International Journal of Modern Physics B

Based on the finite difference-time domain algorithm, the factors influencing second harmonic generation in photonic crystals consisting of centro-symmetric materials are analyzed. The results show that photonic band gap is the key factor inducing the generation of second harmonic (SH). The suitable angle of incidence of pumping wave, waveguide length and fill factor will be helpful for the enhancement of SH. For the structure in this paper, when the angle of incidence is 20°–30°, SH intensity will be five times to that when the angle is nearly 90.° According to the results of our computations, the critical wave-guide length is 50 μm for the maximal intensity of SHG.

Synchronization of multiple identical chaotic systems, coupled in a ring structure, was studied in this paper. Ueda attractor was used as an example to perform the synchronization of several chaotic systems. The bound of the Ueda attractor was also estimated by numerical simulation. The above results were also adopted to design a controller to synchronize chaotic systems. The stability of the synchronization of multiple identical chaotic systems was investigated using Lyapunov's direct method. Some sufficient conditions of asymptotical synchronization were attained from rigorous mathematical theory. Further, numerical results were also demonstrated in order to validate the proposed synchronization approach.

We consider a system consisting of two multiple two-level-atom clusters simultaneously interacting with a single-mode cavity field. Entanglement of the two clusters is investigated by use of the negativity measure. We find that the entanglement can be not only induced by a thermal field but also enhanced by increasing the mean thermal photon number.

The Šil'nikov homoclinic theorem provides one analytic criterion for proving the existence of chaos in three-dimensional autonomous nonlinear systems. In applications of the theorem, however, the existence of a homoclinic orbit that usually determines the geometric structure of the chaotic attractor is not easily verified mainly because there are no available efficient methods. In this paper, based on the undetermined coefficient approach we present a framework of how to find homoclinic orbits in two classes of three-dimensional autonomous nonlinear systems of normal forms, including how to set a reasonable form of expanding series of the homoclinic orbit, how to determine all coefficients in the expansion, and how to find a numerical homoclinic orbit. Numerical examples show that the proposed framework in combination with computer simulation is very efficient.

In the present paper, we have studied the propagation of axial symmetric cylindrical surface waves through rotating cylindrical bore in a micropolar porous medium of infinite extent possessing cubic symmetry. The frequency equation for surface wave propagation in the micropolar porous medium has been derived and liquid filled bore are derived. The effect of the rotation on phase velocity of surface wave has been studied in detail. Radius of bore and other material parameters for empty and liquid filled bore are derived. A particular case of interest has been deduced. Numerical results have been obtained and illustrated graphically to understand the behavior of phase velocity versus wave number of a wave. The results have indicated that the effect of rotation on phase velocity is highly pronounced. Comparisons are made in the absence of rotation.

For second order elliptic equations with rapidly oscillating coefficients, we make some theoretical analysis for a multi-scale finite element algorithm on condition that rapidly oscillating coefficients a^ij belong to Sobolev spaces W^{1, p}(Q)(1≤p<2). Finally, we employ some numerical experiments to demonstrate those theoretical results.

High transparency and conductivity of transparent conducting oxide thin film are very important for improving the efficiency of solar cells. ZnO thin film is a better candidate for transparent conductive layer of solar cell. N-type ZnO thin films were prepared by radio-frequency magnetron sputtering on glass substrates. ZnO thin films underwent annealing treatment after deposition. The influence of the sputtering power on the surface morphology, the electrical and optical properties were studied by AFM, XRD, UV2450 and HMS-3000. The experimental results indicate that the crystal quality of ZnO thin film is improved and all films show higher c-axis orientation with increasing sputtering power from 50 to 125 W. The average transparency of ZnO thin films is higher than 90% in the range of 400–900 nm between the sputtering power of 50–100 W. After the rapid thermal annealing at 550°C for 300 s under N₂ ambient, the minimum resistivity reach to 10^-2Ω⋅cm.

[X]%BaTiO₃[100-x]%CoFe₂O₄ composites (x = 0, 20, 40, 60, 80, and 100) were prepared by the general ceramic method. X-ray diffraction patterns and IR spectra confirmed the presence of two phases beside identified phase in the composites with (x% = 40-80%BaTiO₃).

The temperature variation of conductivity was mainly attributed to change of the drift mobility rather than to the variation of charge carrier concentration. All the composites showed p-type behaviors in the range of temperature 300–400 K. For T > 400 K all composites showed n-type behavior. At this high temperature, the conduction is mainly due to Fe³⁺→Fe²⁺. Hence, there is a p–n transition.

The variation of dielectric constant as a function of temperature showed a peak value at the Curie temperature (around 390 K) of ferroelectric phase in composites. It is also noted that the phase transition temperature T_c varied for different composites.

The relation between charge carrier mobility log(μ_d) versus (1/T) is nearly linear supporting the polaron hopping model for the conduction. The activation energies calculated from resistivity and that from mobility are in close agreement indicating localized model of charge carrier.

The initial permeability increased with increasing temperature which is due to the activation of hopping electrons between Fe³⁺ and Fe²⁺ giving rise to the magnetic moment of the composites.

Two-dimensional problem is systematically investigated for the coupled equations in two-dimensional decagonal quasicrystals, and three general solutions are presented by an operator method. To simplify governing equations, each general solution shall take three different forms expressed in terms of three displacement functions, which satisfy partial three differential equations of second order. To illustrate its utility, the closed-form solutions are obtained for problems of point phonon forces and phason force acting at the apex of a quasicrystal wedge, all in terms of the general solutions. Furthermore, these solutions can be degenerated to those of problems of point forces applied on the boundary of a quasicrystal half-plane.

We derive the effective-field theory from the microscopic Hamiltonian of interacting two-dimensional (pseudo) Dirac electrons by performing a statistic gauge transformation. The quantized Hall conductance are expected to be σ_xy=e²/h(2k-1) where k is arbitrary integer. There are also topological excitations which have fractional charge and obey fractional statistics.