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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

Global attractors of complete conformal foliations

We prove that every complete conformal foliation (M,F) of codimension q{>=}3 is either Riemannian or a (Conf(S{sup q}), S{sup q})-foliation. We further prove that if (M,F) is not Riemannian, it has a global attractor which is either a nontrivial minimal set or a closed leaf or a union of two closed leaves. In this theorem we do not assume that the manifold M is compact. In particular, every proper conformal non-Riemannian foliation (M,F) has a global attractor which is either a closed leaf or a union of two closed leaves, and the space of all nonclosed leaves is a connected q-dimensional orbifold. We show that every countable group of conformal transformations of the sphere S{sup q} can be realized as the global holonomy group of a complete conformal foliation. Examples of complete conformal foliations with exceptional and exotic minimal sets as global attractors are constructed. Bibliography: 20 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Scaling attractors in interacting teleparallel dark energy

It has been proposed recently the existence of a non-minimal coupling between a canonical scalar field (quintessence) and gravity in the framework of teleparallel gravity, motivated by similar constructions in the context of General Relativity. The dynamics of the model, known as teleparallel dark energy, has been further developed, but no scaling attractor has been found. Here we consider a model in which the non-minimal coupling is ruled by a dynamically changing coefficient α≡f{sub ,φ}/(f){sup 1/2}, with f(φ) an arbitrary function of the scalar field φ. It is shown that in this case the existence of scaling attractors is possible, which means that the universe will eventually enter these scaling attractors, regardless of the initial conditions. As a consequence, the cosmological coincidence problem could be alleviated without fine-tunings.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Non-slow-roll dynamics in α-attractors

In this paper we consider the α−attractor model and study inflation under a non-slow-roll dynamics. More precisely, we follow the approach recently proposed by Gong and Sasaki [1] by means of assuming N=N(φ). Within this framework we obtain a family of functions describing the local shape of the potential during inflation. We study a specific model and find an inflationary scenario predicting an attractor at n{sub s}≈0.967 and r≈5.5×10{sup −4}. We further show that considering a non-slow-roll dynamics, the α−attractor model can be broaden to a wider class of models that remain compatible with value of r<0.1. We further explore the model parameter space with respect to large and small field inflation and conclude that the inflaton dynamics is connected to the α− parameter, which is also related to the Kähler manifold curvature in the supergravity (SUGRA) embedding of this model. We also comment on the stabilization of the inflaton's trajectory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Stochastic inflation in phase space: is slow roll a stochastic attractor?

An appealing feature of inflationary cosmology is the presence of a phase-space attractor, ''slow roll'', which washes out the dependence on initial field velocities. We investigate the robustness of this property under backreaction from quantum fluctuations using the stochastic inflation formalism in the phase-space approach. A Hamiltonian formulation of stochastic inflation is presented, where it is shown that the coarse-graining procedure—where wavelengths smaller than the Hubble radius are integrated out—preserves the canonical structure of free fields. This means that different sets of canonical variables give rise to the same probability distribution which clarifies the literature with respect to this issue. The role played by the quantum-to-classical transition is also analysed and is shown to constrain the coarse-graining scale. In the case of free fields, we find that quantum diffusion is aligned in phase space with the slow-roll direction. This implies that the classical slow-roll attractor is immune to stochastic effects and thus generalises to a stochastic attractor regardless of initial conditions, with a relaxation time at least as short as in the classical system. For non-test fields or for test fields with non-linear self interactions however, quantum diffusion and the classical slow-roll flow are misaligned. We derive a condition on the coarse-graining scale so that observational corrections from this misalignment are negligible at leading order in slow roll.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

On the renormalization group perspective of α-attractors

In this short paper we outline a recipe for the reconstruction of F ( R ) gravity starting from single field inflationary potentials in the Einstein frame. For simple potentials one can compute the explicit form of F ( R ), whilst for more involved examples one gets a parametric form of F ( R ). The F ( R ) reconstruction algorithm is used to study various examples: power-law φ {sup n} , exponential and α -attractors. In each case it is seen that for large R (corresponding to large value of inflaton field), F ( R ) ∼ R {sup 2}. For the case of α -attractors F ( R ) ∼ R {sup 2} for all values of inflaton field (for all values of R ) as α → 0. For generic inflaton potential V (φ), it is seen that if V {sup '}/ V →0 (for some φ) then the corresponding F ( R ) ∼ R {sup 2}. We then study α-attractors in more detail using non-perturbative renormalisation group methods to analyse the reconstructed F ( R ). It is seen that α →0 is an ultraviolet stable fixed point of the renormalisation group trajectories.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

The non-equilibrium attractor for kinetic theory in relaxation time approximation

