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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

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

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

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Generating multi-double-scroll attractors via nonautonomous approach

It is a common phenomenon that multi-scroll attractors are realized by introducing the various nonlinear functions with multiple breakpoints in double scroll chaotic systems. Differently, we present a nonautonomous approach for generating multi-double-scroll attractors (MDSA) without changing the original nonlinear functions. By using the multi-level-logic pulse excitation technique in double scroll chaotic systems, MDSA can be generated. A Chua's circuit, a Jerk circuit, and a modified Lorenz system are given as designed example and the Matlab simulation results are presented. Furthermore, the corresponding realization circuits are designed. The Pspice results are in agreement with numerical simulation results, which verify the availability and feasibility of this method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Resonance three-wave interactions and strange attractor

We report it is shown that the incorporation of linear sink/source terms in the three-wave resonance interaction model results in the time dependence of the wave amplitudes, which could exhibit the properties of a strange attractor. This finding demonstrates that the transition to turbulent dynamics of the waves could be related not only to the coupling of wave triads but also to the establishing of the strange attractor-like dynamics within individual wave triads.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

In-in and δN calculations of the bispectrum from non-attractor single-field inflation

In non-attractor single-field inflation models producing a scale-invariant power spectrum, the curvature perturbation on super-horizon scales grows as R∝a{sup 3}. This is so far the only known class of self-consistent single-field models with a Bunch-Davies initial state that can produce a large squeezed-limit bispectrum violating Maldacena's consistency relation. Given the importance of this result, we calculate the bispectrum with three different methods: using quantum field theory calculations in two different gauges, and classical calculations (the δN formalism). All the results agree, giving the local-form bispectrum parameter of f{sup local}{sub NL} = 5(1+c{sub s}{sup 2})/(4c{sub s}{sup 2}). This result is valid for arbitrary values of the speed of sound parameter, c{sub s}, for a particular non-attractor model we consider in this paper.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Reconstructing a f ( R ) theory from the α-Attractors

We show an analogy at high curvature between a f ( R ) = R + aR {sup n} {sup −} {sup 1} + bR {sup 2} theory and the α-Attractors. We calculate the expressions of the parameters a , b and n as functions of α and the predictions of the model f ( R ) = R + aR {sup n} {sup −} {sup 1} + bR {sup 2} on the scalar spectral index n {sub s} and the tensor-to-scalar ratio r . We find that the power law correction R {sup n} {sup −} {sup 1} allows for a production of gravitational waves enhanced with respect to the one in the Starobinsky model, while maintaining a viable prediction on n {sub s}. We numerically reconstruct the full α-Attractors class of models testing the goodness of our high-energy approximation f ( R ) = R + aR {sup n} {sup −} {sup 1} + bR {sup 2}. Moreover, we also investigate the case of a single power law f ( R ) = γ R {sup 2} {sup −} {sup δ} theory, with γ and δ free parameters. We calculate analytically the predictions of this model on the scalar spectral index n {sub s} and the tensor-to-scalar ratio r and the values of δ which are allowed from the current observational results. We find that −0.015 < δ < 0.016, confirming once again the excellent agreement between the Starobinsky model and observation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2012

AN ATTRACTOR FOR THE DYNAMICAL STATE OF THE INTRACLUSTER MEDIUM

Galaxy clusters provide us with important information about the cosmology of our universe. Observations of the X-ray radiation or of the Sunyaev-Zel'dovich effect allow us to measure the density and temperature of the hot intergalactic medium between the galaxies in a cluster, which then allow us to calculate the total mass of the galaxy cluster. However, no simple connection between the density and the temperature profiles has been identified. Here, we use controlled high-resolution numerical simulations to identify a relation between the density and temperature of the gas in equilibrated galaxy clusters. We demonstrate that the temperature-density relation is a real attractor, by showing that a wide range of equilibrated structures all move toward the attractor when perturbed and subsequently allowed to relax. For structures that have undergone sufficient perturbations for this connection to hold, one can therefore extract the mass profile directly from the X-ray intensity profile.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Intermittency at the Boundary of Generalized Synchronization in Mutually Coupled Systems with Complex Attractor Topology

