Estimating the lyapunov-exponent spectrum from short time series of low precision

We propose a new method to compute Lyapunov exponents from limited experimental data. The method is tested on a variety of known model systems, and it is found that the algorithm can be used to obtain a reasonable Lyapunov-exponent spectrum from only 5000 data points with a precision of 10 -lor 10 -2 in three-or four-dimensional phase space, or 10000 data points in five-dimensional phase space. We also apply our algorithm to the daily-averaged data of surface temperature observed at two locations in the United States to quantitatively evaluate atmospheric predictability. PACS numbers: 05.45.+b, 02.60.+y, 47.20.Tg, 92.60.Wc Nonlinear phenomena occur in nature in a wide range of apparently different contexts, yet they often display common features, or can be understood using similar concepts. Deterministic chaos and fractal structure in dissipative dynamical systems are among the most important nonlinear paradigms. The spectrum of Lyapunov exponents provides a quantitative measure of the sensitivity to initial conditions (i.e., the divergence of neighboring trajectories exponentially in time) and is the most useful dynamical diagnostic for chaotic systems. In fact, any system containing at least one positive Lyapunov exponent is defined to be chaotic, with the magnitude of the exponent determining the time scale for predictability. In any well-behaved dissipative dynamical system, one of the Lyapunov exponents must be strictly negative. I If the Lyapunov-exponent spectrum can be determined, the Kolmogorov entropy2 can be computed by summing all of the positive exponents, and the fractal dimension may be estimated using the Kaplan-Yorke conjecture. 3 The Lyapunov-exponent spectrum can be computed relatively easily for known model systems.4 However, it is difficult to estimate Lyapunov exponents from experimental data for a complex system (e.g., the atmosphere). Wolf et al.5 proposed a method to estimate one or two positive exponents. Sano and Sawada 6 and Eckmann et al.7 developed similar procedures to determine several of the Lyapunov exponents (including positive, zero, and even negative values). This is now a very active research area, and several authors8 have introduced further improvements. However, all of these methods require rela-@ 1991 The Americ tively long time series and/or data of high precision (for example, Eckmann et at. used 64000 data points with a precision of 10-4 for the Lorenz equations9), but such high-quality data cannot be obtained in many real-world situations. The infinitesimal length scales used to define Lyapunov exponents are inaccessible in experimental data. 5 The presence of noise or limited precision leads to a length scale Ln below which the structure of the underlying strange attractor is obscured. Also, for a finite data set of N points, there is a minimum length scale Lo-L/N1/D, where L is the horizontal extent of the attractor and D is its information dimension,lo below which structure cannot be resolved. When Lo~ Ln, increasing N is not likely to provide any further information on the structure of the attractor, so that a relatively small data set can be sufficient for computing Lyapunov exponents. Furthermore, if the length scales Lo and Ln are small enough for the chaotic dynamics to be the same as at infinitesimal length scales, then the computation of Lyapunov exponents using these length scales should yield reasonable results. Abraham et at. II have demonstrated that it is possible to calculate the dimensions of attractors from small, noisy data sets. The purpose of this paper is to develop a procedure by which one can evaluate the Lyapunovexponent spectrum from relatively small data sets of low precision. We test the method on a variety of known model systems, and we also use the method to study the predictability of the atmosphere from observational meteorological data. It should be noted, as pointed ou

Phase dynamics of inductively coupled intrinsic Josephson junctions and terahertz electromagnetic radiation

The Josephson effects associated with quantum tunneling of Cooper pairs manifest as nonlinear relations between the superconductivity phase difference and the bias current and voltage. Many novel phenomena appear, such as Shapiro steps in dc cuurent-voltage (IV) characteristics of a Josephson junction under microwave shining, which can be used as a voltage standard. Inversely, the Josephson effects provide a unique way to generate high-frequency electromagnetic (EM) radiation by dc bias voltage. The discovery of cuprate high-Tc superconductors accelerated the effort to develop novel source of EM waves based on a stack of atomically dense-packed intrinsic Josephson junctions (IJJs), since the large superconductivity gap covers the whole terahertz frequency band. Very recently, strong and coherent terahertz radiations have been successfully generated from a mesa structure of $\rm{Bi_2Sr_2CaCu_2O_{8+\delta}}$ single crystal which works both as the source of energy gain and as the cavity for resonance. It is then found theoretically that, due to huge inductive coupling of IJJs produced by the nanometer junction separation and the large London penetration depth of order of $\rm{\mu m}$ of the material, a novel dynamic state is stabilized in the coupled sine-Gordon system, in which $\pm \pi$ kinks in phase differences are developed responding to the standing wave of Josephson plasma and are stacked alternatively in the c-axis. This novel solution of the inductively coupled sine-Gordon equations captures the important features of experimental observations. The theory predicts an optimal radiation power larger than the one available to date by orders of magnitude, and thus suggests the technological relevance of the phenomena.Comment: review article (69 pages, 30 figures

Possible high temperature superconductivity in Ti-doped A-Sc-Fe-As-O (A= Ca, Sr) system

We report a systematic study on the effect of partial substitution of Sc$^{3+}$ by Ti$^{4+}$ in Sr$_{2}$ScFeAsO$_{3}$, Ca$_{2}$ScFeAsO$_{3}$ and Sr$_{3}$Sc$_{2}$Fe$_{2}$As$_{2}$O$_{5}$ on their electrical properties. High level of doping results in an increased carrier concentration and leads to the appearance of superconductivity with the onset of T$_{c}$ up to 45 K.Comment: 8 pages, 4 figures, 2 new figure

