Energy principle of ferroelectric ceramics and single domain mechanical model

Many physical experiments have shown that the domain switching in a ferroelectric material is a complicated evolution process of the domain wall with the variation of stress and electric field. According to this mechanism, the volume fraction of the domain switching is introduced in the constitutive law of ferroelectric ceramic and used to study the nonlinear constitutive behavior of ferroelectric body in this paper. The principle of stationary total energy is put forward in which the basic unknown quantities are the displacement u (i) , electric displacement D (i) and volume fraction rho (I) of the domain switching for the variant I. Mechanical field equation and a new domain switching criterion are obtained from the principle of stationary total energy. The domain switching criterion proposed in this paper is an expansion and development of the energy criterion. On the basis of the domain switching criterion, a set of linear algebraic equations for the volume fraction rho (I) of domain switching is obtained, in which the coefficients of the linear algebraic equations only contain the unknown strain and electric fields. Then a single domain mechanical model is proposed in this paper. The poled ferroelectric specimen is considered as a transversely isotropic single domain. By using the partial experimental results, the hardening relation between the driving force of domain switching and the volume fraction of domain switching can be calibrated. Then the electromechanical response can be calculated on the basis of the calibrated hardening relation. The results involve the electric butterfly shaped curves of axial strain versus axial electric field, the hysteresis loops of electric displacement versus electric filed and the evolution process of the domain switching in the ferroelectric specimens under uniaxial coupled stress and electric field loading. The present theoretic prediction agrees reasonably with the experimental results given by Lynch.

A new dynamic model for study of dislocation pattern formation

Based on the principle given in nonlinear diffusion-reaction dynamics, a new dynamic model for dislocation patterning is proposed by introducing a relaxation time to the relation between dislocation density and dislocation flux. The so-called chemical potential like quantities, which appear in the model can be derived from variation principle for free energy functional of dislocated media, where the free energy density function is expressed in terms of not only the dislocation density itself but also their spatial gradients. The Linear stability analysis on the governing equations of a simple dislocation density shows that there exists an intrinsic wave number leading to bifurcation of space structure of dislocation density. At the same time, the numerical results also demonstrate the coexistence and transition between different dislocation patterns.

A consistent model of isolated force-free magnetic arches

The magnetic flux tube concentrating strong magnetic field is the basic configuration of magneticfield in the solar atmosphere. In the present paper, the equilibrium of isolated magnetic flux tube inthe solar atmosphere is discussed. In the viewpoint of mathematics, the boundary condition is nonlinearand the position of boundary needs to be determined by the physical condition although the equation ofmagnetic potential is linear for the linear force-free field. Analytical solutions to the arches of bothuniform circular cross-section and non-uniform cross section have been obtained. The results show thatthe nonlinear problem may have or not have any solution according to different azimuthal components of the magnetic field; the number of solutions to the nonlinear problem is four at most, and two in some cases. In the present paper, the analytical solutions to the approximations of both fat and slender arches are given in detail, and the general features of magnetic arch structure are shown.

Detailed model and investigation of gain saturation and carrier spatial hole burning for a semiconductor optical amplifier with gain clamping by a vertical laser field

A detailed model for semiconductor linear optical amplifiers (LOAs) with gain clamping by a vertical laser field is presented, which accounts the carrier and photon density distribution in the longitudinal direction as well as the facet reflectivity. The photon iterative method is used in the simulation with output amplified spontaneous emission spectrum in the wide band as iterative variables. The gain saturation behaviors and the noise figure are numerically simulated, and the variation of longitudinal carrier density with the input power is presented which is associated with the ON-OFF state of the vertical lasers. The results show that the LOA can have a gain spectrum clamped in a wide wavelength range and have almost the same value of noise figure as that of conventional semiconductor optical amplifiers (SOAs). Numerical results also show that an LOA can have a noise figure about 2 dB less than that of the SOA gain clamped by a distributed Bragg reflector laser.

Linear and nonlinear intersubband optical properties in a step quantum well with an applied electric field

Within the framework of the effective-mass envelope-function theory, the field-dependent intersubband optical properties of a Al0.4Ga0.6As/Al0.2Ga0.8As/GaAs step quantum well are investigated theoretically based on the periodic boundary condition. A very large Stark shift occurs when the lowest subband electron remains confined to the small well while the higher subband electron confined to the big well. The optical nonlinearity in a step well due to resonant intersubband transition (ISBT) is analyzed using a density-matrix approach. The second-harmonic generation coefficient chi(2 omega)((2)) and nonlinear optical rectification chi(0)((2)) have also been investigated theoretically. The results show that the ISBT in a step well can generate very large second order optical nonlinearities, chi(0)((2)) and chi(2 omega)((2)) can be tuned by the electric field over a wide range.

