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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 55 records · Page 3

Aging and the complexity of cardiovascular dynamics

Biomedical signals often vary in a complex and irregular manner. Analysis of variability in such signals generally does not address directly their complexity, and so may miss potentially useful information. We analyze the complexity of heart rate and beat-to-beat blood pressure using two methods motivated by nonlinear dynamics (chaos theory). A comparison of a group of healthy elderly subjects with healthy young adults indicates that the complexity of cardiovascular dynamics is reduced with aging. This suggests that complexity of variability may be a useful physiological marker.

Non-NASA Center↗

Chaotic Time Series Analysis Method Developed for Stall Precursor Identification in High-Speed Compressors

A new technique for rotating stall precursor identification in high-speed compressors has been developed at the NASA Lewis Research Center. This pseudo correlation integral method uses a mathematical algorithm based on chaos theory to identify nonlinear dynamic changes in the compressor. Through a study of four various configurations of a high-speed compressor stage, a multistage compressor rig, and an axi-centrifugal engine test, this algorithm, using only a single pressure sensor, has consistently predicted the onset of rotating stall.

Source record↗

From STEM to STEAM: Toward a Human-Centered Education

The 20th century was based on local linear engineering of complicated systems. We made cars, airplanes and chemical plants for example. The 21st century has opened a new basis for holistic non-linear design of complex systems, such as the Internet, air traffic management and nanotechnologies. Complexity, interconnectivity, interaction and communication are major attributes of our evolving society. But, more interestingly, we have started to understand that chaos theories may be more important than reductionism, to better understand and thrive on our planet. Systems need to be investigated and tested as wholes, which requires a cross-disciplinary approach and new conceptual principles and tools. Consequently, schools cannot continue to teach isolated disciplines based on simple reductionism. Science; Technology, Engineering, and Mathematics (STEM) should be integrated together with the Arts1 to promote creativity together with rationalization, and move to STEAM (with an "A" for Arts). This new concept emphasizes the possibility of longer-term socio-technical futures instead of short-term financial predictions that currently lead to uncontrolled economies. Human-centered design (HCD) can contribute to improving STEAM education technologies, systems and practices. HCD not only provides tools and techniques to build useful and usable things, but also an integrated approach to learning by doing, expressing and critiquing, exploring possible futures, and understanding complex systems.

Boy, Guy A.↗

Analysis of Cyclic Variability of Heat Release for High-EGR GDI Engine Operation with Observations on Implications for Effective Control

Operation of spark-ignition (SI) engines with high levels of charge dilution through exhaust gas recirculation (EGR) achieves significant engine efficiency gains while maintaining stoichiometric operation for compatibility with three-way catalysts. Dilution levels, however, are limited by cyclic variability-including significant numbers of misfires-that becomes more pronounced with increasing dilution. This variability has been shown to have both stochastic and deterministic components. Stochastic effects include turbulence, mixing variations, and the like, while the deterministic effect is primarily due to the nonlinear dependence of flame propagation rates and ignition characteristics on the charge composition, which is influenced by the composition of residual gases from prior cycles. The presence of determinism implies that an increased understanding the dynamics of such systems could lead to effective control approaches that allow operation near the edge of stability, effectively extending the dilution limit. This nonlinear dependence has been characterized previously for homogeneous charge, port fuel-injected (PFI) SI engines operating fuel-lean as well as with inert diluents such as bottled N2 gas. In this paper, cyclic dispersion in a modern boosted gasoline direct injection (GDI) engine using a cooled external EGR loop is examined, and the potential for improvement with effective control is evaluated through the use of symbol sequence statistics and other techniques from chaos theory. Observations related to the potential implications of these results for control approaches that could effectively enable engine operation at the edge of combustion stability are noted.

Kaul, Brian C↗

On the connection between hydrodynamics and quantum chaos in holographic theories with stringy corrections

