Viscosity solution theory of a class of nonlinear degenerate parabolic equations II. Lipschitz continuity of free boundary

In [1] we construct a unique bounded Hölder continuous viscosity solution for the nonlinear PDEs with the evolutionp-Laplacian equation and its anisotropic version as typical examples. In this part, we investigate the Lipschitz continuity of the free boundary of viscosity solution and its asymptotic spherical symmetricity, however, this result does not include the anisotropic case.This research is supported by the National Natural Sciences Foundation of China.     

On acoustic and electric waves diffraction in piezoelectric medium by a permeable half-plane crack

The problem of electric and acoustic waves diffraction by a half-plane crack in a transversal isotropic piezoelectric medium is investigated. The crack is assumed to be electric permeable and free of tractions. The so-called “quasi-hyperbolic approximation” [15] is adopted. Applying Laplace transformations and Wiener–Hopf technique a closed form solution is obtained. By the means of Cagniard–de Hoop method a detailed dynamic full electroacoustic wavefield’s investigation is conducted. Mode conversion between electric and acoustic waves, effect of electroacoustic head wave, Bleustein–Gulyaev surface wave and the wavefield structure depending on the type of the incident wave (acoustic or electric) and its angle of incidence are analyzed in details. The dynamic field intensity factors at the crack tip depending on the angle of incidence and on time are derived explicitly. Numerical analysis is presented.     

Refraction of light in media

The roles of the magnetic field and electric field of the light are investigated when the light is refracted in the medium. The model of the electron cloud conductor is presented. Electron cloud in a molecule is treated as a conductor and the Faraday’s Law is applied to this conductor that is in the alternating magnetic field of the light. dB _M/dt of the light gives rise to an alternating induced current on the electron cloud conductor, and the light exchanges energy, i.e. the refractive energy, with the electron cloud conductor. Formulas of refractive index, which is the ratio of light speed in vacuum to that in the medium, are derived with this model. These formulas are tested with several mediums and Langevin’s diamagnetic susceptibility of helium gas, and the results are in good agreement with the measured data. The anisotropy and the nonlinearity of the refractive index are explained with the theory described in this work. Supported by Beijing Science and Technology New Star Program (Grant No. 952870400), the Beijing Municipal Commission of Education and the Excellent Young Teachers Program of Ministry of Education of China     

Comparative Study on Large and Small Signal Theory for Intensity Modulation Response of Semiconductor Lasers Including Higher-Order Dispersion Terms

In this article, the comparison of large signal theory and small signal theory has been done with dispersive propagation of optical signal with IMDD (Intensity Modulation Direct Detection) systems for semiconductor lasers with higher-order dispersion terms. The expressions for an exact large signal theory and small signal theory including higher-order dispersion terms for propagation of an optical wave with sinusoidal amplitude and frequency modulation in a dispersive fiber have been derived. It is observed that small signal theory is more sensitive compared to large signal theory in terms of intensity modulation/direct detection systems. Also, it is reported that for large signal analysis the higher-order effects of dispersion can be ignored, whereas for small signal theory, the higher-order effects can be ignored for lower modulation frequencies only. The variation in the transfer function for various values of modulation indices are greater for small signal analysis than for large signal analysis. Also, as the intensity modulation index is increased, there is a decrease in the value of transfer function. The large signal model approximates the small signal model for lower values of the intensity modulation index.     

