Singularity criteria for perturbation series

This paper is concerned with some mathematical aspects of the Van Dyke method inperturbation theory, i.e. the singularity criteria of perturbation series. The author suggestsa sign criterion and a Domb-syke plot for the cases with complex conjugate singularities, thussucceeding in extending the conclusions of Van Dyke's. Subsequently. effects of singularitiesof the lower order upon the criteria are taken into account. In addition, a method of locat-ing singular points is developed by analysing the new perturbation series derived by the Eulertransformation.

Experiments about Simple Liquid Flows in Microtubes

The behavior of micro-scale flow is significant for the performance of Micro-Electro-Mechanical- Systems (MEMS) devices. Some experiments about liquid flow through microtubes with diameters about 3similar to20mum are presented here. The liquids used in our experiments include some simple liquids with small molecules, such as non-ion water and several kinds of organic liquids (CCL4, C6H5C2H5 and Isopropanol etc.). The flow rate and the normalized friction cocfficients were measured in micro-flow experimental apparatus. The results show that when the driven pressure varies from 0 to 1Mpa, the flow behaviors in 20mum microtube for both polar and non-polar liquids are in agreement with Hagen-Poiseuille law of the classical theory. It means that N-S equation based on continuous medium still acts well in this case. For higher pressure drop from 1 to 30Mpa, in the microtubes with diameter of 3similar to10mum, the normalized friction coefficients of organic liquids can't keep constant with pressure increases. However the non-ion water reveals different trends.

消除正弦相位调制干涉仪中光强调制影响的全光纤干涉仪

在激光二极管(LD)正弦相位调制(LD-SPM)干涉仪中,通过注入电流调制激光二极管波长的同时,光源输出的光强也被调制,成为测量误差的主要来源之一。提出一种新的消除激光二极管正弦相位调制干涉仪中光强调制影响的干涉仪,给出了具体的理论分析。该干涉仪采用全光纤结构,有效减小外界干扰对干涉测量的影响;采用容易实现的前置信号处理电路和实时相位检测器对干涉信号进行处理,消除了激光二极管光强调制产生的测量误差;同时实现了物体微小位移的高精度实时测量,测量的重复精度达到1 nm。实验结果与其他消除光强调制影响的方法测得

DIFFERENTIAL GEOMETRICAL METHODS IN THE STUDY OF OPTICAL-TRANSMISSION (SCALAR THEORY) .1. STATIC TRANSMISSION CASE

Static optical transmission is restudied by postulation of the optical path as the proper element in a three-dimensional Riemannian manifold (no torsion); this postulation can be applied to describe the light-medium interactive system. On the basis of the postulation, the behaviors of light transmitting through the medium with refractive index n are investigated, the investigation covering the realms of both geometrical optics and wave optics. The wave equation of light in static transmission is studied modally, the postulation being employed to derive the exact form of the optical field equation in a medium (in which the light is viewed as a single-component field). Correspondingly, the relationships concerning the conservation of optical fluid and the dynamic properties are given, and some simple applications of the theories mentioned are presented.

Blind image restoration based on the theory of high-dimensional space geometry

In practical situations, the causes of image blurring are often undiscovered or difficult to get known. However, traditional methods usually assume the knowledge of the blur has been known prior to the restoring process, which are not practicable for blind image restoration. A new method proposed in this paper aims exactly at blind image restoration. The restoration process is transformed into a problem of point distribution analysis in high-dimensional space. Experiments have proved that the restoration could be achieved using this method without re-knowledge of the image blur. In addition, the algorithm guarantees to be convergent and has simple computation.

Simple method for estimating minimum bend radii of SOI single mode curved rib waveguides

A simple method based on the effective index method was used to estimate the minimum bend radii of curved SOI waveguides. An analytical formula was obtained to estimate the minimum radius of curvature at which the mode becomes cut off due to the side radiative loss.

Calculation of the bulk modulus of simple and complex crystals with the chemical bond method

The relation between the lattice energies and the bulk moduli on binary inorganic crystals was studied, and the concept of lattice energy density is introduced. We find that the lattice energy densities are in good linear relation with the bulk moduli in the same type of crystals, the slopes of fitting lines for various types of crystals are related to the valence and coordination number of cations of crystals, and the empirical expression of calculated slope is obtained. From crystal structure, the calculated results are in very good agreement with the experimental values. At the same time, by means of the dielectric theory of the chemical bond and the calculating method of the lattice energy of complex crystals, the estimative method of the bulk modulus of complex crystals was established reasonably, and the calculated results are in very good agreement with the experimental values.

Calculations of cross sections of resonant two-photon transitions to the second excited 4f5d state in Pr3+: Y3Al5O12 using density matrix theory

The density matrix resonant two-photon absorption (TPA) theory applicable to laser crystals doped with rare earth ions is described. Using this theory, resonant TPA cross sections for transitions from the ground state to the second excited state of the 4f5d configuration in cm(4)s Pr3+:Y3Al5O12 are calculated. The peak value of TPA cross section calculated is 2.75 x 10(-50) cm(4)s which is very close to the previous experimental value 4 x 10(-50) cm(4) s. The good agreement of calculated data with measured values demonstrates that the density matrix resonant TPA theory can predict resonant TPA intensity much better than the standard second-order perturbation TPA theory.

