The 0-1 test algorithm for chaos and its applications

To determine whether a given deterministic nonlinear dynamic system is chaotic or periodic,a novel test approach named zero-one (0-1) test has been proposed recently.In this approach,the regular and chaotic motions can be decided by calculating the parameter K approaching asymptotically to zero or one.In this study,we focus on the 0-1 test algorithm and illustrate the selection of parameters of this algorithm by numerical experiments.To validate the reliability and the universality of this algorithm,it is applied to typical nonlinear dynamic systems,including fractional-order dynamic system.     

Study of electrical and thermoelecrical properties of sulfides Tm x Mn1–x S

Variable-valence Tm _x Mn_1–x S (0 ? x ? 0.15) compounds have been synthesized and their structural, electrical, and thermoelectrical properties have been studied in the temperature range of 80–1100 K. The regions of existence of solid solutions of sulfides Tm _x Mn_1–x S with the NaCl-type fcc lattice have been determined. It has been found that, as thulium ions are substituted for manganese cations, the electrical resistivity increases, and the lattice parameter increases more sharply than that corresponding to the Vegard’s law. The study of the temperature dependences of the thermopower coefficient has revealed that the current carrier sign is retained to 500 K for all the substitution concentrations, and the charge carrier type changes from the hole type to the electron type with variations in the temperature. The experimental data have been explained in terms of the exciton model.     

On the characterization of non-stationary chaotic systems: Autonomous and non-autonomous cases

Properties of non-stationary dynamical systems are studied using the concept of a snapshot attractor which takes into account a large number of initial conditions within the basin of attraction. In this paper, both autonomous and non-autonomous systems are considered. We have discussed three different ways of inducing non-stationarity in a chaotic system—(a) when the parameter changes in a linear fashion, (b) when the parameter changes in a random fashion and (c) when it is governed by an equation inducing a chaotic change in it. Here all the variations are with respect to time. Though the first and second situations have already been considered in Romeiras et al. (1990) [1] and Serquina et al. (2008) [2], the last one has never been considered before. In each case the basic fractal properties and the famous Pesin identity are proved numerically. The Lyapunov exponents, which are calculated via an averaging procedure, lead to the expected values.     

Integrable and nonintegrable classical spin clusters

This study investigates the nonlinear dynamics of a pair of exchange-coupled spins with biaxial exchange and single-site anisotropy. It represents a Hamiltonian system with 2 degrees of freedom for which we have already established the (nontrivial) integrability criteria and constructed the integrals of the motion provided they exist. Here we present a comparative study of the phase-space trajectories for two specific models with the same symmetry properties, one of which (the XY model with exchange anisotropy) is integrable, and the other (the XY model with single-site anisotropy) nonintegrable. In the integrable model, the integrals of the motion (analytic invariants) can be reconstructed numerically by means of time averages of dynamical variables over all trajectories. In the nonintegrable model, such time averages over trajectories define nonanalytic invariants, where the nonanalyticities are associated with the presence of chaotic trajectories. A prominent feature in the nonintegrable model is the occurrence of very long time scales caused by the presence of low-flux cantori, which form sticky coats on the boundary between chaotic regions and regular islands or leaky walls between different chaotic regions. These cantori dominate the convergence properties of time averages and presumably determine the long-time asymptotic properties of dynamic correlation functions. Finally, we present a special class of integrable systems containing arbitrarily many spins coupled by general biaxial exchange anisotropy.     

