A Note on the Legendre Series Solution of the Biharmonic Equation for Cylindrical Problems

The solution of cylindrical problems is addressed. A series solution is considered of the biharmonic equation, in which the series terms of the stress function Φ are expressions based upon Legendre polynomials and logarithmically singular functions. An explicit form of a polynomial supplementing each logarithmically singular part of the series solution is obtained.     

An Incompressible Fluid in a Weakly Deformable Shell. Part I: Analysis of the Model

We consider the flow of a viscous incompressible fluid in a pipe when the boundary is a deformable shell of Naghdi type. We prove that the corresponding system of partial differential equations has a solution when the deformation of the shell is smooth and small enough. We propose an algorithm that uncouples the unknowns and prove its convergence.     

Nonlinear analysis of laser droplet generation by means of 0–1 test for chaos

We apply the recently improved version of the 0–1 test for chaos to real experimental time series of laser droplet generation process. In particular two marginal regimes of dripping are considered: spontaneous and forced dripping. The outcomes of the test reveal that both spontaneous and forced dripping time series can be characterized as chaotic, which coincides with the previous analysis based on nonlinear time series analysis.     

On the two methods of kinetic theory of ECRM

The kinetic theory based on the expansion of local field in the guiding center coordinate system, presented by paper[1]–[3], has successfully developed into a theoretical system. The mathematical background and physical explanation of setting up the guiding center coordinate system is expounded in the paper. By using the methods of the guiding center and waveguide coordinate systems respectively, the same dispersion equations for interaction of an axially symmetrical single momentum electron beam with TE_mn field in the circular waveguide are rigorously derived. A number of mistakes in paper[4] are indicated as well.     

Electroweak tests with τ leptons at LEP

We report on two sensitive tests of lepton universality carried out by the 4 LEP experiments at the Z⁰ pole. From measurements of the τ polarization in e⁺ e^?→τ ⁺ τ ^?, the ratios of the vector and axial vector coupling constants of the electron and the tau lepton to the weak neutral current are obtained to beg _{v e} /g _{a e} =0.066±0.015 andg _{V τ} /g _{A τ} =0.070±0.009 respectively. From measurement of the τ lifetime and the τ leptonic branching ratios, the ratio of the coupling constants describing weak leptonic decays of the τ and the μ is measured to beG _τ /G _μ =0.996±0.008.     

Standard<Emphasis Type="Italic">SU</Emphasis>(5) supergravity grand unification model and predictions

A review is given of the StandardSU(5) supergravity model. This model has passed an important check regarding unification of the electro-weak and the strong couplings using high precision LEP data. It is shown that for a significant domain of the parameter space the model also satisfies constraints on the SUSY spectrum from CDF and LEP, as well as proton stability and cosmological relic density constraints.     

Physics with large extra dimensions

The recent understanding of string theory opens the possibility that the string scale can be as low as a few TeV. The apparent weakness of gravitational interactions can then be accounted by the existence of large internal dimensions, in the sub-millimeter region. Furthermore, our world must be confined to live on a brane transverse to these large dimensions, with which it interacts only gravitationally. In my lecture, I describe briefly this scenario which gives a new theoretical framework for solving the gauge hierarchy problem and the unification of all interactions. I also discuss a minimal embedding of the standard model, gauge coupling unification and proton stability. On leave from: Centre de Physique Théorique, Ecole Polytechnique, 91128 Palaiseau, Cedex, France.     

343 nm飞秒激光制备微孔阵列以增强聚氨酯合成革透湿性

为了提高聚氨酯(PU)合成革透湿性,分别使用343 nm飞秒激光和作为对比的1030 nm飞秒激光及1064 nm纳秒激光制备微孔阵列。采用扫描电镜(SEM)和3D激光扫描显微镜对比研究了微孔形貌。结果表明,343 nm飞秒激光可以制备出效果最佳的微孔。此外,分析了3种激光与PU涂层的作用机理,揭示了343 nm飞秒激光合成革微钻孔过程仅表现为光化学烧蚀,光化学和光热烧蚀同时发生于1030 nm飞秒激光钻孔过程,而1064 nm纳秒激光只显示了光热烧蚀。激光合成革表面钻孔后,测量其透湿性和抗张力。结果显示: 微孔密度越大,皮革透湿性(WVP)越大而抗张力越低,脉冲重叠的增加会导致WVP的增加和抗张力的下降;同时,随着脉冲重叠从91.7%降到50%,微孔直径从45 μm降低到30 μm,而微孔锥度从0.7°增加到12.1°;当脉冲重叠率为91.7%,微孔密度为2550/cm²时,最大的WVP增长率为306%。