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.     

高亮度搪瓷交流电致发光屏的研究

本文报导了通过改进珐琅介质的介电性能,并采用特殊的灼烧工艺,获得高亮度.长寿命的搪瓷交流电致发光(AC—EL)屏的方法。     

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.     

ZnO-Bi2O3系压敏陶瓷的导电过程与等效势垒高度

研究了ZnO-Bi2O3系压敏陶瓷等效势垒高度φeff随着归一化电压的变化规律,发现等效势垒高度φeff随着归一化电压的增加先逐渐增大,达到最大值后持续下降.由于在外加电压作用下反偏势垒高度高于正偏势垒高度,等效势垒高度φeff主要取决于反偏势垒.因此,这种变化规律说明了ZnO压敏陶瓷晶界的导电过程可能存在三个阶段.在低归一化电压区,晶界区域中的电子从正偏势垒区注入到晶界无序层的速率低于电子从晶界无序层抽出到反偏势垒区的速率,从而导致等效势垒高度随着归一化电压的增加逐渐增大.在中等归一化电压区,电子从正偏势垒区注入到晶界无序层的速率和电子从晶界无序层抽出到反偏势垒区的速率相平衡,等效势垒高度达到最大值.在高归一化电压区,电子从正偏势垒区注入到晶界无序层的速率高于电子从晶界无序层抽出到反偏势垒区的速率,等效势垒高度随着归一化电压的增加逐渐下降,直至晶界击穿.同时分析了等效势垒高度φeff对泄漏电流IL的影响,发现泄漏电流与等效势垒高度差Δφ呈指数关系.     

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.     

Simulation and design of a bandpass filter on metasubstrates

This work presents an analysis of the microstrip bandpass filter on metamaterial substrates. The filter is composed of two ring resonators with quarter-wavelength side-coupled sections. The filter input is provided, as well as the output port, using a quarter-wavelength side-coupled microstrip line section. Simulations by finite element method have been carried out to verify the effect of the metamaterial substrate properties on the filter performance, and to compare these results to those obtained considering isotropic substrate.     

Mathematical modelling and numerical simulation of the morphological development of neurons

Background

The morphological development of neurons is a very complex process involving both genetic and environmental components. Mathematical modelling and numerical simulation are valuable tools in helping us unravel particular aspects of how individual neurons grow their characteristic morphologies and eventually form appropriate networks with each other.

Methods

A variety of mathematical models that consider (1) neurite initiation (2) neurite elongation (3) axon pathfinding, and (4) neurite branching and dendritic shape formation are reviewed. The different mathematical techniques employed are also described.

Results

Some comparison of modelling results with experimental data is made. A critique of different modelling techniques is given, leading to a proposal for a unified modelling environment for models of neuronal development.

Conclusion

A unified mathematical and numerical simulation framework should lead to an expansion of work on models of neuronal development, as has occurred with compartmental models of neuronal electrical activity.