Structural studies of the P-T phase diagram of sodium niobate

The crystal structure of sodium niobate (NaNbO₃) has been investigated by energy-dispersive X-ray diffraction at high pressures (up to 4.3 GPa) in the temperature range 300–1050 K. At normal conditions, NaNbO₃ has an orthorhombic structure with Pbcm symmetry (antiferroelectric P phase). Upon heating, sodium niobate undergoes a series of consecutive transitions between structural modulated phases P-R-S-T(1)-T(2)-U; these transitions manifest themselves as anomalies in the temperature dependences of the positions and widths of diffraction peaks. Application of high pressure leads to a decrease in the temperatures of the structural transitions to the R, S, T(1), T(2), and U phases with different baric coefficients. A phase diagram for sodium niobate has been build in the pressure range 0–4.3 GPa and the temperature range 300–1050 K. The dependences of the unit-cell parameters and volume on pressure and temperature have been obtained. The bulk modulus and the volume coefficients of thermal expansion have been calculated for different structural modulated phases of sodium niobate. A phase transition (presumably, from the antiferroelectric orthorhombic P phase to the ferroelectric rhombohedral N phase) has been observed at high pressure (P = 1.6 GPa) and room temperature.     

Manifestation of ray stochastic behavior in a modal structure of the wave field

A ray-based mathematical formalism is described to analyze modal structure variations in a range-dependent wave guide. In the scope of this formalism mode amplitudes are expressed through parameters of ray trajectories. Therefore, the approach under consideration provides a convenient tool to study how chaotic ray motion manifests itself in an irregular range dependence of the modal structure. The phenomenon of nonlinear ray-medium resonance playing a crucial role in the emergence of ray chaos has been interpreted from the viewpoint of normal modes. It has been shown that in terms of modes the coexistence of regular and chaotic rays means the presence of regular and irregular constituents of mode amplitudes. An analog to incoherent summation of rays has been proposed to evaluate mode intensities (squared mode amplitudes) smoothed over the mode number. Numerical calculations have shown that it gives correct results for smoothed mode intensities at surprisingly long ranges.     

On the mathematically reliable long-term simulation of chaotic solutions of Lorenz equation in the interval [0,10000]

Using 1200 CPUs of the National Supercomputer TH-A1 and a parallel integral algorithm based on the 3500th-order Taylor expansion and the 4180-digit multiple precision data,we have done a reliable simulation of chaotic solution of Lorenz equation in a rather long interval 0 t 10000 LTU(Lorenz time unit).Such a kind of mathematically reliable chaotic simulation has never been reported.It provides us a numerical benchmark for mathematically reliable long-term prediction of chaos.Besides,it also proposes a safe method for mathematically reliable simulations of chaos in a finite but long enough interval.In addition,our very fine simulations suggest that such a kind of mathematically reliable long-term prediction of chaotic solution might have no physical meanings,because the inherent physical micro-level uncertainty due to thermal fluctuation might quickly transfer into macroscopic uncertainty so that trajectories for a long enough time would be essentially uncertain in physics.     

Analysis of thermoelastic behaviour of MgO at high temperatures and high pressures

The thermoelastic behaviour of MgO has been studied for the temperature range (300-3000 K) under different compressions down to V/V₀=0.3. It has been shown that a comprehensive study of the thermoelastic properties of MgO can be made with the help of the Anderson-Isaak equation for thermal expansivity and the Vinet equation of state taken together. We have estimated the values of thermal expansivity α, isothermal bulk modulus K_T, their variations with pressure and temperature, the Anderson-Gruneisen parameter and the change in entropy with compression for MgO along isotherms at different temperatures. The results have been discussed and compared with the corresponding values reported in the recent literature.     

