Asymptotic analysis based on K-S constitutive law for a rubber wedge compressed by a line load at its tip

In the present paper, a rubber wedge compressed by a line load at its tip is asymptotically analyzed using a special constitutive law proposed by Knowles and Sternberg (K-S elastic law) [J. Elasticity 3 (1973) 67]. The method of dividing sectors proposed by Gao [Theoret. Appl. Fract, Mech. 14 (1990) 219] is used. Domain near the wedge tip can be divided into one expanding sector and two narrowing sectors. Asymptotic equations of the strain-stress field near the wedge tip are derived and solved numerically. The deformation pattern near a wedge tip is completely revealed. A special case. i.e. a half space compressed by a line load is solved while the wedge angle is pi.

An In-Situ Observation On Initial Aggregation Process Of Colloidal Particles Near Three-Phase Contact Line Of Air, Water And Vertical Substrate

The self-assembling process near the three-phase contact line of air, water and vertical substrate is widely used to produce various kinds of nanostructured materials and devices. We perform an in-situ observation on the self-assembling process in the vicinity of the three phase contact line. Three kinds of aggregations, i.e. particle-particle aggregation, particle-chain aggregation and chain-chain aggregation, in the initial stage of vertical deposition process are revealed by our experiments. It is found that the particle particle aggregation and the particle-chain aggregation can be qualitatively explained by the theory of the capillary immersion force and mirror image force, while the chain-chain aggregation leaves an opening question for the further studies. The present study may provide more deep insight into the self-assembling process of colloidal particles.

The Capillary Force In Micro- And Nano-Indentation With Different Indenter Shapes

The influence of the indenter shapes and various parameters on the magnitude of the capillary force is studied on the basis of models describing the wet adhesion of indenters and substrates joined by liquid bridges. In the former, we consider several shapes, such as conical, spherical and truncated conical one with a spherical end. In the latter, the effects of the contact angle, the radius of the wetting circle, the volume of the liquid bridge, the environmental humidity, the gap between the indenter and the substrate, the conical angle, the radius of the spherical indenter, the opening angle of the spherical end in the truncated conical indenter are included. The meniscus of the bridge is described using a circular approximation, which is reasonable under some conditions. Different dependences of the capillary force on the indenter shapes and the geometric parameters are observed. The results can be applicable to the micro- and nano-indentation experiments. It shows that the measured hardness is underestimated due to the effect of the capillary force. (c) 2008 Elsevier Ltd. All rights reserved.

Compact finite difference - Fourier spectral method for three-dimensional incompressible Navier-Stokes equations

A new compact finite difference-Fourier spectral hybrid method for solving the three dimensional incompressible Navier-Stokes equations is developed in the present paper. The fifth-order upwind compact finite difference schemes for the nonlinear convection terms in the physical space, and the sixth-order center compact schemes for the derivatives in spectral space are described, respectively. The fourth-order compact schemes in a single nine-point cell for solving the Helmholtz equations satisfied by the velocities and pressure in spectral space is derived and its preconditioned conjugate gradient iteration method is studied. The treatment of pressure boundary conditions and the three dimensional non-reflecting outflow boundary conditions are presented. Application to the vortex dislocation evolution in a three dimensional wake is also reported.

Stress-distribution around a rigid line in dissimilar media

The elastic plane problem of a rigid line inclusion between two dissimilar media was considered. By solving the Riemann-Hilbert problem, the closed-form solution was obtained and the stress distribution around the rigid line was investigated. It was found that the modulus of the singular behavior of the stress remains proportional to the inverse square root of the distance from the rigid line end, but the stresses possess a pronounced oscillatory character as in the case of an interfacial crack tip.

等离子体湍流对电子的加速

本文讨论了等离子体湍流对电子加速的两种模型:（1）假定在空间中存在一个空间均匀的等离子体湍流区,当具有一定初始分布的电子束通过此湍流区时,研究湍流场对电子束的加速过程;（2）在某一封闭的区域中,存在着具有一定初始分布和空间均匀的等离子体,当某种类型的等离子体波突然传入此等离子体区,然后考察此区中电子的加速过程。在这两种模型中,可能存在着某种电子消失机制。假定湍谱是幂指数形式,我们给出了不同类型湍流扩散系数的普遍形式。利用较简单的数学方法,求解了包括消失过程的一维准线性动力学方程,对于给定的初始分布,得出了分布函数的解析解,并给出了平均能量时间关系的表达式。另外,对于特定的湍谱指数,解出了当平行电场和湍流同时存在时的分布函数。最后,对所得结果进行了数值分析和讨论。

Numerical study on heavy rigid particle motion in a plane wake flow by spectral element method

Experimental particle dispersion patterns in a plane wake flow at a high Reynolds number have been predicted numerically by discrete vortex method (Phys. Fluids A 1992; 4:2244-2251; Int. J. Multiphase Flow 2000; 26:1583-1607). To address the particle motion at a moderate Reynolds number, spectral element method is employed to provide an instantaneous wake flow field for particle dynamics equations, which are solved to make a detail classification of the patterns in relation to the Stokes and Froude numbers. It is found that particle motion features only depend on the Stokes number at a high Froude number and depend on both numbers at a low Froude number. A ratio of the Stokes number to squared Froude number is introduced and threshold values of this parameter are evaluated that delineate the different regions of particle behavior. The parameter describes approximately the gravitational settling velocity divided by the characteristic velocity of wake flow. In order to present effects of particle density but preserve rigid sphere, hollow sphere particle dynamics in the plane wake flow is investigated. The evolution of hollow particle motion patterns for the increase of equivalent particle density corresponds to that of solid particle motion patterns for the decrease of particle size. Although the thresholds change a little, the parameter can still make a good qualitative classification of particle motion patterns as the inner diameter changes.

