Time shift between unstable periodic orbits of coupled chaotic oscillators

The shift Δt between unstable periodic orbits of coupled oscillators occurring in the chaotic synchronization regime has been studied. It is shown that this time shift is the same for all equiphase orbits with various topological parameters and depends on the coupling parameter ε. This dependence obeys the universal power law Δt ∼ εⁿ with an exponent of n = −1.     

Sticky orbits in a kicked-oscillator model

We study a four-fold symmetric kicked-oscillator map with sawtooth kick function. For the values of the kick amplitude λ =2 cos (2π p/q) with rational p / q, the dynamics is known to be pseudochaotic, with no stochastic web of non-zero Lebesgue measure. We show that this system can be represented as a piecewise affine map of the unit square—the so-called local map—driving a lattice map. We develop a framework for the study of long-time behaviour of the orbits, in the case in which the local map features exact scaling. We apply this method to several quadratic irrational values of λ, for which the local map possesses a full Legesgue measure of periodic orbits; these are promoted to either periodic orbits or accelerator modes of the kicked-oscillator map. By constrast, the aperiodic orbits of the local map can generate various asymptotic behaviours. For some parameter values the orbits remain bounded, while others have excursions which grow logarithmically or as a power of the time. In the power-law case, we derive rigorous criteria for asymptotic scaling, governed by the largest eigenvalue of a recursion matrix. We illustrate the various behaviours by performing exact calculations with algebraic numbers; the hierarchical nature of the symbolic dynamics allows us to sample extremely long orbits with high efficiency, i.e. uniformly on a logarithmic time scale.     

Magnetic and structural phase transitions of MnBi under high magnetic fields

Abstract

High-field x-ray diffraction and magnetization measurements and differential thermal analysis (DTA) were carried out for polycrystalline MnBi with an NiAs-type hexagonal structure to investigate its magnetic and structural phase transitions. The lattice parameter a rapidly decreases below the spin reorientation temperature T_SR(=90 K) in a zero magnetic field. The parameter c decreases gradually with decreasing temperature and exhibits an anomaly in the vicinity of T_SR. By applying a magnetic field of 5 T, the parameter a increases by ～0.05% when T<T_SR and varies smoothly when 8≤T≤300 K. DTA data show that the magnetic phase transition temperature from the ferromagnetic state to the paramagnetic state increases linearly at a rate of 2 KT^?1 with increasing magnetic field up to 14 T.     

Growth of number of periodic orbits of one family of skew product maps

In this article we introduce a one-parameter family of skew product (G_t)_{t ∈ [?ε, ε]} maps exhibiting a heterodimensional cycle such that the number of isolated periodic orbits inside it has not super-exponential growth. The dynamics in the central direction of the maps G_t is described by a one-parameter family of system of iterated functions.     

Few-phonon structure functions for liquid helium II

A semiphenomenological method is formulated for calculating the Fourier transforms of the few-body distribution functions—the few-phonon liquid structure functionsS _s(q ₁,...,q _s–1)—on the basis of a functional Ansatz independent of a superposition approximation. The two-phonon functionS ₂ (q)=S(q) is calculated and compared with the experimentalS(q) to determine the parameters of the functional Ansatz. The procedure is to writeS _s in second-quantized form, to transfer from particle operatorsa _k to operators _k , and then to take expectation values with respect to the ground state |0) of the _k 's. The transformation is, fork0, a _k =(1+v _k ² )^1/2 _k +v _k ² _–k ⁺ . Fork=0, a ₀ ⁺ a₀|0) is written in terms of the othera _k 's as effectively the most general possible expression. This expression is nonlinear and involves arbitrary parametric functions subject to the restrictions that(0|a ₀ ⁺ a₀|0)=N₀, and that theS _s have the proper physical properties. Thes-body functionS _s is then expressed as a functional ofv _k , ands–1 parametric functionsc ₂,...,c_s–1 arising from the expression fora ₀ ⁺ a₀|0). The functionsc ₃, c₄,..., contribute only for smallq. A simple algebraic expression forv _k , containing only a few parameters, is found which yields agreement with experiment forS(q) to within the 10% calculational error. The relative number of particles in the zero-momentum staten ₀ , calculated as a consistency check, turns out to be equal to 0.2. Having determinedv _k andc ₂, S₃ can then be evaluated in a straight-forward manner.S ₃ is explicitly displayed as a functional ofv _k , c₂, andc ₃. It is shown thatc ₃(k, k) can be chosen so thatS ₃(s,p) has the correct known behavior for smalls.     

