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At least 109 records · Page 6

Low-dimensional chaos in magnetospheric activity from AE time series

The magnetospheric response to the solar-wind input, as represented by the time-series measurements of the auroral electrojet (AE) index, has been examined using phase-space reconstruction techniques. The system was found to behave as a low-dimensional chaotic system with a fractal dimension of 3.6 and has Kolmogorov entropy less than 0.2/min. These indicate that the dynamics of the system can be adequately described by four independent variables, and that the corresponding intrinsic time scale is of the order of 5 min. The relevance of the results to magnetospheric modeling is discussed.

Vassiliadis, D. V.↗

Chaotic /strange/ and periodic behavior in instability saturation by the oscillating two-stream instability

The nonlinear Schroedinger equation with linear growth and damping is truncated to three waves. The resulting system of nonlinear ordinary differential equations describes the excitation of linearly damped waves by the oscillating two-stream instability driven by a linearly unstable pump wave. This system represents a simple model for the nonlinear saturation of a linearly unstable wave. The model is examined analytically and numerically as a function of the dimensionless parameters of the system. It is found that the model can exhibit a wealth of characteristic dynamical behavior including stationary equilibria, Hopf bifurcations to periodic orbits, period doubling bifurcations, chaotic solutions characteristic of a strange attractor, tangent bifurcations from chaotic to periodic solutions, transient chaos, and hysteresis. Many of these features are shown to be explainable on the basis of one-dimensional maps. In the case of chaotic solutions, evidence for the presence of a strange attractor is provided by demonstrating Cantor set-like structure (i.e., scale invariance) in the surface of section.

Russell, D. A.↗

Application of non-linear dynamics to the characterization of cardiac electrical instability

Beat-to-beat alternation in the morphology of the ECG has been previously observed in hearts susceptible to fibrillation. In addition, fibrillation has been characterized by some as a chaotic state. Period doubling phenomena, such as alternation, and the onset of chaos have been connected by non-linear dynamical systems theory. In this paper, we describe the use of a technique from nonlinear dynamics theory, the construction of a first return nap, to assess the susceptibility to fibrillation threshhold in canine experiments.

NASA Discipline Cardiopulmonary↗

Topological analysis of chaotic orbits: Revisiting Hyperion

There is emerging interest in the possibility of chaotic evolution in astrophysical systems. To mention just one example, recent well-sampled ground-based observations of the Saturian satellite Hyperion strongly suggest that it is exhibiting chaotic behavior. We present a general technique, the method of close returns, for the analysis of data from astronomical objects believed to be exhibiting chaotic motion. The method is based on the extraction of pieces of the evolution that exhibit nearly periodic behavior-episodes during which the object stays near in phase space to some unstable periodic orbit. Such orbits generally act as skeletal features, tracing the topological organization of the manifold on which the chaotic dynamics takes place. This method does not require data sets as lengthy as other nonlinear analysis techniques do and is therefore well suited to many astronomical observing programs. Well sampled data covering between twenty and forty characteristic periods of the system have been found to be sufficient for the application of this technique. Additional strengths of this method are its robustness in the presence of noise and the ability for a user to clearly distinguish between periodic, random, and chaotic behavior by inspection of the resulting two-dimensional image. As an example of its power, we analyze close returns in a numerically generated data set, based on a model for Hyperion extensively studied in the literature, corresponding to nightly observations of the satellite. We show that with a small data set, embedded unstable periodic orbits can be extracted and that these orbits can be responsible for nearly periodic behavior lasting a substantial fraction of the observing run.

Boyd, Patricia T.↗

Driven and unloading aspects of magnetospheric substorms

Issues concerning the 'driven' versus 'unloading' nature of substorms are presented. The original concepts attendant to this debate are presented and substorms are concluded to inextricably combine aspects that are driven with aspects that represent a loading-unloading system. For isolated substorms, the magnetosphere-ionosphere system is shown to exhibit a bimodal response to solar wind changes. A 20 min response characteristic is associated with the driven aspect of substorms, while a 1 hr response time is associated with unloading. It is found that for strong solar wind input conditions, the magnetospheric response becomes more nearly unimodal. This is interpreted in terms of a nonlinear dynamical evolution of the system. Simple analog models are described which capture the essence of the nonlinear magnetospheric behavior. These models exhibit chaotic transitions for strong driving conditions: this may explain the observed behavior of the magnetosphere during strong geomagnetic activity.