二极管激光侧泵浦单横模100Hz电光调Q激光器

介绍了二极管激光侧泵浦单横模１００Ｈｚ电光调Ｑ激光器的实验结果。泵浦源为一个线阵准连续１００Ｗ二极管激光器，激光工作介质为ＮｄＹＡＧ薄梯形板条，板条与泵浦源间用柱透镜耦合，ＫＤ＊Ｐ电光晶体调Ｑ。在１００Ｈｚ重复频率下，获得单脉冲能量２．３７ｍＪ，脉宽小于７ｎｓ，光束质量因子Ｍ２＝１．１的１．０６μｍ激光，光－光效率为８．５％，斜效率为１８．７％。     

双包层椭圆光波导解析解

解析求解了双包层椭圆光纤中的波动方程，得到了模式精确解有模式特征方程。对基模的特征方程进行了数值计算，给出了不同椭圆比下的归一化双折射和模间色散随归一化频率的变化关系曲线，并与高斯近似解的结果进行了比较。     

Effect of structural variation within cationic azo-surfactant upon photoresponsive function in aqueous solution

The cationic azo-surfactants possessing different spacers and tail alkyl chain lengths have been synthesized by azocoupling ofp-alkylaniline orop-ethoxyaniline with phenol, followed by alkylation and quaternalization with dibromoalkane and trimethylamine, respectively. These surfactants showed a good solubility in water. A reversibletrans-cis isomerization of the azosurfactants by photoirradiation was assessed by UV-Vis absorption spectra. Due to a difference in HLB between thetrans- andcis-surfactants, the observed critical micelle concentration (CMC) values and the electric conductivity of the surfactant solution at above the CMC were significantly affected by the photoinducedtrans-cis isomerization. The azo-surfactants bearing moderate alkyl chain lengths such as surfactants 6 (R₂=C₂H₄, R₃=C₄H₉) and 9 (R₂=C₄H₈, R₃=C₂H₅) were found to be effective to achieve large CMC changes (3.6 mmol/L for 6 and 5.9 mmol/L for 9) by UV-light irradiation. The replacement of the tail chain species also affected the photoresponsive function. The surfactant 12, possessingp-ethoxy group as the tail chain, was found to form a stable micelle aggregation as compared with the structurally related surfactant 10 having ethyl unit as its tail group, but it exhibited a large CMC change (5.3 mmol/L) by UV-light irradiation.     

Decentered twisted Gaussian Schell-model beams and their propagation through a misaligned first-order optical system

The propagation properties of decentered twisted Gaussian Schell-model (DTGSM) beams passing through a misaligned first-order optical system are studied. The explicit expressions for the cross-spectral density function and Wigner distribution function of the output beam are derived, which retain their form unchanged. It is shown that the DTGSM beams preserve their closed property. The second-order moments matrix and the Wigner distribution function evolve with the usual laws, whereas the first-order moments matrix varies, as if a ray passes through such system. The propagation of DTGSM beams through an aligned first-order optical system is treated as the limiting case that corresponds to the vanishing misalignment parameters.     

Stability analysis of abnormal multiplication of plankton using parameter identification technique

This paper presents the mathematical approach for the abnormal multiplication of plankton. An abnormal multiplication can be expressed as an unstable problem and the stability of the system is investigated by introducing eigenvalues of a mathematical equation. The stability of the system can be judged by an eigenvalue based on the Lyapunov's stability theory. In this paper, the Arnoldi‐QR method is used to obtain eigenvalues and eigenvectors of the system. The mode superposition method is employed to create spatial distribution needed to analyse the stability. To obtain the objective eigenvalue, the parameter identification technique is employed. The finite element method is used for the discretization in space. Lake Kasumigaura, which is located in Ibaraki Prefecture in Japan, is selected and actual data in 1975, 1976, 1991 and 2000 are used in order to investigate the stability of the specified lake in Japan. Copyright © 2004 John Wiley & Sons, Ltd.     

Geodesic Acoustic Mode in Toroidally Axisymmetric Plasmas with Non-Circular Cross Sections

The geodesic acoustic mode （GAM）, first predicted by Winsor, Johnson and Dawson in an attempt to explain some experimentally observed low frequency oscillations in stellarators, is a special electrostatic fluid mode with low mode number and coupled with the so-called geodesic curvature of a toroidally confined plasma. The recent on this mode are due to the close relevance of the stabi- lization of drift turbulence by both the zonal flow and the GAM. Previously, the GAM was illustrated in very simple geometries,