Quantifying heart rate dynamics using different approaches of symbolic dynamics

The analysis of symbolic dynamics applied to physiological time series is able to retrieve information about dynamical properties of the underlying system that cannot be gained with standard methods like e.g. spectral analysis. Different approaches for the transformation of the original time series to the symbolic time series have been proposed. Yet the differences between the approaches are unknown. In this study three different transformation methods are investigated: (1) symbolization according to the deviation from the average time series, (2) symbolization according to several equidistant levels between the minimum and maximum of the time series, (3) binary symbolization of the first derivative of the time series. Furthermore, permutation entropy was used to quantify the symbolic series. Each method was applied to the cardiac interbeat interval series RR _i and its difference ΔRR _I of 17 healthy subjects obtained during head-up tilt testing. The symbolic dynamics of each method is analyzed by means of the occurrence of short sequences (“words”) of length 3. The occurrence of words is grouped according to words without variations of the symbols (0V%), words with one variation (1V%), two like variations (2LV%) and two unlike variations (2UV%). Linear regression analysis showed that for method 1 0V%, 1V%, 2LV% and 2UV% changed with increasing tilt angle. For method 2 0V%, 2LV% and 2UV% changed with increasing tilt angle and method 3 showed changes for 0V% and 1V%. Furthermore, also the permutation entropy decreased with increasing tilt angle. In conclusion, all methods are capable of reflecting changes of the cardiac autonomic nervous system during head-up tilt. All methods show that even the analysis of very short symbolic sequences is capable of tracking changes of the cardiac autonomic regulation during head-up tilt testing.     

Dielectric investigations of solid solutions SrTiO3-KTaO3 and SrTiO3-KNbO3

The temperature dependences of the dielectric constant and dielectric hysteresis loops in ceramic samples of (1 ? x)SrTiO_3?x KNbO₃ and (1 ? x)SrTiO_3?x KTaO₃ (0 ≤ x ≤ 0.3) solid solutions prepared using different heat treatments have been investigated. Phase diagrams of the studied solid solutions have been constructed in the T-x coordinates. It has been shown that, after quenching of samples (spontaneous cooling at room temperature after long-term heating at the sintering temperature of the ceramic samples), the temperature of the induced phase transition increases because of the weakening of random electric fields associated with nonisovalent impurities due to their “frozen” nonequilibrium redistribution. For small concentrations x, strong dielectric relaxation is observed in the temperature range of 150–250 K. A model of relaxing centers, which is based on the local charge compensation of heterovalent impurities, has been proposed.     

Morphology and photoluminescence properties of zinc oxide films grown by pulsed laser deposition

Zinc oxide films with different morphologies have been grown by pulsed laser deposition, varying substrate temperature and oxygen pressure. At low oxygen pressure and low substrate temperature continuous films with different roughness have been obtained, while at high substrate temperature a film with sparse hexagonal pyramids has been observed. Increasing the oxygen pressure the film became rougher and at 100 Pa a rod-array has been deposited. The columns of this rod-array grew along the wurtzite c-axis perpendicularly to the substrate surface as proved by X-ray diffraction measurements. Near to the sample borders the columns were slightly tilted towards the center of the sample. The possible growth mechanisms giving rise to the different morphologies have been discussed. Low-temperature photoluminescence measurements allowed to get information about the film quality, showing the variations of the excitonic peak and two defect bands (green and violet-blue) with the different deposition parameters.     

Supertracks,supertrack functions and chaos in the quadratic map

Chaotic behavior for the quadratic map is conjectured to be a bounding phenomenon based on state-space trajectories starting from the maximum in the map. These trajectories, called supertracks, have no sensitivity to initial conditions. The chaotic regime is found to be characterized recursively by these trajectories as functions of the map parameter.     

Schwarzian derivative as a proof of the chaotic behaviour

In recent years, a sufficient condition for determining chaotic behaviours of the non-linear systems has been characterized by the negative Schwarzian derivative (Hac?bekiro?lu et al, Nonlinear Anal.: Real World Appl. 10, 1270 (2009)). In this work, the Schwarzian derivative has been calculated for investigating the quantum chaotic transition points in the high-temperature superconducting frame of reference, which is known as a nonlinear dynamical system that displays some macroscopic quantum effects. In our previous works, two quantum chaotic transition points of the critical transition temperature, T _c, and paramagnetic Meissner transition temperature, T _PME, have been phenomenologically predicted for the mercury-based high-temperature superconductors (Onba?l? et al, Chaos, Solitons and Fractals 42, 1980 (2009); Aslan et al, J. Phys.: Conf. Ser. 153, 012002 (2009); Çataltepe, Superconductor (Sciyo Company, India, 2010)). The T _c, at which the one-dimensional global gauge symmetry is spontaneously broken, refers to the second-order phase transition, whereas the T _PME, at which time reversal symmetry is broken, indicates the change in the direction of orbital current in the system (Onba?l? et al, Chaos, Solitons and Fractals 42, 1980 (2009)). In this context, the chaotic behaviour of the mercury-based high-temperature superconductors has been investigated by means of the Schwarzian derivative of the magnetic moment versus temperature. In all calculations, the Schwarzian derivatives have been found to be negative at both T _c and T _PME which are in agreement with the chaotic behaviour of the system.     