Baker, D. N.↗

Periodic and chaotic spatiotemporal states in a phase-conjugate resonator using a photorefractive BaTiO3 phase-conjugate mirror

The dynamics of an externally pumped phase-conjugate resonator that uses four-wave mixing in BaTi03 is investigated experimentally. The emergence of spatiotemporal instabilities as the degree of transverse confinement is varied by changing the Fresnel number is described in detail. Local intensity time series show that relaxing the transverse confinement leads the system from a stationary state to periodic, then to quasi-periodic, motions and finally to chaotic behavior. In some regions of parameter space two frequencies are identified in the power spectra of the time series, indicating a route to chaos following the Ruelle-Takens-Newhouse scheme. Wave-front topological defects are identified by interferometry. As the system's confinement is varied, the phase-defect density and the spatial correlation index are found to follow similar trends, indicating that the observed spatiotemporal dynamics may indeed be an example of defect-mediated turbulence.

Liu, Siuying R.↗

Approximate constants of motion for classically chaotic vibrational dynamics - Vague tori, semiclassical quantization, and classical intramolecular energy flow

Substantial short time regularity, even in the chaotic regions of phase space, is found for what is seen as a large class of systems. This regularity manifests itself through the behavior of approximate constants of motion calculated by Pade summation of the Birkhoff-Gustavson normal form expansion; it is attributed to remnants of destroyed invariant tori in phase space. The remnant torus-like manifold structures are used to justify Einstein-Brillouin-Keller semiclassical quantization procedures for obtaining quantum energy levels, even in the absence of complete tori. They also provide a theoretical basis for the calculation of rate constants for intramolecular mode-mode energy transfer. These results are illustrated by means of a thorough analysis of the Henon-Heiles oscillator problem. Possible generality of the analysis is demonstrated by brief consideration of classical dynamics for the Barbanis Hamiltonian, Zeeman effect in hydrogen and recent results of Wolf and Hase (1980) for the H-C-C fragment.

Shirts, R. B.↗

Detection of chaotic determinism in time series from randomly forced maps

Time series from biological system often display fluctuations in the measured variables. Much effort has been directed at determining whether this variability reflects deterministic chaos, or whether it is merely "noise". Despite this effort, it has been difficult to establish the presence of chaos in time series from biological sytems. The output from a biological system is probably the result of both its internal dynamics, 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, i.e., a positive characteristic exponent that leads to sensitivity to initial conditions. 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.

Non-NASA Center↗

Chaos, Percolation and the Coronavirus Spread

The dynamics of the spreading of the COVID-19 virus has similar features to the turbulent flow, chaotic maps and other non-linear systems: a small seed grows exponentially and eventually saturates. Like in the percolation model, the virus is mostly dangerous if the probability of transmission (or the bond probability p in the percolation model) is high. This suggests a relation with the population density, ρ s , which must be higher than a certain value (ρ s > 1000 persons/km 2 ). A ‘seed’ implanted in such towns grows vigorously and affects nearby places at distance x. Thus, the spreading is governed by the ratio ρ = ρ s /x. Assuming a power law dependence τ of the number of positives to the virus N + from ρ, we find τ = 0.55, 0.75 and 0.96 for S.Korea, Italy and China respectively.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Chaos in driven Alfven systems

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.

Hada, T.↗

Evolution of the Earth-Moon system

The tidal evolution of the Earth-Moon system is reexamined. Several models of tidal friction are first compared in an averaged Hamiltonian formulation of the dynamics. With one of these models, full integrations of the tidally evolving Earth-Moon system are carried out in the complete, fully interacting, and chaotically evolving planetary system. Classic results on the history of the lunar orbit are confirmed by our more general model. A detailed history of the obliquity of the Earth which takes into account the evolving lunar orbit is presented.

