Study by differential scanning calorimetry of the structure of aliphatic chains and water in Cs soaps-water systems

Summary Caesium stearate- and caesium palmitate-water systems are investigated by DSC measurements. Thermodynamical data of transition between crystallized form and mesomorphic state indicate a greater disorder of the chains for these soaps than for lecithin, in the same lamellar structure. The study of the water melting in an extended range of concentration allows us to distinguish different behaviors: the simplest two phases model for the two extremes ranges of concentration (y < 20% and > 60%) is proposed to explain the stability of the freezing temperature and enthalpy; the solubilization of conter-ions in water and the bonding of some water molecules could explain the depression of freezing temperature and the decrease of enthalpy, in the intermediate range of concentration.

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Résumé Nous avons étudié par DSC les transitions de phase dans les systemes stearate et palmitate de cesium-eau. Les parametres thermodynamiques de la fusion des chaines paraffiniques révèle que dans les phases mésomorphis le désordre des chaines est plus grand que dans les systemes lecithine-eau. L'étude de la fusion de l'eau, a l'intérieur d'une phase lamellaire bien caractérisée, nous permet de distinguer plusieurs comportements: le modele le plus simple ä deux phases permet d'interpreter la stabilité de l'enthalpie et de la température de fusion dans les deux domaines extremes de concentration en eau (y < 20% et > 60%); la solubilisation des contre ions dans l'eau et la fixation de quelques molecules d'eau pourrait expliquer l'abaissement de la température de fusion et la diminution d'enthalpie, dans le domaine intermédaire de concentration.

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With 4 figures and 1 table     

亚纯函数的波莱耳方向的分布

本文对亚纯函数的波莱耳方向的分布作了研究,主要结果为:命函数f(z)于开平面亚纯,其级ρ为有穷正数。若对于某个非负整数l,f^(l)(z)(f⁽⁰⁾ ≡f)以某值α₀(有穷或否)为亏值,则当f(z)的波莱耳方向多于一条时,必存在两条波莱耳方向,其夹角不超过π/ρ;当f(z)仅有一条波莱耳方向时,必有ρ≤1/2,     

非线性介质F－P干涉仪光束输出特性的理论研究

本文对准直光束射入含有非线性介质的Ｆ－Ｐ干涉仪内的光场分布进行了研究．由于非线性介质与光的作用，从Ｆ－Ｐ干涉仪出射的光束截面上的相移随位置的改变呈一定的分布，进而引起了干涉仪的透射率和输出光束重新分布。当干涉仪两个面的反射系数较大时，输出光束截面出现光强和相移的跃变．这种现象与以前在平面波假设下所得的光强分布所得结论有较大的不同．     

Multi-Scale Analysis of Energy Transfer in Scalar Turbulence

The energy transfer of homogeneous scalar turbulence is studied numerically by triad interaction in spectral space. The different transfer properties between turbulent kinetic energy and turbulent scalar energy reveal that non-local energy transfer exists as important as the local energy transfer in scalar turbulence. The non-local energy transfer of scalar turbulence results from non-local triad interaction. As a result there will be longer inertiaconvective range in scalar turbulence than the inertial subrange in turbulent kinetic transfer at Reλ = Peλ. The non-local transfer of turbulent scalar energy generates more energy transfer into dissipation range. The discovery of non-local transfer of turbulent scalar energy indicates that this phenomenon should be concerned carefully in numerical scheme and subgrid modelling of direct numerical simulation or large eddy simulation scalar turbulence.     

A difference scheme for a parabolic system modelling the thermoelastic contacts of two rods

In this article, we study a sequence of finite difference approximate solutions to a parabolic system, which models two dissimilar rods that each rod is fixed at one end and is free to expand or contact at the other end. A finite difference scheme is derived by the method of reduction of order on nonuniform mesh. The unique solvability, unconditional stability, and convergence of the difference scheme are proved. The convergence order is of order two in both time and space. The convergence of iterative algorithm for the difference scheme are also discussed. A numerical example is presented to demonstrate the theoretical results. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Magnetic properties of erbium iron garnet in high magnetic fields up to 150kOe

The magnetic properties of single crystals of erbium iron garnet (ErIG) were studied in applied fields up to 150kOe between 1.4 and 300K. At low temperature, the macroscopic easy direction of the bulk magnetization is [100]; below the compensation temperature (80±2K), the magnetization presents non-linear field evolution. On the assumption of an isolated ground doublet, the anisotropy constantsK _i (i=1,2) of ErIG are given byK _i (Er)+K _i (YIG); theK _i are calculated as a function of theG andg tensor components. It is worthwhile noting that theK _i (Er) are strongly temperature dependent; so at low temperature the anisotropy of the garnet is determined by the rare earth ions, while in the 50 K regionK ₁(Er) becomes comparable toK ₁(YIG) with the opposite sign which results in a very weak anisotropy of the garnet. Above 50 K,K ₁(YIG) is predominant and the Fe³⁺ ions determine the garnet anisotropy.