Investigation of current–voltage and capacitance–voltage characteristics of Ag/perylene-monoimide/n-GaAs Schottky diode

Ag/perylene-monoimide(PMI)/n-GaAs Schottky diode was fabricated and the current–voltage (I–V) characteristics at a wide temperature range between 75 and 350 K and also the capacitance–voltage (C–V) characteristics at room temperature for 1 MHz have been analyzed in detail. The measured I–V characteristics exhibit a good rectification behavior at all temperature values. By using standard analysis methods, the ideality factor and the barrier height are deduced from the experimental data and also the variations of these parameters with the temperature are analyzed. In addition, by means of the Cheung and Cheung method, the series resistance and some other electrical properties are calculated for the diode. Finally, capacitance–voltage characteristics of device have been analyzed at the room temperature. From analyzing the capacitance measurements, Schottky barrier height is determined and then compared with the value which calculated from the I–V measurements at room temperature. Also, the concentration of ionized donors, built-in potential and some other parameters of diode are found using C–V characteristics.     

Slow variations of the electroconductivity of distilled water

The conductivity of distilled water with a slow change in temperature has been measured experimentally and studied. Periodic variations in the electrical conductivity of water have been found, which are observed at the rate of temperature change dT/dt < 0.1 K/h. The periods were longer than 24 h; the amplitudes of the variation ranged from +2.7% to–2.3%. The possible causes of the observed phenomena are discussed.     

On the mechanisms of photogeneration of charge carriers in PEPC-C60 composites

Photogeneration of electric charge carriers at high strengths of the external electric field and the temperature of transition to the viscous-flow state (T _visc) of thin PEPC-C₆₀ composite films obtained by casting from a toluene solution have been studied. The rheology of the composite films has been investigated by the nondestructive optical method. The consistent correlated change in the values of T _visc and the effective temperature in the expression for the photogeneration quantum yield (T ₀) in the Meltz representation with variations in the C₆₀ concentration has been established. The difference between T _visc and T ₀ in thin composite films does not exceed 2–3% of T _visc (T ₀).     

Nonlinear coherent dynamics of an atom in an optical lattice

We consider a simple model of the lossless interaction between a two-level single atom and a standing-wave single-mode laser field which creates a one-dimensional optical lattice. The internal dynamics of the atom is governed by the laser field, which is treated as classical with a large number of photons. The center-of-mass classical atomic motion is governed by the optical potential and the internal atomic degrees of freedom. The resulting Hamilton-Schrö dinger equations of motion are a five-dimensional nonlinear dynamical system with two integrals of motion, and the total atomic energy and the Bloch vector length are conserved during the interaction. In our previous papers, the motion of the atom has been shown to be regular or chaotic (in the sense of exponential sensitivity to small variations of the initial conditions and/or the system’s control parameters) depending on the values of the control parameters, atom-field detuning, and recoil frequency. At the exact atom-field resonance, the exact solutions for both the external and internal atomic degrees of freedom can be derived. The center-of-mass motion does not depend in this case on the internal variables, whereas the Rabi oscillations of the atomic inversion is a frequency-modulated signal with the frequency defined by the atomic position in the optical lattice. We study analytically the correlations between the Rabi oscillations and the center-of-mass motion in two limiting cases of a regular motion out of the resonance: (1) far-detuned atoms and (2) rapidly moving atoms. This paper is concentrated on chaotic atomic motion that may be quantified strictly by positive values of the maximal Lyapunov exponent. It is shown that an atom, depending on the value of its total energy, can either oscillate chaotically in a well of the optical potential, or fly ballistically with weak chaotic oscillations of its momentum, or wander in the optical lattice, changing the direction of motion in a chaotic way. In the regime of chaotic wandering, the atomic motion is shown to have fractal properties. We find a useful tool to visualize complicated atomic motion-Poincaré mapping of atomic trajectories in an effective three-dimensional phase space onto planes of atomic internal variables and momentum. The Poincaré mappings are constructed using the translational invariance of the standing laser wave. We find common features with typical nonhyperbolic Hamiltonian systems-chains of resonant islands of different sizes imbedded in a stochastic sea, stochastic layers, bifurcations, and so on. The phenomenon of the atomic trajectories sticking to boundaries of regular islands, which should have a great influence on atomic transport in optical lattices, is found and demonstrated numerically.     