I demonstrate that the concept of a non-equilibrium attractor can be extended beyond the lowest-order moments typically considered in hydrodynamic treatments. Using a previously obtained exact solution to the relaxation-time approximation Boltzmann equation for a transversally homogeneous and boost-invariant system subject to Bjorken flow, I derive an equation obeyed by all moments of the one-particle distribution function. Using numerical solutions, I show that, similar to the pressure anisotropy, all moments of the distribution function exhibit attractor-like behavior wherein all initial conditions converge to a universal solution after a short time with the exception of moments which are sensitive to modes with zero longitudinal momentum and high transverse momentum. In addition, I compute the exact solution for the distribution function itself on very fine lattices in momentum space and demonstrate that (a) an attractor for the full distribution function exists and (b) solutions with generic initial conditions relax to this solution, first at low momentum and later at high momentum.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Testing α -attractor quintessential inflation against CMB and low-redshift data

Due to universality and attractor properties, α-attractor quintessential inflation establishes direct relations between inflationary observables such as the scalar tilt n s and the tensor-to-scalar ratio r, and late-time dark energy equation of state parameters w 0 and w a . In this work, we examine three different physically motivated regimes, considering complete freedom in the parameter α, models inspired by supergravity where α takes on values up to α = 7/3, and Starobinsky inflation (α = 1). We investigate the consistency and constraints imposed by Cosmic Microwave Background measurements from the Planck satellite, B-mode polarization data from the BICEP/Keck collaboration, and low-redshift observations. Additionally, we consider small-scale CMB measurements released by the Atacama Cosmology Telescope, which give results approaching the Harrison– Zel’dovich spectrum (n s ≈ 1). Here α-attractors lead to an improved fit over $\Lambda$CDM. For the large-scale CMB measurements, α ≳ 2 models can provide equally good fits as $\Lambda$CDM

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1987

Strange attractors in weakly turbulent Couette-Taylor flow

An experiment is conducted on the transition from quasi-periodic to weakly turbulent flow of a fluid contained between concentric cylinders with the inner cylinder rotating and the outer cylinder at rest. Power spectra, phase-space portraits, and circle maps obtained from velocity time-series data indicate that the nonperiodic behavior observed is deterministic, that is, it is described by strange attractors. Various problems that arise in computing the dimension of strange attractors constructed from experimental data are discussed and it is shown that these problems impose severe requirements on the quantity and accuracy of data necessary for determining dimensions greater than about 5. In the present experiment the attractor dimension increases from 2 at the onset of turbulence to about 4 at a Reynolds number 50-percent above the onset of turbulence.

Brandstater, A.↗
NASA NTRS1988

Thermal attractor in chaotic convection with high-Prandtl-number fluids

The onset of chaotic convection in large-Prandtl-number fluids has been found to occur in the form of elongated cells with aperiodic boundary-layer instabilities. The dynamics of this phenomenon has been monitored in the physical domain, and also in the spectral and phase spaces. In order to describe more precisely the underlying mechanisms of chaotic thermal convection, the notion of 'thermal attractor' is introduced in the physical domain and a systematic study is conducted of the evolution of the spectral energy surfaces. A relationship between this thermal attractor and the presence of a strange attractor in the phase space is proposed.

Vincent, Alain P.↗
NASA NTRS1988

Modelling the slow climatic attractor

Attempts to model the evolution of the slow-response parts of the climatic system such as the global ice mass are reviewed, and the fundamental laws governing the complete complex multidomain slow system, called the slow climatic attractor, are analyzed. The uses of paleoclimatic records are discussed, and a low-order model for the late Quaternary variations that constitutes a credible global representation of the slow climatic attractor is presented. It is shown that although according to the model the climatic system is centered on an unstable equilibrium, the points of the limit cycle attractor are quite stable and robust. It is also noted that one major deficiency of the model is its inability to portray the geographic spatial variability of climatic mean states. However, at least with regard to atmospheric CO2, estimates of the geographic fields of all significant atmospheric and surface boundary layer climate variables are deducible.

Saltzman, Barry↗
NASA NTRS1992

The dimension of attractors underlying periodic turbulent Poiseuille flow

A lower bound on the Liapunov dimenison, D-lambda, of the attractor underlying turbulent, periodic Poiseuille flow at a pressure-gradient Reynolds number of 3200 is calculated, on the basis of a coarse-grained (16x33x8) numerical solution, to be approximately 352. Comparison of Liapunov exponent spectra from this and a higher-resolution (16x33x16) simulation on the same spatial domain shows these spectra to have a universal shape when properly scaled. On the basis of these scaling properties, and a partial exponent spectrum from a still higher-resolution (32x33x32) simulation, it is argued that the actual dimension of the attractor underlying motion of the given computational domain is approximately 780. It is suggested that this periodic turbulent shear flow is deterministic chaos, and that a strange attractor does underly solutions to the Navier-Stokes equations in such flows.