APPLICATION OF ULTRAMICROELECTRODES IN STUDIES OF HOMOGENEOUS CATALYTIC REACTIONS .2. A THEORY OF QUASI-1ST AND 2ND-ORDER HOMOGENEOUS CATALYTIC REACTIONS

The analytical expressions of quasi-first and second order homogeneous catalytic reactions with different diffusion coefficients at ultramicrodisk electrodes under steady state conditions are obtained by using the reaction layer concept. The method of treatment is simple and its physical meaning is clear. The relationship between the diffusion layer, reaction layer, the electrode dimension and the kinetic rate constant at an ultramicroelectrode is discussed and the factor effect on the reaction order is described. The order of a catalytic reaction at an ultramicroelectrode under steady state conditions is related not only to C(Z)*/C(O)* but also to the kinetic rate constant and the dimension of the ultramicroelectrode; thus the order of reaction can be controlled by the dimension of the ultramicroelectrode. The steady state voltammetry of the ultramicroelectrode is one of the most simple methods available to study the kinetics of fast catalytic reactions.

A theory of nonlinear AC response in coated composites

A method for determining effective dielectric responses of Kerr-like coated nonlinear composites under the alternating current (AC) electric field is proposed by using perturbation approach. As an example, we have investigated the composite with coated cylindrical inclusions randomly embedded in a host under an external sinusoidal field with finite frequency omega. The local field and potential of composites in general consists of components with all harmonic frequencies. The effective nonlinear AC responses at all harmonics are induced by the coated nonlinear composites because of the nonlinear constitutive relation. Moreover, we have derived the formulae of effective nonlinear AC responses at the fundamental frequency and the third harmonic in the dilute limit.

中强地震震源的破裂过程

With the large developments of the seismic sources theory, computing technologies and survey instruments, we can model and rebuild the rupture process of earthquakes more realistically. On which earthquake sources' properties and tectonic activities law are realized more clearly. The researches in this domain have been done in this paper as follows. Based on the generalized ray method, expressions for displacement on the surface of a half-space due to an arbitrary oriented shear and tensile dislocation are also obtained. Kinematically, fault-normal motion is equivalent to tensile faulting. There is some evidence that such motion occurs in many earthquakes. The expressions for static displacements on the surface of a layered half-space due to static point moment tensor source are given in terms of the generalized reflection and transmission coefficient matrix method. The validity and precision of the new method is illustrated by comparing the consistency of our results with the analytical solution given by Okada's code employing same point source and homogenous half-space model. The computed vertical ground displacement using the moment tensor solution of the Lanchang_Gengma earthquake displays considerable difference with that of a double couple component .The effect of a soft layer at the top of the homogenous half-space on a shallow normal-faulting earthquake is also analyzed. Our results show that more seismic information would be obtained utilizing seismic moment tensor source and layered half-space model. The rupture process of 1999 Chi-Chi, Taiwan, earthquake investigated by using co-seismic surface displacement GPS observations and far field P-wave records. In according to the tectonic analysis and distributions of aftershock, we introduce a three-segment bending fault planes into our model. Both elastic half-space models and layered-earth models to invert the distribution of co-seismic slip along the Chi-Chi earthquake rupture. The results indicate that the shear slip model can not fit horizontal and vertical co-seismic displacements together, unless we add the fault-normal motion (tensile component) in inversions. And then, the Chi Chi earthquake rupture process was obtained by inversion using the seismograms and GPS observations. Fault normal motions determined by inversion, concentrate on the shallow northern bending fault from Fengyuan to Shuangji where the surface earthquake ruptures reveal more complexity and the developed flexural slip folding structures than the other portions of the rupture zone For understanding the perturbation of surface displacements caused by near-surface complex structures, We have taken a numeric test to synthesize and inverse the surface displacements for a pop-up structure that is composed of a main thrust and a back thrust. Our result indicates that the pop-up structure, the typical shallow complex rupture that occurred in the northern bending fault zone form Fengyuan to Shuangji, can be modeled better by a thrust fault added negative tensile component than by a simple thrust fault. We interpret the negative tensile distributions, that concentrate on the shallow northern bending fault from Fengyuan to Shuangji, as a the synthetic effect including the complexities of property and geometry of rupture. The earthquake rupture process also reveal the more spatial and temporal complexities form Fenyuan to SHuangji. According to the three-components teleseismic records, the S-wave velocity structure beneath the 59 teleseismic stations of Taiwan obtained by using the transform function method and the SA techniques. The integrated results, the 3D crustal structure of Taiwan reveal that the thickest part of crustal local in the western Central Range. This conclusion is consistent with the result form the Bouguer gravity anomaly. The orogenic evolution of Taiwan is young period, and the developing foot of Central Range dose not in static balancing. The crustal of Taiwan stays in the course of dynamic equilibrium. The rupture process of 2003)2,24,Jiashi, Xinjiang earthquake was estimated by the finite fault model using far field broadband P wave records of CDSN and IRIS. The results indicate that the earthquake focal is north dip trust fault including some left-lateral strike slip. The focal mechanism of this earthquake is different form that of earthquakes occurred in 1997 and 1998, but similar to that of 1996, Artux, Xinjiang earthquake. We interpreted that the earthquake caused trust fault due to the Tarim basin pushing northward and orogeny of Tianshan mountain. In the end, give a brief of future research subject: Building the Real Time Distribute System for rupture process of Large Earthquakes Based on Internet.