Structure and dielectric properties of Bi6 − x Sr x Ti2 − x Nb2 + x O18 (x = 0–2) solid solutions

The structural and electrophysical characteristics of a series of solid solutions of layered perovs-kite-like oxides Bi_{6 ? x} Sr _x Ti_{2 ? x} Nb_{2 + x} O₁₈ (x = 0, 0.25, 0.5, 1.0, 1.5, 2.0) have been studied. The temperature dependences of the relative permittivity ?/?₀(T) and dielectric loss tangent tanδ have been measured. The dependences of the maximum of the permittivity ?/?₀, Curie temperature T _C, lattice parameters, and the unit cell volume on x have been obtained. The structural parameter a, which corresponds to the polar direction, and the value of the orthorhombic distortion of the unit cell have been found to demonstrate noticeable negative deviations from the Vegard’s law. It has been established that the variations of the orthorhombic distortion correlate with the variations of the permittivity maximum; however, they do not markedly influence the Curie temperature that varies linearly over entire range of changes in x.     

The evolution of chaotic dynamics for fractional unified system

Based on reliable numerical approach, this Letter studies the chaotic behavior of the fractional unified system. The lowest orders for this system to have a complete chaotic attractor (the attractor covers the three equilibrium points of the classical unified system) at different parameter values are obtained. A striking finding is that with the increase of the parameter α of the fractional unified system from 0 to 1, the lowest order for this system to have a complete chaotic attractor monotonically decreases from 2.97 to 2.07. Because of the inherent attribute (memory effects) of fractional derivatives, this finding reveals that the chaotic behavior of fractional (classical) unified system becomes stronger and stronger when α increases from 0 to 1. Furthermore, this Letter introduces a novel measure to characterize the chaos intensity of fractional (classical) differential system.     

Magnetooptik und elektronische Struktur der magnetisch ordnenden Europiumchalkogenide

The absorption coefficient and the interband Faraday rotation of EuS, EuSe and EuTe thin films have been measured as function of the photon energy (1–6 eV), the temperature (2.7–300 K) and the applied magnetic field (0–11.5 kOe). In addition a magnetic field modulation technique has been developed, with a resolution of 2 ? 10^?4 deg. This allows the measurement of the Faraday rotation in fields of only 100 Oe, which is important for metamagnetic samples with low critical fields. A Kramers-Kronig transformation of the Faraday rotation leads to the circular dichroism and from these two quantities and the optical constants the off-diagonal elements of the conductivity tensor have been computed. From a comparison of this experimental result with values obtained from a modified atomic model, we deduce the character of the involved transitions and the spin polarization of the occupied ground states (4f ⁷,p(anion)). In addition the ratio of exchange splitting to band width of the empty 5d final state can be evaluated. The fine structure of the first main peak is discussed in terms of Kasuya's coupling scheme between the 4f ⁶ multiplett and the excited 5d electron. In the antiferromagnetic EuTe the temperature dependence of the Faraday rotation does not follow the net magnetization of the sample for all photon energies, but some transitions show a “ferromagnetic” behavior. This is interpreted in Slater's model of the magnetic Brillouin zone.