Linear polarization of photoluminescence in quantum wires

The linear character of the polarization of the luminescence in porous Si is studied experimentally, and the corresponding luminescence characteristics in quantum wires are studied theoretically using a quantum cylindrical model in the framework of the effective-mass theory. From the experimental and theoretical results it is concluded that there is a stronger linear polarization parallel to the wire direction than there is perpendicular to the wire, and that it is connected with the valence band structure in quantum confinement in two directions. The theoretical photoluminescence spectra of the parallel and perpendicular polarization directions, and the degree of polarization as functions of the radius of the wire and the temperature are obtained for In0.53Ga0.47As quantum wires and porous silicon. From the theory, we demonstrated that the degree of polarization decreases with increasing temperature and radius, and that this effect is more apparent for porous Si. The theoretical results are in good agreement with the experimental results for the InGaAs quantum wires, and in qualitative agreement with those for the porous silicon.

Entanglement dynamics and chaos in the Dicke model

We study dynamical properties of quantum entanglement in the Dicke model with and without the rotating-wave approximation. Specifically, we investigate the maximal entanglement and mean entanglement which reflect the underlying chaos in the system, and a good classical-quantum correspondence is found. We also show that the maximal linear entropy can be more sensitive to chaos than the mean linear entropy.

Simulated morphological landscape of polymer single crystals by phase-field model

The novel phase field model with the "polymer characteristic" was established based on a nonconserved spatiotemporal Ginzburg-Landau equation (TDGL model A). Especially, we relate the diffusion equation with the crystal growth faces of polymer single crystals. Namely, the diffusion equations are discretized according to the diffusion coefficient of every lattice site in various crystal growth faces and the shape of lattice is selected based on the real proportion of the unit cell dimensions.

Graft chain propagation rate coefficients of acrylic acid in melt graft copolymerization with linear low density polyethylene

Graft chain propagation rate coefficients (k(p.g)) for grafting AA onto linear low density polyethylene (LLDPE) in the melt in ESR tubes have been measured via Fourier transform infrared (FTIR) spectroscopy and electron spin resonance (ESR) spectroscopy in the temperature range from 130 to 170 degrees C. To exclude the effect of homopolymerization on the grafting. the LLDPE was pre-irradiated in the air by electron beam to generate the peroxides and then treated with iodide solution to eliminating one kind of peroxides, hydroperoxide. The monomer conversion is determined by FTIR and the chain propagation free-radical concentration is deduced from the double integration of the well-resolved ESR spectra, consisting nine lines in the melt. The temperature dependence of k(p.g) is expressed:The magnitude of k(p.g) from FTIR and ESR analysis is in good agreement with the theoretical data deduced from ethylene-AA copolymerization, suggesting this method could reliably and directly provide the propagation rate coefficient. The comparison of k(p.g) with the data extrapolated from solution polymerization at modest temperature indicates that the extrapolated data might not be entirely fitting to discuss the kinetics behavior in the melt.

Relaxation behavior of polymer blends with complex morphologies: Palierne emulsion model for uncompatibilized and compatibilized PP/PA6 blends

This paper deals with the dynamic rheological behavior of polypropylene/polyamide6 (PP/PA6) uncompatibilized blends and those compatibilized with a maleic anhydride grafted PP (PP/PP-g-MAH/PA6). The terminal relaxation times of the blends predicted by the Palierne emulsion model were compared with those obtained from experimental relaxation time spectra. The Palierne model succeeded well in describing PP/PA6 uncompatibilized blends with relatively low dispersed phase contents (10 wt%) and failed doing so for those of which the dispersed contents were high (30 wt%). It also failed for the compatibilized ones, irrespective of the dispersed phase content (10 or 30 wt%) and whether or not interface relaxation was taken into consideration. In the case of the uncompatibilized blend with high dispersed-phase content, interconnections among inclusions of the dispersed phase were responsible for the failure of the Palierne model. As for the compatiblized blends, in addition to particle interconnections, the existence of emulsion-in-emulsion (EE) structures was another factor responsible for the failure of Palieme model.

Simultaneous spectrophotometric determination of trace iron (III) and aluminum (III) with hybrid linear analysis

Hybrid linear analysis (HLA) was applied to resolution of overlapping spectra of Fe3+-salicylfluorone and Al3+-salicylfluorone complexes and simultaneous spectrophotometric determination of Fe3+ and Al3+. The absorbance matrix of 7 standard mixtures at 41 measuring points ranged from the wavelength of 550 nm to 630 nm was used for calibration. To avoid the effect of interaction between the two components on the determination, the column vector of K matrix obtained from the standard mixtures with least squares was used as the pure spectrum of component. The recoveries of the two elements for the analysis of the synthetic samples were 93.3% similar to 107.5% in the range of the concentration ratio of Fe3+:Al3+ = 10:1 to 1:8. Comparing with the partial least squares (PIS) model, the HLA method was simple, accuracy and precise.

