Dust-Cloud Structures behind a Shock Wave Moving Over a Deposited Layer of Fine Particles

The present paper investigates dispersed-phase flow structures of a dust cloud induced by a normal shock wave moving at a constant speed over a flat surface deposited with fine particles. In the shock-fitted coordinates, the general equations of dusty-gas

Kinking of an interface crack between 2 dissimilar anisotropic elastic solids

A detailed analysis of kinking of an interface crack between two dissimilar anisotropic elastic solids is presented in this paper. The branched crack is considered as a distributed dislocation. A set of the singular integral equations for the distribution function of the dislocation density is developed. Explicit formulas of the stress intensity factors and the energy release rates for the branched crack are given for orthotropic bimaterials and misoriented orthotropic bicrystals. The role of the stress parallel to the interface, sigma0 is taken into account in these formulas. The interface crack can advance either by continued extension along the interface or by kinking out of the interface into one of the adjoining materials. This competition depends on the ratio of the energy release rates for interface cracking and for kinking out of the interface and the ratio of interface toughness to substrate toughness. Throughout the paper, the influences of the inplane stress sigma0 on the stress intensity factors and the energy release rates for the branched crack, which can significantly alter the conditions for interface cracking, are emphasized.

Collapsed isoparametric element as a singular element for a crack normal to the bi-material interface

It is shown that the variable power singularity of the strain field at the crack tip can be obtained by the simple technique of collapsing quadrilateral isoparametric elements into triangular elements around the crack tip and adequately shifting the side-nodes adjacent to this crack tip. The collapsed isoparametric elements have the desired singularity at crack tip along any ray. The strain expressions for a single element have been derived and in addition to the desired power singularity, additional singularities are revealed. Numerical examples have shown that triangular elements formed by collapsing one side lead to excellent results.

Crack extension and kinking in laminates and bicrystals

Singular fields at the tip of an interface crack in anisotropic solids are reviewed with emphasis on establishing a framework to quantify fracture resistance under mixed mode conditions. The concepts of mode mixity and surface toughness are unified by using generalized interface traction components. The similarity between the anisotropic theory and existing isotropic theory is shown. Explicit formulae are given for misoriented orthotropic bimaterials with potential applications envisioned including composite laminates and semiconductor crystals. Competition between crack extension along the interface and kinking into the substrate is investigated using a boundary layer formulation. Several case studies reveal the role of anisotropy. An explicit complex variable representation for orthotropic materials and a solution to a dislocation interacting with a crack are presented in two self-contained Appendices.

Some theorems in asymptotic analysis

Basing ourselves on the analysis of magnitude of order, we strictly prove fundamental lemmas for asymptotic integral, including the cases of infinite region. Then a general formula for asymptotic expansion of integrals is given. Finally, we derive a sufficient condition for an ordinary differential equation to possess a solution of the Frobenius series type at finite irregular singularities or branching points.

Naive asymptotic expansion of the water wave generated by a slowly moving body

It is pointed out that the naive asymptotic expansion does not satisfy all the body boundary condition. A nonhomogeneous body boundary condition is obtained from this expansion. It is this condition that the additional wave term must satisfy. Moreover, because of this condition, the wave term must appear. It is pointed out that the zeroth approximation in the naive asymptotic expansion has weak singularity and the singularities become still stronger in the subsequent approximations.

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.

洛仑兹脉冲光束的复振幅包络解和复解析信号解的比较研究

使用复振幅包络表示式和复解析信号表示式推导了洛仑兹脉冲光束的传输公式．通过具体数值计算对脉冲光束的复振幅包络解和复解析信号解在不同带宽时的传输进行了对比研究．数值结果表明脉冲光束为窄带时，在传输方向轴中心的一定范围内两种解是一致的，而对于宽带脉冲光束，复振幅包络解在轴中心较近的距离即表现出奇异性，复解析信号解才是符合物理意义的表示式．由数值计算得出了选择脉冲光束研究方法的条件，并从所得公式对复振幅包络解出现奇异性的现象进行了解释．

Raman evidence for atomic correlation between the two constituent tubes in double-walled carbon nanotubes

Four well-resolved peaks with very narrow linewidths were found in the D-band and G'-band features of double-walled carbon nanotubes (DWNTs). This fact implies the occurrence of additional van Hove singularities (vHSs) in the joint density of states (JDOS) of DWNTs, which is consistent with theoretical calculations. According to their peak frequencies and theoretical analysis, the two outer peaks can be deduced to originate from a strong coupling between the two constituent tubes of commensurate DWNTs and the two inner peaks were curvature-related and assigned to originate from the two tubes with a weak coupling. This observation and elucidation constitute the first Raman evidence for atomic correlation and the resulting electronic structure change of the two constituent tubes in DWNTs. This result opens the possibility of predicting and modifying the electronic properties of DWNTs for their electronic applications.