Optical one-way quantum computing with a simulated valence-bond solid

One-way quantum computation proceeds by sequentially measuring individual spins (qubits) in an entangled many-spin resource state. It remains a challenge, however, to efficiently produce such resource states. Is it possible to reduce the task of generating these states to simply cooling a quantum many-body system to its ground state? Cluster states, the canonical resource for one-way quantum computing, do not naturally occur as ground states of physical systems. This led to a significant effort to identify alternative resource states that appear as ground states in spin lattices. An appealing candidate is a valence-bond-solid state described by Affleck, Kennedy, Lieb, and Tasaki (AKLT). It is the unique, gapped ground state for a two-body Hamiltonian on a spin-1 chain, and can be used as a resource for one-way quantum computing. Here, we experimentally generate a photonic AKLT state and use it to implement single-qubit quantum logic gates.Comment: 11 pages, 4 figures, 8 tables - added one referenc

Modeling quark-hadron duality for relativistic, confined fermions

We discuss a model for the study of quark-hadron duality in inclusive electron scattering based on solving the Dirac equation numerically for a scalar confining linear potential and a vector color Coulomb potential. We qualitatively reproduce the features of quark-hadron duality for all potentials considered, and discuss similarities and differences to previous models that simplified the situation by treating either the quarks or all particles as scalars. We discuss the scaling results for PWIA and FSI, and the approach to scaling using the analog of the Callan-Gross relation for y-scaling.Comment: 38 pages, 21 figure

Tunable nano Peltier cooling device from geometric effects using a single graphene nanoribbon

Based on the phenomenon of curvature-induced doping in graphene we propose a class of Peltier cooling devices, produced by geometrical effects, without gating. We show how a graphene nanorib- bon laid on an array of curved nano cylinders can be used to create a targeted and tunable cooling device. Using two different approaches, the Nonequlibrium Green's Function (NEGF) method and experimental inputs, we predict that the cooling power of such a device can approach the order of kW/cm2, on par with the best known techniques using standard superlattice structures. The struc- ture proposed here helps pave the way toward designing graphene electronics which use geometry rather than gating to control devices.Comment: 12 pages, 5 figure

Time evolution of the Rabi Hamiltonian from the unexcited vacuum

The Rabi Hamiltonian describes a single mode of electromagnetic radiation interacting with a two-level atom. Using the coupled cluster method, we investigate the time evolution of this system from an initially empty field mode and an unexcited atom. We give results for the atomic inversion and field occupation, and find that the virtual processes cause the field to be squeezed. No anti-bunching occurs.Comment: 25 pages, 8 figures, RevTe

Structural and transport properties of Sr2VO{3-delta}FeAs superconductors with different oxygen deficiencies

Sr2VO{3-delta}FeAs superconductors with different oxygen deficiencies have been successfully fabricated. It is found that the superconducting transition temperature drops down monotonically with the increase of oxygen deficiency. The diminishing of superconductivity is accompanied by the enhancement of residual resistivity, indicating an unraveled scattering effect induced by the oxygen deficiency. The highest superconducting transition temperature at about 40 K is achieved near the stoichiometrical sample Sr$_2$VO$_{3}$FeAs. Surprisingly, the X-ray photoelectron spectroscopy (XPS) shows that the vanadium has a "5+" valence state in the samples. The Hall effect measurements reveal that the density of charge carriers (electron-like here) varies qualitatively with the increase of oxygen deficiency. Magnetotransport measurements show that the superconducting transition changes from one-step-like shape at low fields to two-step-like one at high fields, indicating a high anisotropy.Comment: 6 pages, 6 figure

Effect of two bands on critical fields in MgB2 thin films with various resistivity values

Upper critical fields of four MgB2 thin films were measured up to 28 Tesla at Grenoble High Magnetic Field Laboratory. The films were grown by Pulsed Laser Deposition and showed critical temperatures ranging between 29.5 and 38.8 K and resistivities at 40 K varying from 5 to 50 mWcm. The critical fields in the perpendicular direction turned out to be in the 13-24 T range while they were estimated to be in 42-57 T the range in ab-planes. In contrast to the prediction of the BCS theory, we did not observe any saturation at low temperatures: a linear temperature dependence is exhibited even at lowest temperatures at which we made the measurements. Moreover, the critical field values seemed not to depend on the normal state resistivity value. In this paper, we analyze these data considering the multiband nature of superconductivity in MgB2 We will show how the scattering mechanisms that determine critical fields and resistivity can be different.Comment: 17 pages, 3 figure

Thermal Impact on Spiking Properties in Hodgkin-Huxley Neuron with Synaptic Stimulus

The effect of environmental temperature on neuronal spiking behaviors is investigated by numerically simulating the temperature dependence of spiking threshold of the Hodgkin-Huxley neuron subject to synaptic stimulus. We find that the spiking threshold exhibits a global minimum in a "comfortable temperature" range where spike initiation needs weakest synaptic strength, indicating the occurrence of optimal use of synaptic transmission in neural system. We further explore the biophysical origin of this phenomenon in ion channel gating kinetics and also discuss its possible biological relevance in information processing in neural systems.Comment: 10 pages, 4 figure