the deep-water acoustic waveguide with a periodic range dependence is considered. It is investigated how the phenomenon of ray and wave chaos affects the sound scattering at a strong mesoscale inhomogeneity of the refractive index caused by the synoptic eddy. Methods derived in the theory of dynamical and quantum chaos are applied. When studying the properties of wave chaos we decompose the wave field into a sum of Floquet modes analogous to quantum states with fixed quasi-energies. It is demonstrated numerically that the "stable islands" from the phase portrait of the ray system reveal themselves in the coarse-grained Wigner functions of individual Floquet modes. A perturbation theory has been derived which gives an insight into the role of the mode-medium resonance in the formation of Floquet modes. It is shown that the presence of a weak internal-wave-induced perturbation giving rise to ray and wave chaos strongly increases the sensitivity of the monochromatic wave field to an appearance of the eddy. To investigate the sensitivity of the transient wave field we have considered variations of the ray travel times--arrival times of sound pulses coming to the receiver through individual ray paths--caused by the eddy. It turns out that even under conditions of ray chaos these variations are relatively predictable. This result suggests that the influence of chaotic-ray motion may be partially suppressed by using pulse signals. However, the relative predictability of travel time variations caused by a large-scale inhomogeneity is not a general property of the ray chaos. This statement is illustrated numerically by considering an inhomogeneity in the form of a perfectly reflecting bar. PMID:16196683
Transition to chaos of thermocapillary convection
NASA Astrophysics Data System (ADS)
Li, Kai; Tang, Ze Mei; Aa, Yan; Hu, Wen-Rui
Transition of fluid convection to chaos in dissipative dynamical systems is a subject of great interest for both its theoretical and practical aspects in the fluid mechanics. Extensive studies have shown that there are several routes of the buoyant natural convection to chaos depending on parameters of the dissipative dynamical systems such as the Rayleigh number, the Prandtl number and geometry aspect. Another important type of natural convection is thermocapillary convection driven by the surface-tension gradient prominent in fluid systems with interface in the microgravity condition or in small-scaled terrestrial configurations (The relative importance of the gravity effect to the capillary effect is scaled by the static Bond number, , and the dynamic Bond number, , the geometrical scale of the system in the terrestrial experiments, therefore, was significantly reduced to make the capillary effect dominant). The thermocapillary convection has become one of the fundamental subjects in the microgravity fluid physics and space fluid/heat management. However, most studies now available were focused on the onset of oscillatory thermocapillary convection, the initial regime of the route to chaos. A complete route to chaos in such a new sort of dissipative system is still an attractive open question, especially in the experimental study. In present study, the route to chaos of the thermocapillary convection has been investigated. Several routes to chaos, e.g. period oscillatory convection to quasi-period oscillatory convection with 2 to 3 major frequencies, a series of successive period doubling bifurcations and their combination, of the thermocapillary flow is reported through the temperature measurements and the corresponding real time analysis of frequency spectra accomplished by Fast-Fourier-Transformation (FFT) or numerically. The corresponding phase diagrams are also provided.
Chaos and complexity in astrophysics
Oded Regev
2007-05-16
Methods and techniques of the theory of nonlinear dynamical systems and patterns can be useful in astrophysical applications. Some works on the subjects of dynamical astronomy, stellar pulsation and variability, as well as spatial complexity in extended systems, in which such approaches have already been utilized, are reviewed. Prospects for future directions in applications of this kind are outlined.
On the evidence of deterministic chaos in ECG: Surrogate and predictability analysis
NASA Astrophysics Data System (ADS)
Govindan, R. B.; Narayanan, K.; Gopinathan, M. S.
1998-06-01
The question whether the human cardiac system is chaotic or not has been an open one. Recent results in chaos theory have shown that the usual methods, such as saturation of correlation dimension D2 or the existence of positive Lyapunov exponent, alone do not provide sufficient evidence to confirm the presence of deterministic chaos in an experimental system. The results of surrogate data analysis together with the short-term prediction analysis can be used to check whether a given time series is consistent with the hypothesis of deterministic chaos. In this work nonlinear dynamical tools such as surrogate data analysis, short-term prediction, saturation of D2 and positive Lyapunov exponent have been applied to measured ECG data for several normal and pathological cases. The pathology presently studied are PVC (Premature Ventricular Contraction), VTA (Ventricular Tachy Arrhythmia), AV (Atrio-Ventricular) block and VF (Ventricular Fibrillation). While these results do not prove that ECG time series is definitely chaotic, they are found to be consistent with the hypothesis of chaotic dynamics.