High index of refraction via quantum interference in a three-level system of Er^3＋-doped yttrium aluminium garnet crystal

A simple three-level system is proposed to produce high index of refraction with zero absorption in an Er^3＋-doped yttrium aluminium garnet （YAG） crystal, which is achieved for a probe field between the excited state 4I13/2 and ground state 4I15/2 by adjusting a strong coherent driving field between the upper excited state 4I11/2 and 4I15/2. It is found that the changes of the frequency of the coherent driving field and the concentration of Er^3＋ ions in the YAG crystal can maximize the index of refraction accompanied by vanishing absorption. This result could be useful for the dispersion compensation in fibre communication, laser particle acceleration, high precision magnetometry and so on.     

Optimization of the surface texture for silicon carbide sliding in water

Surface texturing has been recognized as an effective means to improve the tribological performances of sliding surfaces. Usually, generation additional hydrodynamic pressure to increase the load carrying capacity is regarded as the most significant effect of surface texture. In the case of silicon carbide sliding against identical material in water, the experimental results indicate that surface texture is also helpful to improve the running-in progress to smooth the contact surfaces, showing another reason to result in low friction. Based on the consideration of enhancing the generation of hydrodynamic pressure and improving running-in progress, a surface texture pattern, which was combined with large (circle, 350 μm in diameter) and small (rectangular, 40 μm in length) dimples, was designed to maximize the texture effect on the load carrying capacity of SiC surfaces sliding in water. The friction coefficient of such textured surface was evaluated and compared with that of untextured and those only with large or small dimples only. The friction reduction mechanisms of the patterns with different dimples in size are discussed.     

Dielectric and optical properties of polymer-liquid crystal composite

Dielectric properties of polymer-liquid crystal mixture, having constituent polymer, poly-butyl methacrylate (PBMA) and liquid crystal, cholesteryl nonanoate, are reported as a function of frequency and temperature. The measurement has been done in a temperature range of 300-375 K and frequency range of 100 Hz-10 MHz. The dielectric permittivity and dielectric loss shows significant changes with the addition of polymer molecules in liquid crystal. The significant feature of composite formation is that the pure liquid crystal and polymer do not show dielectric relaxation in the frequency range covered, while the composite shows relaxation peak at a particular frequency. The optical transmittance of pure liquid crystal and composite has also been measured and compared.     

Stability of chirped bright and dark soliton-like solutions of the cubic complex Ginzburg-Landau equation with variable coefficients

We consider an inhomogeneous optical fiber system described by the generalized cubic complex Ginzburg-Landau (CGL) equation with varying dispersion, nonlinearity, gain (loss), nonlinear gain (absorption) and the effect of spectral limitation. Exact chirped bright and dark soliton-like solutions of the CGL equation were found by using a suitable ansatz. Furthermore, we analyze the features of the solitons and consider the problem of stability of these soliton-like solutions under finite initial perturbations. It is shown by extensive numerical simulations that both bright and dark soliton-like solutions are stable in an inhomogeneous fiber system. Finally, the interaction between two chirped bright and dark soliton-like pulses is investigated numerically.     

The destabilizing effect of boundary slip on Bénard convection

We investigate the influence of slip boundary conditions on the onset of Bénard convection in an infinite fluid layer. It is shown that the critical Rayleigh number is a decreasing function of the slip length, and therefore boundary slip is seen to have a destabilizing effect. Chebyshev‐tau and compound matrix formulations for solving the eigenvalue problem are presented. Copyright © 2005 John Wiley & Sons, Ltd.     

Isotopic families of contact manifolds for elliptic PDE

A test for a function to be a solution of an elliptic PDE is given in terms of extensions, as solutions, from the boundaries inside the domains belonging to an isotopic family. It generalizes a result of Ehrenpreis for spheres moved along a straight line.

     

The Chang-Łoś-Suszko theorem in a topological setting

The Chang-Łoś-Suszko theorem of first-order model theory characterizes universal-existential classes of models as just those elementary classes that are closed under unions of chains. This theorem can then be used to equate two model-theoretic closure conditions for elementary classes; namely unions of chains and existential substructures. In the present paper we prove a topological analogue and indicate some applications.     

Study of asymmetric charge writing on Pb(Zr,Ti)O3 thin films by Kelvin probe force microscopy

Polycrystalline Pb(Zr_0.55Ti_0.45)O₃ thin film was deposited on Pt/Ti/SiO₂/Si(1 0 0) by radio-frequency-magnetron sputtering method, and the writing of charge bits on the surface of PZT thin film was studied by Kelvin probe force microscopy. It is found that the surface potential of the negative charge bits are higher than those of the corresponding positive ones. When ferroelectric polarization switching occurs, the potential difference becomes even more remarkable. A qualitative model was proposed to explain the origin of the asymmetric charge writing. It is demonstrated that the internal field in the interface layer, which is near the ferroelectric/electrode interface in ferroelectric film, is likely to be the cause for the occurrence of this phenomenon.     

EXISTENCE OF PERIODIC SOLUTIONS OF SYSTEM OF DIFFERENCE EQUATIONS

This paper studies the nonautonomous nonlinear system of difference equationsΔx(n)=A(n)x(n)+f(n,x(n)),n∈Z,(*) where x(n)∈R~N,A(n)=(a_(ij)(n))N×N is an N×N matrix,with a-(ij)∈C(R,R) for i,j= 1,2,3,...,N,and f=(f_1,f_2,...,f_N)~T∈C(R×R~N,R~N),satisfying A(t+ω)=A(t),f(t+ω,z)=f(t,z) for any t∈R,(t,z)∈R×R~N andωis a positive integer.Sufficient conditions for the existence ofω-periodic solutions to equations (*) are obtained.     

Experimental intensity patterns obtained from a 2D shearing interferometer with adaptable sensitivity

The interferometric intensity patterns from a 2D shearing interferometer are shown and discussed. The intensity patterns can be obtained in two different approaches incorporating differential and extended wavefront controlled displacements. The reliable directional sensitivity of this interferometer allows the optimization of the measurement parameters to estimate the wavefront of the intensity patterns by regularization techniques.