A perturbation boundary integral equation method for analysis of interaction between foundation and nonlinear rock and soil medium

A scheme is developed for analysing the interaction between a foundation and a nonlinear rock and soil medium, in which the foundation is considered as a linear elastic body and a typical boundary integral equation method (BIEM) is employed. On the basis of taking the nonlinear properties of the medium into account, a perturbation BIEM is developed. The fundamental equations for the nonlinear coupling analysis are formulated, and typical problems are solved and discussed by the present method.     

Existence and Uniqueness of the Solution of Nonlinear Population Evolution Equations

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Excitation of stable transverse wavepackets with quadratic and cubic susceptibilities

We have identified a family of (2+1)D spatial solitary waves which can stably propagate in bulk media in the presence of coexisting diffraction, self-focusing Kerr and quadratic nonlinearities. In a conspicuous range of excitation conditions close to the stationary solutions, the emerging wavepackets are immune to the detrimental occurrence of filamentation and collapse, typical of pure Kerr media. The presence of a second-order contribution to the cubic nonlinear response is, therefore, able to prevent optical damage in applications relying on self-guidance. We show that the cross-phase modulation plays an important effect on stability. Our estimate shows that the effects of the cubic susceptibility cannot be neglected below a certain beam size in realistic crystals (e.g. KTP or similar).     

Limitation of Auger electron spectroscopy in the determination of the metal-on-oxide growth mode: Pd on MgO(100)

A discussion on the use of Auger electron spectroscopy as a quantitative tool to determine the growth mode of metals on single crystal oxide surfaces is presented. In the case of Pd grown epitaxially on MgO(100), the three-dimensional character of the growth is easily seen at coverage above one monolayer. However, in the submonolayer regime, and mainly at low substrate temperatures, the AES results are ambiguous. The combination of AES with the more sensitive helium-atom diffraction method allows us to demonstrate that the growth is three-dimensional from the early stages, the particles becoming flatter when the substrate temperature decreases. We compare our results with other growth studies on different metal/oxide systems. At low temperature, the ideal growth modes are not always observed, the final morphology of the films being determined mainly by kinetic effects. Thus a pseudo-Stranski-Krastanov growth mode is often obtained with formation of 2D islands followed by 3D clustering from a critical submonolayer coverage.     

A peculiarity of diffraction measurements using a Gaussian laser beam

Numerical modelling of the Gaussian beam diffraction by a wire near the Fraunhofer limit is presented. Two cases are considered: the case of the wire being on the axis of the beam and the case of the wire being off-axis. For the case where the wire is on the axis, the displacements of the diffracted minima are calculated. For the off-axis case, the changes in the positions of the maxima and minima and the power density are calculated. The conditions are determined at which the measurements made using a Gaussian beam can be calculated using the formula for plane waves. This work arises in connection with research being performed into the Doppler spectrum of big particles.     

A NEW FIXED POINT THEOREM FOR CONE MAPS AND ITS APPLICATIONS

1IntroductionLetEbearealBanachspace.AnonemptyconvexclosedsetPCEiscalledaconeinEifitsatisfiesthefollowingtwoconditionsf(i)xEP,A20impliesAxEP,(n)xEP,--xEPimpliesx=0.AconePiscalledsolidifitcontainsinteriorpoints,i.e.,P/gi.TheconePinEdefinesapartialorderingx5…     

Ⅱ－Ⅵ族应变层超晶格的X射线衍射分析

本文报导了用计算机控制的衍射仪（ＣｕＫα辐射）测量的金属有机化学汽相沉淀（ＭＯＣＶＤ）方法生长的Ⅱ－Ⅵ族应变层超晶格的Ｘ射线衍射曲线，观察到了超晶格结构的多级卫星峰，且卫星峰的强度随角度呈周期性变化．对这种卫星峰形成包络的衍射曲线，用Ｘ射线运动学衍射理论进行了分析和讨论，这种讨论有助于理解Ｘ射线衍射曲线中卫星峰的形成．同时用光致发光和包络峰宽度的方法估算了样品的结构参数．     

Correlation integral as a tool for distinguishing between dynamics and statistics in time series data

We propose a new test for time series data for proper choice of processing technique: dynamical or statistical. It is based upon the normalized slope of the correlation integral (, m) = m⁻¹d(ln C()) /d ln , where m is the embedding dimension. It is shown that when does not tend to 0 on the resolved range of scales as m grows, then there will be serious limitations for dynamical methods even if the data are dynamical by nature. In the latter case it means that the length of time series does not allow to resolve small scales, and on large scales the delay reconstruction for any m mixes true and false neighbours of points and therefore restricts the application of dynamical techniques, such as estimating Lyapunov exponents or predicting time series.     

衍射光学元件的解析分析方法

从波动光学传播的菲涅尔衍射出发，探讨一次光学转换形成任意要求的图形的问题。导得两平行传播平面的函数关系，从而在确定像面分布的条件下可以逆求出原始面的振幅与倍相分布。文中给出了几个实例，充分表明这是有实用价值的一种衍射光学元件设计方法。     

Photoelectron diffraction study of a catalytically active overlayer: C2H2 on Pd{111}

A quantitative structure determination of a newly discovered (2×2) adsorption phase of acetylene chemisorbed on Pd{111} has been performed by scanned-energy mode photoelectron diffraction: this phase corresponds to the threshold coverage for the catalytic conversion of acetylene to benzene. The carbon atoms in the C₂H₂ molecule are located almost over bridge sites with a C–C bond length of 1.34+0.10 Å, the centre of the molecule being positioned almost over a hollow site. Of the two hollow sites the hcp site (directly above a second layer Pd atom) is favoured, particularly by a subset of the data most sensitive to this aspect of the structure, but the full analysis indicates that the fcc site (above a third layer Pd atom) cannot formally be excluded. The adsorption site adopted by acetylene in the higher coverage phase on Pd{111} is essentially identical. This is the dominant structure in the coverage regime which is catalytically active for the conversion of acetylene to benzene. The implications of these findings for acetylene coupling reactions over Pd{111} are discussed.