Touma, Jihad↗

Potential Predictability of the Monsoon Subclimate Systems

While El Nino/Southern Oscillation (ENSO) phenomenon can be predicted with some success using coupled oceanic-atmospheric models, the skill of predicting the tropical monsoons is low regardless of the methods applied. The low skill of monsoon prediction may be either because the monsoons are not defined appropriately or because they are not influenced significantly by boundary forcing. The latter characterizes the importance of internal dynamics in monsoon variability and leads to many eminent chaotic features of the monsoons. In this study, we analyze results from nine AMIP-type ensemble experiments with the NASA/GEOS-2 general circulation model to assess the potential predictability of the tropical climate system. We will focus on the variability and predictability of tropical monsoon rainfall on seasonal-to-interannual time scales. It is known that the tropical climate is more predictable than its extratropical counterpart. However, predictability is different from one climate subsystem to another within the tropics. It is important to understand the differences among these subsystems in order to increase our skill of seasonal-to-interannual prediction. We assess potential predictability by comparing the magnitude of internal and forced variances as defined by Harzallah and Sadourny (1995). The internal variance measures the spread among the various ensemble members. The forced part of rainfall variance is determined by the magnitude of the ensemble mean rainfall anomaly and by the degree of consistency of the results from the various experiments.

Yang, Song↗

Terrestrial Planet Growth in Circumbinary Disks

We examine the accu~ulation of terrestrial from circumbinary disks surrounding pairs of stars with masses of either 0.5 solar masses each or 0.8 and 0.2 solar masses and orbital separations of 0.05 AU to 0.4 AU by performing numerical simulations of the late stages of planetary growth. Initial disks contain about 2.6 Earth masses of lunar to Mars-sized bodies orbiting within 2 AU of the center of mass of the system, plus giant planets with masses and orbits analogous to those of Jupiter and Saturn. We also performed simulations using analogous disks orbiting single 1 solar mass stars. The dynamics of planetary growth is quite chaotic because the gravitational perturbations resulting from close approaches greatly amplify differences in orbits. Thus, several simulations of each configuration were run with very slightly different initial conditions to enable us to distinguish systematic effects resulting from differences in the binary orbit (or differences of the initial orbits of the bodies within the disk) from pseudo-random variability in outcomes resulting from chaos. Most runs simulated 200 million years of evolution. At least one terrestrial planet remained at the end of each run; one simulation produced 6 terrestrial planets in a configuration that appears to be quite stable. The systems that formed around stars with binary apastron separations of less than 0.2 AU contained on average slightly more planets than those that formed around single stars, with the outermost planet typically orbiting at a greater distance from the system barycenter. Greater stellar separations tended to result in fewer planets, with the inner planet orbiting farther from the stars. More eccentric binaries have a more pronounced effect for the same apastron distance. The statistical distribution of final systems is not sensitive to moderate differences in the initial eccentricities of the bodies in the disk.

Lissauer, J. J.↗

Data-Driven Exploration of Climate Attractor Manifolds For Long-Term Predictability

Focal Area: This white paper responds to Focal Area 3. We seek to gain insight into decadal-scale climate predictability by applying novel manifold-finding probabilistic AI techniques to the complex data produced by Earth System models (ESMs) such as E3SM. The associated portfolio of research activities leverages DOE’s asset mix of HPC platforms, climate expertise, climate simulation codes, and AI expertise. Science Challenge: Climate and climate models are dynamical systems exhibiting properties that are interpretable through chaos theory. The theory contains an important concept that is relevant to multi-decade-scale climate prediction: a chaotic attractor. While the space containing all the possible states of the Earth’s atmosphere and ocean, the possible weather, is large, the realized states tend to stay near the smaller-dimensioned attractor. This behavior is responsible for the “order behind the irregularity” [1] of climate phenomena. Climate change can be thought of as a change in the properties of the attractor, and predicting the climate over years to decades is equivalent to predicting how those properties will change. To date, the attractor has been a useful conceptual tool, but has not been amenable to direct characterization. A new development is the advent of efficient high-dimensional manifold-finding probabilistic AI techniques, which permit a data-driven characterization of the ESM attractor and its probability distribution over weather states. Such a characterization would result in a natural dimensional reduction — a “non-linear Principal Components Analysis (PCA) adapted to climate simulation data” — leading to important advances in scenario-based long-term climate prediction, long-term prediction of water cycle extremes, ESM verification, inter-model comparison, and process model development.