Pole-skipping is a recently discovered signature of many-body quantum chaos in collective energy dynamics. It establishes a precise connection between resummed, all-order hydrodynamics and the underlying microscopic chaos. In this paper, we demonstrate the existence of pole-skipping in holographic conformal field theories with higher-derivative gravity duals. In particular, we first consider Einstein-Hilbert gravity deformed by curvature-squared ( R 2 ) corrections and then type IIB supergravity theory with the α ' 3 R 4 term, where α ' is set by the length of the fundamental string. The former case allows us to discuss the effects of leading-order 1 /N c corrections (with N c being the number of colours of the dual gauge group) and phenomenological coupling constant dependence. In Einstein-Gauss-Bonnet theory, pole-skipping turns out to be valid non-perturbatively in the Gauss-Bonnet coupling. The α ' 3 R 4 deformation enables us to study perturbative inverse ’t Hooft coupling corrections ( α ' 3 ~ 1 /λ 3/2 ) in SU( N c ), \( \mathcal{N}=4 \) supersymmetric Yang-Mills theory with infinite N c . While the maximal Lyapunov exponent characterising quantum chaos remains uncorrected, the butterfly velocity is shown to depend both on N c and the coupling. Several implications of the relation between hydrodynamics and chaos are discussed, including an intriguing similarity between the dependence of the butterfly velocity and the ratio of shear viscosity to entropy density on stringy corrections.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Theory of the nucleus as applied to quantum chaos

A critical analysis of the present-day concept of chaos in quantum systems as nothing but a quantum signature of chaos in classical mechanics is given. It is proposed to specify a regular versus a chaotic behavior on the basis of symmetries of the system being considered and global integrals of motion that are associated with these symmetries in accordance with the Liouville-Arnold theorem rather than on the basis of the concept of Lyapunov’s instability of trajectories. Numerical criteria of quantum chaos that follow from the proposed concept are analyzed.

74 ATOMIC AND MOLECULAR PHYSICS↗

Understanding chaos via nuclei

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.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Optimal system size for complex dynamics in random neural networks near criticality

In this article, we consider a model of dynamical agents coupled through a random connectivity matrix, as introduced by Sompolinsky et al. [Phys. Rev. Lett. 61(3), 259–262 (1988)] in the context of random neural networks. When system size is infinite, it is known that increasing the disorder parameter induces a phase transition leading to chaotic dynamics. We observe and investigate here a novel phenomenon in the sub-critical regime for finite size systems: the probability of observing complex dynamics is maximal for an intermediate system size when the disorder is close enough to criticality. We give a more general explanation of this type of system size resonance in the framework of extreme values theory for eigenvalues of random matrices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Optimization of global model composed of radial basis functions using the term-ranking approach

A term-ranking method is put forward to optimize the global model composed of radial basis functions to improve the predictability of the model. The effectiveness of the proposed method is examined by numerical simulation and experimental data. Numerical simulations indicate that this method can significantly lengthen the prediction time and decrease the Bayesian information criterion of the model. The application to real voice signal shows that the optimized global model can capture more predictable component in chaos-like voice data and simultaneously reduce the predictable component (periodic pitch) in the residual signal.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Kinetic theory for classical and quantum many-body chaos

For perturbative scalar field theories, the late-time-limit of the out-of-time-ordered correlation function that measures (quantum) chaos is shown to be equal to a Boltzmann-type kinetic equation that measures the total gross (instead of net) particle exchange between phase-space cells, weighted by a function of energy. This derivation gives a concrete form to numerous attempts to derive chaotic many-body dynamics from ad hoc kinetic equations. A period of exponential growth in the total gross exchange determines the Lyapunov exponent of the chaotic system. Physically, the exponential growth is a front propagating into an unstable state in phase space. As in conventional Boltzmann transport, which follows from the dynamics of the net particle number density exchange, the kernel of this kinetic integral equation for chaos is also set by the 2-to-2 scattering rate. This provides a mathematically precise statement of the known fact that in dilute weakly coupled gases, transport and scrambling (or ergodicity) are controlled by the same physics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

An effective field theory for non-maximal quantum chaos

In non-maximally quantum chaotic systems, the exponential behavior of out-of-time-ordered correlators (OTOCs) results from summing over exchanges of an infinite tower of higher “spin” operators. We construct an effective field theory (EFT) to capture these exchanges in (0 + 1) dimensions. The EFT generalizes the one for maximally chaotic systems, and reduces to it in the limit of maximal chaos. The theory predicts the general structure of OTOCs both at leading order in the 1/N expansion (N is the number of degrees of freedom), and after resuming over an infinite number of higher order 1/N corrections. These general results agree with those previously explicitly obtained in specific models. We also show that the general structure of the EFT can be extracted from the large q SYK model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Transient spatiotemporal chaos in the Morris-Lecar neuronal ring network

Transient behavior is thought to play an integral role in brain functionality. Numerical simulations of the firing activity of diffusively coupled, excitable Morris-Lecar neurons reveal transient spatiotemporal chaos in the parameter regime below the saddle-node on invariant circle bifurcation point. The neighborhood of the chaotic saddle is reached through perturbations of the rest state, in which few initially active neurons at an effective spatial distance can initiate spatiotemporal chaos. The system escapes from the neighborhood of the chaotic saddle to either the rest state or to a state of pulse propagation. The lifetime of the chaotic transients is manipulated in a statistical sense through a singular application of a synchronous perturbation to a group of neurons.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Poincaré recurrence statistics as an indicator of chaos synchronization