Collective excitations in the coupled quantum wires

The dielectric response of an electron system composed of an array of parallel quantum wires with weak coupling and strong coupling are studied, and the dispersions of the collective excitations and the single particle excitations (SPE) as functions of wave-vectors are given. It is found that for the nearly isolated quantum wires with several subbands occupation, there are a series of intra-subband collective excitations between corresponding intra-subband SPE spectra. There also exist inter-subband collective excitations when q(x) not equal 0 (q(x) is the wave-vector component in the modulation direction), whose energies are close by the corresponding inter-subband SPE spectra. The energy of the intra-subband mode decreases and that of inter-subband mode increases with q(x) increasing. The collective excitation dispersions show obvious anisotropy in the 1D quantum limit. The calculated results agree with the experiment well. The coupling between quantum wires affects markedly both the collective and single-particle excitations spectra. The system changes to a near-two-dimensional electron system gradually with increasing coupling.

Observation of the resonant Raman behavior of individual single-walled carbon nanotubes

The different resonant Raman scattering process of single-walled carbon nanotubes (SWNTs) has been found between the Stokes and anti-Stokes sides of the radial breathing modes (RBMs), and this provides strong evidence that Raman spectra of some special diametric SWNTs are in resonance with their electronic transitions between the singularities in the one-dimensional electronic density of states in the valence and conduction bands, and other SWNTs axe beyond the resonant condition. Because of the coexistence of resonant and non-resonant Raman scattering processes for different diametric SWNTs, the relative intensity of each RBM does not reflect the proportion of a particular SWNT.

Topological constraints on scroll and spiral waves in excitable media

A conservation equation for topological charges of phase singularities (scroll and spiral waves) in excitable media is given. It provides some topological properties of scroll (spiral) waves: for example, the topological charge of the generated or annihilated spiral pair must be opposite. Additionally, we obtain another equation on scroll waves, which shows that singular filaments of scroll waves occur on a set of one-dimensional curves which may be either closed loops or infinite lines.

奇异性分析方法及其在储层预测中的应用研究

In research field of oil geophysical prospecting, reservoir prediction is refers to forecasting physical properties of petroleum reservoir by using data of seismic and well logging, it is a research which can guide oil field development. Singularities of seismic and logging data are caused by the heterogeneity of reservoir physical property. It's one of important methods that using singularity characteristics of seismic and logging data to study the reservoir physical property in recently. Among them, realization of reservoir quantitative prediction by analyzing singularity of the data and enhancing transition description of data is difficulty in method research. Based on wavelet transform and the fractal theory, the paper studied the singularity judgment criterion for seismic and logging data, not only analyzed quantitative relation between singularity data and reservoir physical property, but also applied it in practical reservoir prediction. The main achievements are: 1. A new method which provides singular points and their strength information estimation at only one single scale is proposed by Herrmann (1999). Based on that, the dissertation proposed modified algorithm which realized singularity polarity detection. 2. The dissertation introduced onset function to generalize the traditional geologic boundaries variations model which used singularity characteristics to represent the abruptness of the lithologic velocity transition. We show that singularity analysis reveals generic singularity information conducted from velocity or acoustic impedance to seismogram based on the convolution seismic-model theory. Theory and applications indicated that singularity information calculated from seismic data was a natural attribute for delineating stratigraphy boundaries due to its excellent ability in detecting detailed geologic features. We demonstrated that singularity analysis was a powerful tool to delineate stratigraphy boundaries and inverse acoustic impedance and velocity. 3. The geologic significances of logging data singularity information were also presented. According to our analysis, the positions of singularities indicate the sequence stratigraphic boundary, and there is subtle relationship between the singularity strength and sedimentary environment, meanwhile the singularity polarity used to recognize stratigraphic base-level cycle. Based on all those above, a new method which provided sedimentary cycle analysis based on the singularity information of logging data in multiple scales was proposed in this dissertation. This method provided a quantitative tool for judging interface of stratum sequence and achieved good results in the actual application.