Comparison of non-linear optical susceptibilities of KNbO3 and LiNbO3

From the chemical bond viewpoint, second-order non-linear optical (NLO) tenser coefficients of KNbO3 and LiNbO3 crystals have been calculated. By using the bond-valence theory of complex crystals and the modified bond-charge model, we were able to determine contributions of each type of constituent chemical bond to the total second-order NLO susceptibility. The tenser values thus calculated are in good agreement with experimental data. From the comparison of NLO tenser coefficients of these two crystals, we found that the major NLO contributors are KO12 groups and LiO6 octahedra not the distorted NbO6 octahedra. The difference between their NLO properties arises from their different structural characters, and the high coordination number of constituent elements in KNbO3 makes its valence electrons become more delocalised compared with those of LiNbO3. (C) 1997 Elsevier Science Ltd. All rights reserved.

Crystallization behavior of blends of high-density polyethylene with novel linear low-density polyethylene

Blends of high-density polyethylene (HDPE) with novel linear low-density polyethylene (LLDPE) samples in the whole range of compositions were investigated by means of differential scanning calorimetry (DSC), small-angle X-ray scattering (SAXS) and wide-angle X-ray diffraction (WAXD). The LLDPEs are ethylene/octene-1 copolymers prepared with a single-site catalyst, with a narrower distribution of branches compared to Ziegler-Natta type polymers. It was found that cocrystallization or separate crystallization in the blends profoundly depends on the content of branches in the LLDPE, while the critical branch content of the novel LLDPE for separate crystallization is much lower than that of commercial LLDPE (prepared with Ziegler-Natta catalysts). This implies that the miscibility of linear and branched polyethylene is also affected by the distribution of branches. The marked expansion of the unit cell in cocrystals, which are formed by HDPE with the novel LLDPE, indicates that the branches are included in the crystal lattice during the cocrystallization process. The result is very helpful to understand the phenomenon that the unit cell dimensions of commercial branched polyethylene are larger than those of linear polyethylene.

Dynamics of nonlinear error growth and season-dependent predictability of El Nino events in the Zebiak-Cane model

With the intermediate-complexity Zebiak-Cane model, we investigate the 'spring predictability barrier' (SPB) problem for El Nino events by tracing the evolution of conditional nonlinear optimal perturbation (CNOP), where CNOP is superimposed on the El Nino events and acts as the initial error with the biggest negative effect on the El Nino prediction. We show that the evolution of CNOP-type errors has obvious seasonal dependence and yields a significant SPB, with the most severe occurring in predictions made before the boreal spring in the growth phase of El Nino. The CNOP-type errors can be classified into two types: one possessing a sea-surface-temperature anomaly pattern with negative anomalies in the equatorial central-western Pacific, positive anomalies in the equatorial eastern Pacific, and a thermocline depth anomaly pattern with positive anomalies along the Equator, and another with patterns almost opposite to those of the former type. In predictions through the spring in the growth phase of El Nino, the initial error with the worst effect on the prediction tends to be the latter type of CNOP error, whereas in predictions through the spring in the decaying phase, the initial error with the biggest negative effect on the prediction is inclined to be the former type of CNOP error. Although the linear singular vector (LSV)-type errors also have patterns similar to the CNOP-type errors, they cover a more localized area than the CNOP-type errors and cause a much smaller prediction error, yielding a less significant SPB. Random errors in the initial conditions are also superimposed on El Nino events to investigate the SPB. We find that, whenever the predictions start, the random errors neither exhibit an obvious season-dependent evolution nor yield a large prediction error, and thus may not be responsible for the SPB phenomenon for El Nino events. These results suggest that the occurrence of the SPB is closely related to particular initial error patterns. The two kinds of CNOP-type error are most likely to cause a significant SPB. They have opposite signs and, consequently, opposite growth behaviours, a result which may demonstrate two dynamical mechanisms of error growth related to SPB: in one case, the errors grow in a manner similar to El Nino; in the other, the errors develop with a tendency opposite to El Nino. The two types of CNOP error may be most likely to provide the information regarding the 'sensitive area' of El Nino-Southern Oscillation (ENSO) predictions. If these types of initial error exist in realistic ENSO predictions and if a target method or a data assimilation approach can filter them, the ENSO forecast skill may be improved. Copyright (C) 2009 Royal Meteorological Society