The dynamics of the autonomous and non-autonomous Rössler system is studied using the Poincaré recurrence time statistics. It is shown that the probability distribution density of Poincaré recurrences represents a set of equidistant peaks with the distance that is equal to the oscillation period and the envelope obeys an exponential distribution. The dimension of the spatially uniform Rössler attractor is estimated using Poincaré recurrence times. The mean Poincaré recurrence time in the non-autonomous Rössler system is locked by the external frequency, and this enables us to detect the effect of phase-frequency synchronization.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Relation between delayed feedback and delay-coupled systems and its application to chaotic lasers

We present a systematic approach to identify the similarities and differences between a chaotic system with delayed feedback and two mutually delay-coupled systems. We consider the general case in which the coupled systems are either unsynchronized or in a generally synchronized state, in contrast to the mostly studied case of identical synchronization. We construct a new time-series for each of the two coupling schemes, respectively, and present analytic evidence and numerical confirmation that these two constructed time-series are statistically equivalent. From the construction, it then follows that the distribution of time-series segments that are small compared to the overall delay in the system is independent of the value of the delay and of the coupling scheme. By focusing on numerical simulations of delay-coupled chaotic lasers, we present a practical example of our findings.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Routes to spatiotemporal chaos in Kerr optical frequency combs

We investigate the various routes to spatiotemporal chaos in Kerr optical frequency combs, obtained through pumping an ultra-high Q-factor whispering-gallery mode resonator with a continuous-wave laser. The Lugiato–Lefever model is used to build bifurcation diagrams with regards to the parameters that are externally controllable, namely, the frequency and the power of the pumping laser. We show that the spatiotemporal chaos emerging from Turing patterns and solitons display distinctive dynamical features. Experimental spectra of chaotic Kerr combs are also presented for both cases, in excellent agreement with theoretical spectra.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Smooth local subspace projection for nonlinear noise reduction

Many nonlinear or chaotic time series exhibit an innate broad spectrum, which makes noise reduction difficult. Local projective noise reduction is one of the most effective tools. It is based on proper orthogonal decomposition (POD) and works for both map-like and continuously sampled time series. However, POD only looks at geometrical or topological properties of data and does not take into account the temporal characteristics of time series. Here, we present a new smooth projective noise reduction method. It uses smooth orthogonal decomposition (SOD) of bundles of reconstructed short-time trajectory strands to identify smooth local subspaces. Restricting trajectories to these subspaces imposes temporal smoothness on the filtered time series. It is shown that SOD-based noise reduction significantly outperforms the POD-based method for continuously sampled noisy time series.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A test for a conjecture on the nature of attractors for smooth dynamical systems

Dynamics arising persistently in smooth dynamical systems ranges from regular dynamics (periodic, quasiperiodic) to strongly chaotic dynamics (Anosov, uniformly hyperbolic, nonuniformly hyperbolic modelled by Young towers). The latter include many classical examples such as Lorenz and Hénon-like attractors and enjoy strong statistical properties. It is natural to conjecture (or at least hope) that most dynamical systems fall into these two extreme situations. We describe a numerical test for such a conjecture/hope and apply this to the logistic map where the conjecture holds by a theorem of Lyubich, and to the 40-dimensional Lorenz-96 system where there is no rigorous theory. The numerical outcome is almost identical for both (except for the amount of data required) and provides evidence for the validity of the conjecture.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Intermittent and sustained periodic windows in networked chaotic Rössler oscillators

Route to chaos (or periodicity) in dynamical systems is one of fundamental problems. Here, dynamical behaviors of coupled chaotic Rössler oscillators on complex networks are investigated and two different types of periodic windows with the variation of coupling strength are found. Under a moderate coupling, the periodic window is intermittent, and the attractors within the window extremely sensitively depend on the initial conditions, coupling parameter, and topology of the network. Therefore, after adding or removing one edge of network, the periodic attractor can be destroyed and substituted by a chaotic one, or vice versa. In contrast, under an extremely weak coupling, another type of periodic window appears, which insensitively depends on the initial conditions, coupling parameter, and network. It is sustained and unchanged for different types of network structure. It is also found that the phase differences of the oscillators are almost discrete and randomly distributed except that directly linked oscillators more likely have different phases. These dynamical behaviors have also been generally observed in other networked chaotic oscillators.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