The mechanisms of occurrence and characteristics of intermittency at the boundary of generalized synchronization in mutually coupled systems with complex (two-sheet) chaotic attractor topology are investigated. It has been established that the occurrence of intermittency in this case is due to the imaging point jump from one sheet of the chaotic attractor to another. At the same time, distributions of laminar phase durations and dependences of average laminar phase durations on the supercriticality parameter obey exponential laws.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1993

An Unipolar Terminal-Attractor Based Neural Associative Memory with Adaptive Threshold and Perfect Convergence

For the first time, a unipolar terminal-attractor based neural associative memory (TABAM)system with adaptive threshold and perfect convergence is presented. By adaptively setting thethreshold values for the dynamic iteration for the unipolar binary neuron states with terminal-attractors and inner-product approach, we demonstrate via computer simulation the achievement ofperfect convergence and correct retrieval. The simulation is completed with a small number of storedstates (M) and a small number of neurons (N) but a large M/N ratio. An experiment with exclusive-or logic operation using LCTV SLMs is used to show feasibility of the optoelectronic implementationof the models.

Associative↗
DOE OSTI2020

DNA Reaction–Diffusion Attractor Patterns

Abstract Living systems can form and recover complex chemical patterns with precisely sized features in the ranges of tens or hundreds of microns. We show how designed reaction–diffusion processes can likewise produce precise patterns, termed attractor patterns, that reform their precise shape after being perturbed. We use oligonucleotide reaction networks, photolithography, and microfluidic delivery to form precisely controlled attractor patterns and study the responses of these patterns to different localized perturbations. Linear and “hill”‐shaped patterns formed and stabilized into shapes and at time scales consistent with reaction–diffusion models. When patterns were perturbed in particular locations with UV light, they reliably reformed their steady‐state profiles. Recovery also occurred after repeated perturbations. By designing the far‐from‐equilibrium dynamics of a chemical system, this study shows how it is possible to design spatial patterns of molecules that are sustained and regenerated by continually evolving towards a specific steady state configuration.

Dorsey, Phillip James↗
DOE OSTI2020

DNA Reaction–Diffusion Attractor Patterns

Living systems can form and recover complex chemical patterns with precisely sized features in the ranges of tens or hundreds of microns. We show how designed reaction-diffusion processes can likewise produce precise patterns, termed attractor patterns, that reform their precise shape after being perturbed. We use oligonucleotide reaction networks, photolithography and microfluidic delivery to form precisely controlled attractor patterns and study the responses of these patterns to different localized perturbations. Linear and ‘hill’-shaped patterns formed and stabilized into shapes and at time scales consistent with reaction-diffusion models. When patterns were perturbed in particular locations with UV light, they reliably reformed their steady state profiles. Recovery also occurred after repeated perturbations. As a result, by designing the far-from-equilibrium dynamics of a chemical system, this study shows how it is possible to design spatial patterns of molecules that are sustained and regenerated by continually evolving towards a specific steady state configuration

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Entropy functional and the holographic attractor mechanism

We provide a field theory interpretation of the attractor mechanism for asymptotically AdS 4 dyonic BPS black holes whose entropy is captured by the supersymmetric index of the twisted ABJM theory at Chern-Simons level one. Here, we holographically compute the renormalized off-shell quantum effective action in the twisted ABJM theory as a function of the supersymmetric fermion masses and the arbitrary vacuum expectation values of the dimension one scalar bilinear operators and show that extremizing the effective action with respect to the vacuum expectation values of the dimension one scalar bilinears is equivalent to the attractor mechanism in the bulk. In fact, we show that the holographic quantum effective action coincides with the entropy functional and, therefore, its value at the extremum reproduces the black hole entropy.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

Relativistic hydrodynamic attractors with broken symmetries: non-conformal and non-homogeneous

Standard textbooks will state that hydrodynamics requires near-equilibrium to be applicable. Recently, however, out-of-equilibrium attractor solutions for hydrodynamics have been found in kinetic theory and holography in systems with a high degree of symmetry, suggesting the possibility of a genuine out-of-equilibrium formulation of hydrodynamics. This work demonstrates that attractor solutions also occur in non-conformal kinetic theory and spatially non-homogeneous systems, potentially having important implications for the interpretation of experimental data in heavy-ion and proton-proton collisions and relativistic fluid dynamics as a whole.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

