Parametric excitation of waves on a free boundary of a horizontal fluid layer

We consider the dynamical stability of horizontal fluid layer, performing harmonic oscillations in vertical direction. The continued fractions approach allowed us to avoid the conventional restriction to the case of small viscosity and almost-resonant frequencies. Our numerical results cover a wide range of the parameters (viscosity, amplitude and frequency of the oscillation, and depth of the layer). To cite this article: V.I. Yudovich et al., C. R. Mecanique 332 (2004).     

Periodization of random media and representative volume element size for linear composites

Several existing numerical studies show that the effective linear properties of random composites can be accurately estimated using small volumes subjected to periodic boundary conditions – more suitable than homogeneous strain or stress boundary conditions – providing that a sufficient number of realizations are considered. Introducing the concept of periodization of random media, this Note gives a new definition of representative volume element which leads to estimates of its minimum size in agreement with existing theoretical results. A qualitative convergence criterion for the numerical simulations is proposed and illustrated with finite element computations. To cite this article: K. Sab, B. Nedjar, C. R. Mecanique 333 (2005).     

A variational approach to a micro-structured theory of solid-fluid mixtures

Summary In this paper, we present a micro-structured model for describing global deformations of heterogeneous mixtures. In particular, for a saturated solid-fluid mixture, we regard the solid volume fraction as a microstructural parameter so as to enlarge the space of admissible deformations with respect to the classical theory of mixtures. According to the variational approach, the governing equations are obtained as the stationarity of a suitable action functional. The micro-structured model is then forced to establish a second-gradient mixture theory, by introducing among the considered state parameters a suitable internal constraint. Finally, we determine under which (integrability) conditions the additional balance laws, typically employed to close the theory of porous media endowed with the volume fraction, can fit the variational framework. The authors wish to thank Prof. Francesco dell'Isola from University of Rome La Sapienza for his constructive criticism about the variational approach to continuum mechanics and the interpretation of the volume-fraction balance law.     

Pulsatile flow between permeable beds

Pulsatile flow of a viscous fluid between two permeable beds is analyzed. The flow between and through the permeable beds are governed by the Navier-Stokes equations and Darcy's law, respectively. The velocity field and the volume flux are obtained for several cases and discussed. Further, when the permeability parameter k→0, the results agree with those of Wang (J. Appl. Mech. 38 (1971) 553).     

On sums of degrees of the partial quotients in continued fraction expansions of Laurent series

For any formal Laurent series with coefficients cn lying in some given finite field, let x=[a₀(x);a₁(x),a₂(x),…] be its continued fraction expansion. It is known that, with respect to the Haar measure, almost surely, the sum of degrees of partial quotients grows linearly. In this note, we quantify the exceptional sets of points with faster growth orders than linear ones by their Hausdorff dimension, which covers an earlier result by J. Wu.     

体积差的等周不等式

首次提出并建立了凸体的体积差函数的等周不等式,它是经典等周不等式的推广.作为应用,对星体建立了体积差函数的对偶等周不等式和广义对偶等周不等式.     

光度法对不同土地利用类型河流在不同水期氮磷分布特性及定量源解析研究

氮和磷是水环境生物生长和繁殖必须的营养成分,影响水体初级生产力的水平,且水体富营养化水平与氮磷形态密切相关,随着水体环境的改变,沉积物会向水体释放氮磷,造成二次污染。同时,对外源氮磷污染来源的贡献进行定量识别,可有效管理和控制水体氮磷污染负荷。毗河和石亭江是沱江的重要支流,影响着长江母亲河的水质。采用钼锑抗分光光度法和连续提取法研究在枯水期和丰水期毗河和石亭江水体和表层沉积物中总氮(TN)、总磷(TP)及各形态氮磷的分布特性,对比不同土地利用类型河流氮磷行为特性及释放风险,并采用Multiple Linear Regression of the Absolute Principal Component Scores(APCS-MLR)受体模型进行氮磷污染源的识别和量化。研究结果表明：(1)研究区水体和表层沉积物中氮磷均处于不同程度的污染水平,水体枯水期TP的主要贡献者是颗粒态无机磷(PIP)和颗粒态有机磷(POP),而丰水期却是颗粒态无机磷(PIP)和溶解态无机磷(DIP),两水期水体中TN的主要贡献者是硝态氮(NO^-₃-N)和有机氮(ON)...     

In-situ polymerized cross-linked binder for cathode in lithium-sulfur batteries

Volume expansion and polysulfide shuttle effect are the main barriers for the commercialization of lithium-sulfur(Li-S) battery.In this work,we in-situ polymerized a cross-linked binder in sulfur cathode to solve the aforementioned problems using a facile method under mild conditions.Polycarbonate diol(PCDL),triethanolamine(TEA) and hexamethylene diisocyanate(HDI) were chosen as precursors to prepare the cross-linked binder.The in-situ polymerized binder(PTH) builds a strong network in sulfur cathode,which could restrain the volume expansion of sulfu r.Moreover,by adopting functional groups of oxygen atoms and nitrogen atoms,the binder could effectively facilitate transportation of Li-ion and adsorb polysulfide chemically.The Li-S battery with bare sulfur and carbon/sulfur composite cathodes and cross-linked PTH binder displays much better electrochemical performance than that of the battery with PVDF.The PTH-bare S cathode with a mass loading of 5.97 mg/cm^2 could deliver a capacity of 733.3 mAh/g at 0.2 C,and remained 585.5 mAh/g after 100 cycles.This in-situ polymerized binder is proved to be quite effective on restraining the volume expansion and suppressing polysulfide shuttle effect,then improving the electrochemical performance of Li-S battery.     

超短脉冲激光光束在一维反射型体全息光栅中的衍射

基于Kogelnik的耦合波理论,研究了在色散效应的影响下,超短脉冲激光光束在反射型体全息光栅中衍射的性质.研究给出了衍射光及透射光在频谱域及时间域的振幅及强度分布、光栅的光谱宽度及衍射效率随光栅参量及入射条件的变化.数值研究的结果表明,在光栅记录介质色散效应的影响下,衍射光束的光谱宽度减小,脉冲展宽,衍射效率降低.通过适当的选取光栅参量及入射条件,可以控制衍射和透射光束的频谱和时间强度分布,得到满意的衍射和透射光束的带宽和波形,从而可以将其应用于脉冲整形等技术中.     

交换半群环的分式环

设含幺交换环Ｒ对其乘法子集Ｔ的分式环为ＲＴ，交换幺半群Ｓ在其子半群∑处局部化为Ｓ∑本文证明了Ｒ［Ｓ］对于Ａ的分环式环Ｒ［Ｓ］ＡＭ 构于半群环ＲＴ［Ｓ∑］。