Spectral effects for an ultrashort pulse train propagating in a two-level atom medium

We investigate the spectra of a femtosecond pulse train propagating in a resonant two-level atom (TLA) medium. it is found that higher spectral components can be produced even for a 2 pi femtosecond pulse train. Furthermore, the spectral effects depend crucially on both the relative shift phi and the delay time tau between the successive pulses of the femtosecond pulse train.

Exchange energy shifts under dense plasma conditions

The variation of the energy interval between the intercombination line ( 1s2p(P-3(1))-> 1s(2)) and the resonance line ( 1s2p(P-1(1))-> 1s(2)) of He-like aluminium with plasma density and temperature is investigated. Since such energy interval is equivalent to the exchange energy of the state 1s2p(P-3(1)), we consider the dependence of this energy shift on the plasma environment. It was found that the shifts of exchange energy increase ( decrease) with the increase of electron density ( electron temperature), and the shifts of exchange energy become more sensitive to the electron density as the electron temperature decreases, i. e. in the strongly coupled plasma regime. An approximately linear relation is found between the shifts of exchange energy and the electron density. The results show that dense plasma effects are very important for the simulation of the spectral fine structure. The relative shifts between the intercombination ( 1s2p(P-3(1))-> 1s(2)) and the resonance line ( 1s2p(P-1(1))-> 1s(2)) are discussed for diagnostic applications.

等离子体效应对类氦氖Kα线系电偶极辐射的影响

采用离子球模型，通过自洽求解Boltzmann方程和Poisson方程，得到类氦氖离子Kα线系的两条电偶极辐射光谱能量随等离子体环境的漂移．结果显示，Kα线系电偶极谱线随等离子体电子密度增大发生红移，红移量与等离子体电子密度有近似的正比关系；随着等离子体电子温度的降低，光谱红移对等离子体电子密度的敏感性增大。另外，所研究的两条谱线间的能量间隔随等离子体电子密度的增大而减小，减小量随等离子体电子密度的变化也呈现出近似的线性规律。值得注意的是，类氦氖Kα线系中两条电偶极谱线分别为互组合线与共振谱线，而其能量差

Conical emission by femtosecond pulses with different spectral bandwidths

Conical emission (CE) has been investigated experimentally by laser pulses with different pulse durations and spectral bandwidths. The results show that the overall CE curve will shift as the varying of spectral bandwidth of pump laser pulse. But for pump laser pulses which have same spectral bandwidth but different pulse duration, the CE angles will be same at the spectral region close to the pump wavelength while will be different at the spectral region far away from the pump wavelength. We have also fitted the measured CE angles with X-wave model. The calculated curves and the measured CE curves match reasonably well. The best fits indicate that the group velocity of the filament pulse may be greatly controlled by controlling the spectral bandwidth of pump laser pulse. (C) 2008 Elsevier B.V. All rights reserved.

Conical Emission Patterns by Femtosecond Pulses with Different Spectral Bandwidths

Different conical emission (CE) patterns are obtained experimentally at various incident powers and beam sizes of pump laser pulses with pulse durations of 7 fs, 44 fs and 100 fs. The results show that it is the incident power but not the incident power density that determines a certain CE pattern. In addition, the critical powers for similar CE patterns are nearly the same for the laser pulses with the same spectral bandwidth. Furthermore, as far as a certain CE pattern is concerned, the wider the spectral bandwidth of pump laser pulse is, the higher the critical power is. This will hopefully provide new insights for the generation of CE pattern in optical medium.

Spectral analysis and control to obtain sub-5 fs pulses by femtosecond filamentation

A spectral-filter method is numerically demonstrated to obtain sub-5 fs pulses by using femtosecond filamentation in fused silica. Instead of employing spectral phase compensation, by properly employing a high-pass filter to select the broadened high-frequency spectra that are located almost in phase in the tailing edge of the self-compressed pulses owing to self-steepening, as short as single-cycle pulses can be obtained. For instance, for an input pulse with a duration of 50 fs and energy 2.2 mu J, the minimum pulse duration can reach to similar to 4 fs (about 1.5 cycles) by applying a proper spectral filter. (C) 2008 Optical Society of America

Spectral evolution of angularly resolved third-order harmonic generation by infrared femtosecond laser-pulse filamentation in air

We experimentally investigate the evolution of an angularly resolved spectrum of third harmonic generated by infrared femtosecond laser pulse filamentation in air. We show that at low pump intensity, phase matching between the fundamental and third-harmonic waves dominates the nonlinear optical effect and induces a ring structure of the third-harmonic beam, whereas at high pump intensity, the dispersion properties of air begin to affect the angular spectrum, leading to the formation of a nonlinear X wave at third harmonic.