α-attractor dark energy in view of next-generation cosmological surveys

The α-attractor inflationary models are nowadays favored by CMB Planck observations. Their similarity with canonical quintessence models motivates the exploration of a common framework that explains both inflation and dark energy. Here, we study the expected constraints that next-generation cosmological experiments will be able to impose for the dark energy α-attractor model. We systematically account for the constraining power of SNIa from WFIRST, BAO from DESI and WFIRST, galaxy clustering and shear from LSST and Stage-4 CMB experiments. We assume a tensor-to-scalar ratio, 10 -3 < r < 10 -2 , which permits to explore the wide regime sufficiently close, but distinct, to a cosmological constant, without need of fine tunning the initial value of the field. We find that the combination S4CMB + LSST + SNIa will achieve the best results, improving the FoM by almost an order of magnitude; respect to the S4CMB + BAO + SNIa case. We find this is also true for the FoM of the w 0 -w a parameters. Therefore, future surveys will be uniquely able to probe models connecting early and late cosmic acceleration.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Phenomenology and cosmology of no-scale attractor models of inflation

We have recently proposed attractor models for modulus fixing, inflation, supersymmetry breaking and dark energy based on no-scale supergravity. In this paper we develop phenomenological and cosmological aspects of these no-scale attractor models that underpin their physical applications. We consider models in which inflation is driven by a modulus field (T-type) with supersymmetry broken by a Polonyi field, or a matter field (φ-type) with supersymmetry broken by the modulus field. We derive the possible patterns of soft supersymmetry-breaking terms, which depend in T-type models whether the Polonyi and/or matter fields are twisted or not, and in φ-type models on whether the inflaton and/or other matter fields are twisted or not. In φ-type models, we are able to directly relate the scale of supersymmetry breaking to the inflaton mass. We also discuss cosmological constraints from entropy considerations and the density of dark matter on the mechanism for stabilizing the modulus field via higher-order terms in the no-scale K¨ahler potential.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Preheating after multifield inflation with nonminimal couplings. I. Covariant formalism and attractor behavior

This is the first of a three-part series of papers, in which we study the preheating phase for multifield models of inflation involving nonminimal couplings. We study the single-field attractor behavior that these models exhibit during inflation and quantify its strength and parameter dependence. We further demonstrate that the strong single-field attractor behavior persists after the end of inflation. Preheating in such models therefore generically avoids the “dephasing” that typically affects multifield models with minimally coupled fields, allowing efficient transfer of energy from the oscillating inflaton condensate(s) to coupled perturbations across large portions of parameter space. We develop a doubly covariant formalism for studying the preheating phase in such models and identify several features specific to multifield models with nonminimal couplings, including effects that arise from the nontrivial field-space manifold. In papers II and III, we apply this formalism to study how the amplification of adiabatic and isocurvature perturbations varies with parameters, highlighting several distinct regimes depending on the magnitude of the nonminimal couplings ${{\xi}}_{I}$.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1990

Upper semicontinuous global attractors for viscous flow

A particular form of regularization of the Navier-Stokes equations is studied. It is shown that as the regularization parameter goes to zero, the global attractor for the regularized system converges to the global attractor for the conventional Navier-Stokes system.

Ou, Yuh-Roung↗
NASA NTRS1990

A chaotic attractor in timing noise from the Vela pulsar?

Fourteen years of timing residual data from the Vela pulsar have been analyzed in order to determine if a chaotic dynamical process is the origin of timing noise. Using the correlation sum technique, a dimension of about 1.5 is obtained. This low dimension indicates underlying structure in the phase residuals which may be evidence for a chaotic attractor. It is therefore possible that nonlinear dynamics intrinsic to the spin-down may be the cause of the timing noise in the Vela pulsar. However, it has been found that the stimulated random walks in frequency and frequency derivative often used to model pulsar timing noise also have low fractal dimension, using the same analysis technique. Recent work suggesting that random processes with steep power spectra can mimic strange attractors seems to be confirmed in the case of these random walks. It appears that the correlation sum estimator for dimension is unable to distinguish between chaotic and random processes.

Harding, Alice K.↗