Relaxation-chaos phenomena in celestial mechanics. I. On wisdom's model for the 3/1 kirkwood gap

Sudden eccentricity increases of asteroidal motion in 3/1 resonance with Jupiter were discovered and explained by J. Wisdom through the occurrence of jumps in the action corresponding to the critical angle (resonant combination of the mean motions). We pursue some aspects of this mechanism, which could be termed relaxation-chaos: that is, an unconventional form of homoclinic behavior arising in perturbed integrable Hamiltonian systems for which the KAM theorem hypothesis do not hold. © 1987.

Toda and Volterra lattice equations from discrete symmetries of KP hierarchies

The discrete models of the Toda and Volterra chains are being constructed out of the continuum two-boson KP hierarchies. The main tool is the discrete symmetry preserving the Hamiltonian structure of the continuum models. The two-boson currents of KP hierarchy are being associated with sites of the corresponding chain by successive actions of discrete symmetry.

Anelastic relaxation due to OH pairs in NbZr alloys

In the last 30 years several studies have been made to understand the relaxation mechanisms of the hydrogen atoms present in transition metals and their alloys. In this work, we observed the stress-induced ordering of hydrogen atoms around the interstitial oxygen atoms near the niobium matrix atoms. We studied this relaxation process by measuring the attenuation of longitudinal ultrasonic waves. These measurements were made in Nb1.0%Zr polycrystalline alloys at 10 and 30 MHz, pure and doped with 0.7 and 4.2 at.% hydrogen. The results revealed a thermally activated relaxation structure around 202 K and 235 K for 10 MHz and 30 MHz respectively. This relaxation structure increases with increasing hydrogen concentration. © 1994.

Lattice dynamics of noble metals on effective three-body interaction

Quite recently we modified the original model of Sarkar et al. for cubic metals in extending the ion-ion interaction, ion-electron interaction and the introduction of crystal equilibrium condition. We applied our scheme to alkali metals. We studied here the lattice dynamics of noble metals on our approach by calculating phonon dispersion relations along the three principal symmetry directions, [ξ00], [ξξ00] and [ξξξ] and the (θ-T) curves of three noble metals: copper, silver and gold. We obtained reasonable agreement with the experimental findings.

Toda lattice field theories, discrete W algebras, Toda lattice hierarchies and quantum groups

In analogy with the Liouville case we study the sl3 Toda theory on the lattice and define the relevant quadratic algebra and out of it we recover the discrete W3 algebra. We define an integrable system with respect to the latter and establish the relation with the Toda lattice hierarchy. We compute the relevant continuum limits. Finally we find the quantum version of the quadratic algebra.

Uniaxial stress relaxation measurement in fluoroindate glasses

Glasses of composition 40InF3-20SrF2-16BaF2-20ZnF 2-2GdF3-2NaF (mol%) have been prepared under controlled atmosphere. The time response of the stresses under the application of a constant strain was determined by microellipsometer technique, performed in ambient atmosphere at T < Tg = 294°C. The glasses show a Newtonian behavior at small stress level. During the relaxation process, very small grooves perpendicular to the applied strain appeared on the glass surface and affected its behavior after a time. The formation of these grooves is associated with the ambient atmosphere. Measurements in dry atmosphere showed that humidity was an important parameter in the relaxation process.

Thermally activated dynamics of the tilts of the CuO6 octahedra, hopping of interstitial O, and possible instability towards the LTT phase in La2CuO4+δ

The anelastic spectrum (dynamic Young's modulus and elastic energy absorption) of La2CuO4+δ has been measured between 1 and 700 K with 0<δ<0.02. The spectrum of stoichiometric La2CuO4 in the low-temperature orthorhombic (LTO) phase is dominated by two intense relaxation processes which cause softenings of 16% around 150 K and 9% below 30 K at f∼1 kHz. The relaxation at 150 K is attributed to the presence of a fraction of the CuO6 octahedra which are able to change their tilted configuration by thermal activation between orientations which are nearly energetically equivalent, possibly within the twin boundaries. The relaxation below 30 K is governed by tunneling, and involves a considerable fraction of the lattice atoms. It is proposed that the double-well potentials for the low-temperature relaxation are created by the tendency of the LTO phase to form low-temperature tetragonal (LTT) domains, which however are not stabilized like when La is partially substituted with Ba. On doping with excess O, the relaxation rates of these processes are initially enhanced by hole doping, while their intensities are depressed by lattice disorder; an explanation of this behavior is provided. Excess O also causes two additional relaxation processes. The one appearing at lower values of δ is attributed to the hopping of single interstitial O2- ions, with a hopping rate equal to τ-1=2×10-14exp(-5600/T) s. The second process is slower and can be due to O pairs or other complexes containing excess O.

Vortex lattice and matching fields for a long superconducting wire

We investigate the flux penetration patterns and matching fields of a long cylindrical wire of circular cross section in the presence of an external magnetic field. For this study we write the London theory for a long cylinder both for the mixed and Meissner states, with boundary conditions appropriate for this geometry. Using the Monte Carlo simulated annealing method, the free energy of the mixed state is minimized with respect to the vortex position and we obtain the ground state of the vortex lattice for N=3 up to 18 vortices. The free energy of the Meissner and mixed states provides expressions for the matching fields. We find that, as in the case of samples of different geometry, the finite-size effect provokes a delay on the vortex penetration and a vortex accumulation in the center of the sample. The vortex patterns obtained are in good agreement with experimental results.