COMPARISON OF SHORT AND LONG FATIGUE CRACK GROWTH IN 7075-T6 ALUMINUM

The fatigue crack growth rates of physically-short cracks (0.5 ≤a≤ 1.0 mm), intermediate cracks (1 < a≤ 2 mm) and long cracks (7 < a < 25 mm) were compared using SEN type tensile specimens in 7075-T6 aluminum alloy with load ratios, R, of 0.05, ? 1 and 0.5 under constant amplitude testing at room temperature. It was found that the short cracks grew much faster than long cracks based on applied δK with da/dN≤ 10^?7 m/cycle. Even the intermediate cracks grew faster than the long cracks below 10^?7 m/cycle. The transition crack lengths where similitude with δK existed was between 1 and 2 mm. Mean stress effects were similar for R= 0.05 and ? t, but R= 0.5 caused increased crack growth rates. The above differences are partially attributed to crack closure effects. Based upon plastic zone sizes, LEFM was justifiable with all the experiments.     

Revival Hamiltonians,Phase Operators and Non-Gaussian Squeezed States

Abstract

The phase operators P ^± of the electromagnetic field, whose classical analogues are exp (? iθ), θ being the classical phase, and the number operator N associated with a harmonic oscillator mode are used to construct a class of operators T _m = N(P ^?)^m and T ⁺ _m = (P ⁺)^m N, m = 1, 2,…. It is shown that T _m, T ⁺ _m and N satisfy a simple algebra. T _m and T ⁺ _m are used to construct model Hamiltonians H _m describing the coupling of a two-level atom to a field that leads to decay and exact revivals in the atomic dynamics. In the second part of the paper, a family of unitary operators U _m is constructed in terms of T _m and T ⁺ _m. For m = 1 and m = 2 the states generated by U _m from the vacuum are non-Gaussian squeezed states. The variance properties of the squeezed states so constructed are analysed and compared with those of the Gaussian squeezed states. It is shown that the non-Gaussian squeezed states constructed in this paper have small values for the variance product that rise only logarithmically with for large values of , the mean number of quanta.     

PHOTONIC MATERIALS AND DEVICES Progress in relating rare-earth ion 4f and 5d energy levels to host bands in optical materials for hole burning,quantum information and phosphors

Rare-earth ions play an important role in modern technology as optically active elements in solid-state luminescent materials. In many of these materials, interactions between the electronic band states of the host crystal and the rare-earth ion's localized 4f ^N and 4f ^N?1 5d states influence the material's optical properties. The importance of these interactions is discussed for material applications in photon-gated hole burning, quantum information and phosphors. Material dependent trends in the relative binding energies of the 4f ^N states and the host bands have been observed and are summarized. An empirical model for the ion dependence of the 4f electron binding energies is formulated in terms of atomic number and compared with previous models. These models are extended to describe the 4f ^N?1 5d states with one additional parameter. Improved estimates for the free-ion ionization potentials used in the model are also presented and discussed.     