54 ENVIRONMENTAL SCIENCES↗

Physics of the magnetotail current sheet

The Earth's magnetotail plays an important role in the solar-wind-magnetosphere coupling. At the midplane of the magnetotail is a current sheet where the dominant magnetic field component reverses sign. The charged particle motion in and near the current sheet is collisionless and nonintegrable, exhibiting chaotic scattering. The current understanding of the dynamical properties of the charged particle motion is discussed. In particular, the relationships between particle dynamics and global attributes of the system are elucidated. Geometrical properties of the phase space determine important physical observables on both micro- and macroscales.

Chen, James↗

Regular and Chaotic Quantum Dynamics of Two-Level Atoms in a Selfconsistent Radiation Field

Dynamics of two-level atoms interacting with their own radiation field in a single-mode high-quality resonator is considered. The dynamical system consists of two second-order differential equations, one for the atomic SU(2) dynamical-group parameter and another for the field strength. With the help of the maximal Lyapunov exponent for this set, we numerically investigate transitions from regularity to deterministic quantum chaos in such a simple model. Increasing the collective coupling constant b is identical with 8(pi)N(sub 0)(d(exp 2))/hw, we observed for initially unexcited atoms a usual sharp transition to chaos at b(sub c) approx. equal to 1. If we take the dimensionless individual Rabi frequency a = Omega/2w as a control parameter, then a sequence of order-to-chaos transitions has been observed starting with the critical value a(sub c) approx. equal to 0.25 at the same initial conditions.

Konkov, L. E.↗

Dynamical responses of constrained pipe conveying fluids and its dependence on the modeling of the contact force

Accurately modeling the impact force used in the analysis of loosely constrained cantilevered pipes conveying fluid is imperative. If little information is known of the motion-limiting constraints used in experiments, the analysis of the system may yield inaccurate predictions. Here in this work, multiple forcing representations of the impact force are defined and analyzed for a cantilevered pipe that conveys fluid. Depending on the representation of the impact force, the dynamics of the pipe can vary greatly when only the stiffness of the constraints is known from experiments. Three gap sizes of the constraints are analyzed, and the representation of the impact force used to analyze the system is found to significantly affect the response of the pipe at each gap size. An investigation on the effects of the vibro-impact force representation is performed through using basin of attraction analysis and nonlinear characterization of the system’s response.

42 ENGINEERING↗

Topological edge modes without symmetry in quasiperiodically driven spin chains

Here we construct an example of a 1d quasiperiodically driven spin chain whose edge states can coherently store quantum information, protected by a combination of localization, dynamics, and topology. In a sharp departure from topological phases in static and periodically driven (Floquet) spin chains, this model does not rely upon microscopic symmetry protection: Instead, the edge states are protected purely by emergent dynamical symmetries. We explore the dynamical signatures of this emergent dynamical symmetry-protected topological (EDSPT) order through exact numerics, time evolving block decimation, and analytic high-frequency expansion, finding evidence that the EDSPT is a stable dynamical phase protected by bulk many-body localization up to (at least) stretched-exponentially long timescales, and possibly beyond. We argue that EDSPTs are special to the quasiperiodically driven setting, and cannot arise in Floquet systems. Moreover, we find evidence of a type of boundary critical with no known static or Floquet analogue, in which the edge spin dynamics transition from quasiperiodic to chaotic, leading to bulk thermalization.

36 MATERIALS SCIENCE↗