Lattice dynamics of metallic glass Ca70Mg30 on the model of Bhatia and Singh

The lattice dynamical studies of the metallic glass Ca70Mg30 by Bhatia and Singh on their model contained two shortcomings, firstly the electron-ion interaction matrix was wrong and secondly, the numerical value of the bulk modulus of the electron gas was accepted arbitrarily. By modifying the electron-ion dynamical matrix and determining all the model parameters from the experimental data, we made a fresh study of the lattice dynamics of Ca70Mg30 and compared it to the earlier studies of Bhatia and Singh and also with experimental phonons.

Relaxation effects on the negatively charged Mg impurity in zincblende GaN

The electronic structure of Mg impurity in zincblende (c-)GaN is investigated by using the ab initio full potential linear-augmented plane-wave method and the local density-functional approximation. Full geometry optimization calculations, including nearest and next-nearest neighbor displacements, are performed for the impurity in the neutral and negatively charged states. A value of 190 ± 10 meV was obtained for the Franck-Condon shift to the thermal energy, which is in good agreement with that observed in recent low temperature photoluminescence and Hall-effect measurements. We conclude that the nearest and next-nearest neighbors of the Mg impurity replacing Ga in C-GaN undergo outward relaxations which play an important role in the determination of the center acceptor energies.

Lattice constellations and codes from quadratic number fields

We propose new classes of linear codes over integer rings of quadratic extensions of Q, the field of rational numbers. The codes are considered with respect to a Mannheim metric, which is a Manhattan metric modulo a two-dimensional (2-D) grid. In particular, codes over Gaussian integers and Eisenstein-Jacobi integers are extensively studied. Decoding algorithms are proposed for these codes when up to two coordinates of a transmitted code vector are affected by errors of arbitrary Mannheim weight. Moreover, we show that the proposed codes are maximum-distance separable (MDS), with respect to the Hamming distance. The practical interest in such Mannheim-metric codes is their use in coded modulation schemes based on quadrature amplitude modulation (QAM)-type constellations, for which neither the Hamming nor the Lee metric is appropriate.

Effect of barium titanate seed particles on the sintering and lattice parameters in PbMg1/3Nb2/3O3 ceramics

PbMg1/3Nb2/3O3 (PMN) powder was prepared by citrate organic solution, and barium titanate (BT) seed particles were added to encourage the perovskite phase formation. Sintering was followed using the constant heating rate mode of a dilatometer, and it was observed that the seed concentration affected the PMN shrinkage rate and crystal structure. The study of the lattice parameters of the samples after the sintering process indicates that the diffusion of the titanium and of the barium inside perovskite and pyrochlore PMN phases occurs. Moreover, this substitution provoked a decrease of the lattice parameters as showed by the Rietveld refinement.

Light-induced electric dipole relaxation in synthetic and natural alexandrite

We present results of thermally stimulated depolarization current (TSDC) measurements in synthetic and natural alexandrite, which show TSDC bands related to the presence of electric dipoles in both types of samples. Synthetic material shows a wide TSDC band with a peak at 179 K, which can be fitted by two distinct relaxing dipole distributions. For natural alexandrite the TSDC band has a maximum around 195 K and can be fitted by three different distributions. Both samples present one of the calculated curves with a peak about 179 K, with activation energy of 0.57 eV and constant relaxation time of 1 × 10-14 sec. Photo-induced TSDC shows that TSDC bands can also be generated by simultaneous application of light and an electric field at 77 K.

Effects of thermal treatment on phase transitions and on the mechanical relaxation in poly(vinylidene fluoride)

This work reports on the effects from thermal treatment in poly(vinylidene fluoride), PVDF, obtained with differential scanning calorimetry (DSC) and dynamic thermal analysis (DMA) measurements. It is shown that in successive DMA measurements performed with one sample the α relaxation peak almost disappears while the γ′ peak appears. The α relaxation peak, at ∼100°C in DMA measurements, is attributed to the preferential orientation of chains in the amorphous phase while the γ′ relaxation peak, at ∼50°C, is related to the thermal treatment to which the sample was submitted.

Transparent Er3+-activated lead fluorogermanate glass ceramics

Transparent glass ceramics containing β-PbF2:Er 3+ nanocrystals were obtained through appropriate thermal treatments of a glass of molar composition 60PbGeO3-10PbF2-30CdF 2 doped with 0.5 mol% Er3+. Their optical properties, as well as upconversion processes among erbium ions in the glass and glass ceramic matrix were studied. From absorption spectra, Judd-Ofelt parameters and radiative transition rates for several excited levels were calculated. Emission spectra in the visible and NIR regions were collected, and stimulated emission cross sections were obtained by McCumber theory for the 4F 13/2→4I15/2 transition at 1.5 μm. Red and green upconversion emissions were measured in glass and glass ceramics upon excitation at 980 nm; lifetimes were measured in order to assess the upconversion mechanisms.