Polarization-independent Beam Splitter Based on Light Reflection by a Uniaxial Crystal Surface,and an Immersion Method for Determining the Crystal's Principal Refractive Indices

Abstract

Light travelling in an isotropic medium of refractive index n and incident on a uniaxial crystal whose optic axis is parallel to the surface and to the plane of incidence is reflected without a change of polarization when n = N _g = (N _o N _e)^1/2, where N _o and N _e are the crystal's ordinary and extraordinary refractive indices. This is true for all incident polarization states and at all angles of incidence and can be used to design a new polarization-independent beam splitter. For a positive uniaxial crystal (N _e > N _o), total internal reflection occurs at and above a critical angle equal to arcsin (N _o/N _e)^1/2, so that the incident light beam is deflected without attenuation or change of polarization. When n = N _g the reflectance at normal incidence for unpolarized or circularly polarized incident light is a minimum: R _0min = (N_a - N_g)/(N_a + N_g), where N _a = ½(N _o + N _e). This suggests a liquid immersion method in which n and R _0min determine N _g and N _a, hence N _o and N _e of the crystal.     

Friction and wear behaviour of β-silicon nitride–steel couples under unlubricated conditions

Abstract

The friction and wear behaviour of colloidally processed and pressureless sintered β-silicon nitride (Si₃N₄) ceramics against steel DIN Ck45K under unlubricated condition were investigated using a pin on disk tribometer. β-silicon nitride (Si₃N₄) ceramics consolidated by slip casting from suspensions with different solid loading have been studied, aiming at increasing the use of β-Si₃N₄ as cutting tools in industrial applications. The morphology of the worn surfaces of β-silicon nitride ceramics was analysed by scanning electron microscopy (SEM) and energy dispersion spectroscopy (EDS). Under the conditions used, it was found that β-Si₃N₄ ceramics exhibited a low wear rate (10^?6 mm³ N^?1 m^?1) and the frictional behaviour of β-Si₃N₄ ceramics–steel couples depended on a metallic layer transferred from the steel disk to the β-Si₃N₄ ceramic pin.     

CdSe/CdS core/shell quantum dots as sensitizer of a photorefractive polymer composite

Abstract

CdSe/CdS core/shell, tri-n-octylphosphine oxide passivated, quantum dots are used to sensitize a photorefractive polymer composite. The composite also consists of poly(N-vinylcarbazole) as the nominally charge transporting matrix and an electro-optic chromophore. The efficacy of sensitization and consequent photorefractive performance is investigated using transmission spectroscopy and ellipsometry, two-beam coupling and degenerate four-wave mixing experiments. The photorefractive nature of the photo-induced grating is confirmed by the observation of asymmetric two-beam coupling. Four-wave mixing reveals record diffraction efficiencies for a nano-particle-sensitized photorefractive polymer at the field levels applied (1.3% at 70 V.μm^?1). A recently developed analytical technique is used to extract space-charge field rise time values from degenerate four-wave mixing transients. In turn, analysis of the dependence of the rise time on applied field is used to determine the zero-field charge dissociation efficiency to be 3.6 × 10^?5 ± 0.5 × 10^?5. It is further shown that the magnitude of this parameter accounts for most of the difference in photorefractive response rate between the present material and a similar C₆₀ sensitized composite.     

A new parameter for (normalized) evaluation of H-index: countries as a case study

It is known that the H-indexes of individuals, research groups, institutions, scientific journals, and countries strongly depend on the field of study, slowly increase with the number of publications, N, and can be described by empirical power-law functions of the type H?=?C?×?N^a (C and a are constants and depend on the specific field being analyzed). In this paper, we use this function and propose a new index [Montazerian–Zanotto–Eckert (MZE)], which is normalized by the number of publications and typically varies from ??1 to +?1, to characterize the relative standing of a research group, institution, or author to those of his/her peer groups. Due to the rich statistics available, as an example, here we analyzed and tested the new parameter against the citation-related performance (H-index) of countries. We found that the MZE index readily distinguishes between countries that stand above or below the average (for any given number of publications). Generally, publications of countries with a positive MZE index are more interesting or visible than the average. Analyzing publication output in this manner instead of the H-index allows for a less biased comparison between researchers, journals, universities, or countries for any particular combination of H-index and publication output.