Keefe, Laurence↗
NASA NTRS1992

Optical implementation of terminal-attractor-based associative memory

For the purpose of reducing the spurious states in a Hopfield neural net for associative memory, we invoke terminal attractors. In achieving the optical implementation of the terminal-attractor-based associative memory (TABAM) as described in this paper, we first prove the existence of the terminal-attractor model with binary neuron representation. We then present several one- and two-dimensional optical architectures for the TABAM. Finally, as an example, we experimentally demonstrate an inner-product optical neural model using liquid-crystal spatial light modulators with engineering approximations and discuss how to apply the inner-product model to build a two-dimensional parallel processing TABAM.

Liu, Hua-Kuang↗
NASA NTRS1993

A study of roll attractor and wing rock of delta wings at high angles of attack

Wing rock is a high angle of attack dynamic phenomenon of limited cycle motion predominantly in roll. The wing rock is one of the limitations to combat effectiveness of the fighter aircraft. Roll Attractor is the steady state or equilibrium trim angle (phi(sub trim)) attained by the free-to-roll model, held at some angle of attack, and released form rest at a given initial roll (bank) angle (phi(sub O)). Multiple roll attractors are attained at different trim angles depending on initial roll angle. The test facility (Vigyan's low speed wind tunnel) and experimental work is presented here along with mathematical modelling of roll attractor phenomenon and analysis and comparison of predictions with experimental data.

Niranjana, T.↗
DOE OSTI2015

On the Existence of Regular Global Attractor for p-Laplacian Evolution Equation

In this study, we consider the nonlinear evolution equation of parabolic type u{sub t}−div(|∇u|{sup p−2}∇u)+f(u)=g. We analyze the long time dynamics (in the sense of global attractors) under very general conditions on the nonlinearity f. Since we do not assume any polynomial growth condition on it, the main difficulty arises at first in the proof of well-posedness. In fact, the very first contribution to this problem is a pioneering paper (Efendiev and Ôtano, Differ Int Equ 20:1201–1209, 2007) where the well-posedness result has been shown by exploiting the technique from the theory of maximal monotone operators. However, from some physical aspects, to obtain the solution in variational sense might be demanding which requires limiting procedure on the approximate solutions. In this work, we are interested in variational (weak) solution. The critical issue in the proof of well-posedness is to deal with the limiting procedure on f which is overcome utilizing the weak convergence tecniques in Orlicz spaces (Geredeli and Khanmamedov, Commun Pure Appl Anal 12:735–754, 2013; Krasnosel’skiĭ and Rutickiĭ, Convex functions and Orlicz spaces, 1961). Then, proving the existence of the global attractors in L{sup 2}(Ω) and in more regular space W{sub 0}{sup 1,p}(Ω), we show that they coincide. In addition, if f is monotone and g=0, we give an explicit estimate of the decay rate to zero of the solution.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Polynomial law for controlling the generation of n-scroll chaotic attractors in an optoelectronic delayed oscillator

Controlled transitions between a hierarchy of n-scroll attractors are investigated in a nonlinear optoelectronic oscillator. Using the system's feedback strength as a control parameter, it is shown experimentally the transition from Van der Pol-like attractors to 6-scroll, but in general, this scheme can produce an arbitrary number of scrolls. The complexity of every state is characterized by Lyapunov exponents and autocorrelation coefficients.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

The in-phase states of Josephson junctions stacks as attractors

The aim of this investigation is to show that the coherent, in-phase states of intrinsic Josephson junctions stacks are attractors of the stacks' states when the applied external magnetic field h{sub e} and the external current γ vary within certain domains. Mathematically the problem is to find the solutions of the system of perturbed sine-Gordon equations for fixed other parameters and zero or random initial conditions. We determine the region in the plane (h{sub e}, γ), where the in-phase states are attractors of the stack's states for arbitrary initial perturbations. This is important, because the in-phase states are required for achieving terahertz radiation from the Josephson stacks.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Random attractor of non-autonomous stochastic Boussinesq lattice system

In this paper, we first consider the existence of tempered random attractor for second-order non-autonomous stochastic lattice dynamical system of nonlinear Boussinesq equations effected by time-dependent coupled coefficients and deterministic forces and multiplicative white noise. Then, we establish the upper semicontinuity of random attractors as the intensity of noise approaches zero.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Periodicity, chaos, and multiple attractors in a memristor-based Shinriki's circuit

In this contribution, a novel memristor-based oscillator, obtained from Shinriki's circuit by substituting the nonlinear positive conductance with a first order memristive diode bridge, is introduced. The model is described by a continuous time four-dimensional autonomous system with smooth nonlinearities. The basic dynamical properties of the system are investigated including equilibria and stability, phase portraits, frequency spectra, bifurcation diagrams, and Lyapunov exponents' spectrum. It is found that in addition to the classical period-doubling and symmetry restoring crisis scenarios reported in the original circuit, the memristor-based oscillator experiences the unusual and striking feature of multiple attractors (i.e., coexistence of a pair of asymmetric periodic attractors with a pair of asymmetric chaotic ones) over a broad range of circuit parameters. Results of theoretical analyses are verified by laboratory experimental measurements.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