     

Anion conduction in fluorozirconate glasses

Fluorozirconate glasses have been prepared and their ionic conductivity measured as a function of composition and temperature. All compositions are good fluoride ion conductors with conductivities at 250°C in the 10^?6–10^?5 (Ω-cm)^?1 range and activation energies between 0.7 and 0.9 eV. The fluoride ion to metal ratio was varied in the ZrF₄/1bBaF₂/1bThF₄/1bNaF system by replacing ZrF₄and/or BaF₂ with NaF. When Na⁺ substitutes for Ba⁺² a systematic decrease in the conductivity, σ, and the activation energy, E_a, is seen. This is explained on the basis of a reduction of carriers and on the modification of the network by Na⁺ ions. No systematic variation in σ or E_a were seen when Na⁺ replaces Zr⁺⁴. A change in slope of the log σ vs 1/T plot was seen at the glass transition temperature in La-containing glasses.     

Investigation of optical damage in the nonlinear optical crystal (−)2-(α-methylbenzylamino)-5-nitropyridine

Abstract

Pulsed laser induced surface damage experiments were made on the cleaved (001) face of (—)2-(α-methylbenzylamino)-5-nitropyridine (MBANP) crystals using a pulse length of 25 ns FWHM. The highest single pulse damage threshold value was 24·2 J cm^?2 at a wavelength of 1064 nm for light polarized along the crystallographic a axis, whereas the lowest was 1·8 J cm^?2 at 532 nm for light polarized along the crystallographic b axis. The extent of the mechanical distortion of the (001) crystal plane consequent upon the absorption of a 25 ns FWHM, 10 J cm^?2 pulse from a Nd:YAG laser operating at the wavelength 1064 nm has been measured by a non-destructive and non-invasive technique.     

Comparisons of Designs and Estimation Procedures for Estimating Parameters in a Two-Stage Nested Process

For the usual two-stage nested random model, N observations are to be used to estimate some or all of these parameters: μ (the general mean), σ _a ² (the between classes variance component), σ _b ² (the within classes variance component) and ρ = σ _a ²/σ _b ² Using the traditional analysis of variance estimator, with fixed number of classes, (k), an allocation procedure to minimize the variance of the estimator is derived to estimate σ _a ² or ρ: p + 1 observations in each of r classes and p observations in each of k ? r classes, where N = pk + r, 0 ≤ r < k. The optimal number of classes (k) is conjectured to be the closest integer to

For large N, this implies that the optimal number of classes to estimate σ _a ² would be approximately k ₁ = N _ρ/(1 + ρ) with an average of 1 + ρ^?1 observations per class; the optimal number of classes to estimate ρ would be approximately Nρ/(1 + 2ρ) with an average of 2 + ρ^?1 observations per class. Hence if ρ > 1, p = 1 for σ _a ² and p = 2 for .

Investigations on the effect of using an incorrect value of ρ in k ₁ and k ₂ show that if 0.5 < ρ₁/ρ < 2.0, where ρ₁ is the value of ρ used, the loss in efficiency is generally less than 10%. Comparisons with the variances of hypothetical estimators in which k need not be an integer show that the integral requirement results in only a small loss of efficiency. Percent efficiencies of the estimates of the other parameters when a sampling plan is designed to minimize the variance of one estimator are presented for selected values of N and p.

Alternative estimators are considered for μ and σ _a ² and are found to be useful when the sampling is decidedly unbalanced and ρ is quite large. A computing procedure is developed for restricted maximum likelihood estimation of the variance components.     

Physical and mechanical properties of highly textured polycrystalline Nb4AlC3 ceramic

Abstract

Highly textured polycrystalline Nb₄AlC₃ ceramic was fabricated by slip casting in a strong magnetic field followed by spark plasma sintering. Its Lotgering orientation factor was determined on the textured top and side surfaces as f_(00l) ～1.0 and f_(hk0)=0.36, respectively. This ceramic showed layered microstructure at the scales ranging from nanometers to millimeters. The as-prepared ceramic had excellent anisotropic physical properties. Along the c-axis direction, it showed higher hardness, bending strength, and fracture toughness of 7.0 GPa, 881 MPa and 14.1 MPa m^1/2, respectively, whereas higher values of electrical conductivity (0.81×10⁶ Ω^?1 m^?1), thermal conductivity (21.20 W m^?1 K^?1) and Young’s modulus (365 GPa) were obtained along the a- or b-axis direction.     

FATIGUE CRACK GROWTH IN D16T A1-ALLOY SHEET SUBJECTED TO BIAXIAL OUT-OF-PHASE LOADING

Abstract— Fractographic peculiarities of fatigue crack development are studied in cruciform specimens of D16T aluminium alloy under out-of-phase biaxial tension and tension-compression. In the range of the biaxial load ratios λ from ?0.5 to +0.5 and an R-ratio of 0.3, fatigue striation formation took place beyond a crack growth rate near to 4 × 10^?8 m/cycle. The striation spacing and the crack growth rate increase as the φ-angle of the out-of-phase biaxial loads increases in the range of φ-angles from 0° to 180°. The ratio between the increment of crack growth, da/dN, and the striation spacing, δ, is approximately 1 to 1 when da/dN is greater than 4 × 10^?8 m/cycle. The relationship between the number of cycles from the beginning of a test up to the growth rate of 10^?6 m/cycle (N_d), and the crack growth period, N_P, from when the crack initiates up to the instant when that growth rate is reached, was determined for different λ ratios and φ angles. The value of N_d decreases as the φ angle is increased in the range from 0° to 1807deg;. Cycle loading parameters must be taken into account in order to describe the crack growth period when using a unified method that involves an equivalent stress intensity factor K_e=K_IF₁(λ, R)F₂(φ). The values of F₂(φ) were determined. The calculated fatigue crack growth period, N_c, applicable up to and including the stage of fatigue striation formation (predicted by using both of the F₁(λ, R) and F₂(φ) functions) is correlated with the experimental data and the error is of the order of 15%.     

Hot working and crystallographic texture analysis of magnesium AZ alloys

Abstract

The hot working behaviour of magnesium AZ (e.g. AZ31; Al: 3%, Zn: 1%) alloys and their associated crystallographic texture evolution is reviewed. Under hot working conditions, the stress–strain curves show flow softening at all the temperatures and strain rates indicating dynamic recrystallisation (DRX) is predominant. The mean size of the recrystallised grains in all the alloys decreases as the value of Zener–Hollomon parameter Z increases. The hot working range of the alloys dwell between 200 and 500°C and the strain rates between 10^?3 and 5 s^?1. The hot working of AZ series alloy shows discontinuous DRX as the main mechanism. Equal channel angular processing shows continuous DRX. The constitutive equation development shows a linear relationship between the stress and the Z parameter. The activation energy for the alloys ranges from 112 to 169 kJ mol^?1 and Z values range from 10 to 10 s^?1. Textural examinations show basal texture as the predominant orientation.     

Space charge limited conduction and determination of density of localised states in semiconductor cobalt doped TiO2

Abstract

The space charge limited conduction (SCLC) mechanism in Co doped TiO₂ has been investigated at different temperatures. At lower electric fields, ohmic behaviour is observed while at higher electric fields nonohmic behaviour is observed. The results obtained confirm the presence of SCLC in Co doped TiO₂. The electronic parameters such as the position of the Fermi level above the valence band edge E _F, the density of states in valence band N _V and effective mass of holes m _h were found as 12·32 meV, 1·26 × 10¹⁵ m^?3 and 1·33 × 10^?7 m_e, respectively. The distribution of localised states in the forbidden band gap of the Co doped TiO₂ was characterised by current–voltage measurements and the density of localised states near the Fermi level N(E_F) was found to be 2·11 × 10¹⁷ eV^?1 m^?3.