Electrostatic contribution to the ion solvation energy: cavity effects

Ion solvation process has been analysed for the spherically symmetrical system where an ion is located inside a cavity surrounded by an isotropic nonlocal dielectric medium. It has been proven that for any dielectric properties of the medium, the electric field outside the cavity as well as the ion solvation energy depend only on the total ion charge but not of the particular distribution of the ion charge density inside the cavity. These characteristics remain unchanged if the charge is displaced from the external boundary of the cavity into it. Analytical formulas for them have been derived for a particular model of the nonlocal dielectric function. Comparison of results for the solvation energy on the basis of this new theory and of the conventional approach (disregarding the existence of the cavity) shows a significant difference between their predictions if the ion charge is displaced inside the ion cavity.     

The influence of Hall current on the rotating oscillating flows of an Oldroyd-B fluid in a porous medium

In this article, analysis is presented to study the effect of Hall current on the rotating flow of a non-Newtonian fluid in a porous medium taking into consideration the modified Darcy's law. The Oldroyd-B fluid model is used to characterize the non-Newtonian fluid behavior. The governing equations for unsteady rotating flow have been modeled in a porous medium. The analysis includes the flows induced by general periodic oscillations and elliptic harmonic oscillations of a plate. The effect of the various emerging parameters is discussed on the velocity distribution. The analytical results are confirmed mathematically by giving comparison with previous studies in the literature. It is observed that the velocity distribution increases with an increase of Hall parameter. The behavior of permeability is similar to that of the Hall parameter.     

Propagation of magnetoelastic shear waves across layers in a periodically layered medium

The paper is concerned with magnetoelastic shear waves propagating in regularly layered magnetostrictive media at a right angle to the layer interfaces __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 6, pp. 54–60, June 2006.     

Doubly nonlinear parabolic-type equations as dynamical systems

In this paper, we study a class of doubly nonlinear parabolic PDEs, where, in addition to some weak nonlinearities, also some mild nonlinearities of porous media type are allowed inside the time derivative. In order to formulate the equations as dynamical systems, some existence and uniqueness results are proved. Then the existence of a compact attractor is shown for a class of nonlinear PDEs that include doubly nonlinear porous medium-type equations. Under stronger smoothness assumptions on the nonlinearities, the finiteness of the fractal dimension of the attractor is also obtained.     

Mathematical modelling of flow through consolidated isotropic porous media

A new mathematical model is proposed for time-independent laminar flow through a rigid isotropic and consolidated porous medium of spatially varying porosity. The model is based upon volumetric averaging concepts. Explicit assumptions regarding the mean geometric properties of the porous microstructure lead to a relationship between tortuosity and porosity. Microscopic inertial effects are introduced through consideration of flow development within the pores. A momentum transport equation is derived in terms of the fluid properties, the porous medium porosity and a characteristic length of the microstructure. In the limiting cases of porosity unity and zero, the model yields the required Navier-Stokes equation for free flow and no flow in a solid, respectively.     

横观各向同性三维热弹性力学通解及其势理论法

通过引入两个位移函数，对用位移表达的运动平衡方程作了简化．利用算子理论，严格地导出了横观各向同性非耦合热弹性动力学问题的通解．对于静力学问题，通解的形式可进一步简化成用4个准调和函数来表示．具体考察了横观各向同性体内平面裂纹上下表面有对称分布温度作用的问题，推广了势理论方法，导出了一个积分方程和一个微分-积分方程．针对币状裂纹表面受均布温度作用情形，给出了具体的解。     

水相中RuCl2(TPPTS)2-(S,S)-DPENDS催化苄叉丙酮的不对称加氢反应

 将水溶性手性二胺 (S,S)-1,2-二苯基乙二胺二磺酸钠 ((S,S)-DPENDS) 与钌膦配合物 ([RuCl2(TPPTS)2]2) 原位生成的催化剂用于催化水相中苄叉丙酮的不对称加氢反应. 在优化条件下, 羰基加氢产物 4-苯基-3-丁烯-2-醇的选择性可达 96.0%, 对映选择性可达 71.2%. 经正己烷简单萃取后即可实现催化剂与加氢产物的分离, 循环使用 5 次后, 目标产物 4-苯基-3-丁烯-2-醇选择性和对映选择性没有明显下降.     

飞秒光学外差光学克尔效应和低频拉曼光谱技术研究离子液体[bmim][PF6]的低频光谱

利用飞秒光学外差光学克尔效应技术获得了咪唑类离子液体1-丁基-3-甲基咪唑六氟磷酸盐([bmim][PF6])体系中反映分子间相互作用的低频光谱. 结果分析中, 利用Brownian振子时间相关函数的精确表达式对光学克尔效应动力学数据中的核振动部分进行模拟, 在时域上获得各个振动组分的时间演化行为, 并进而通过快速Fourier变换获得各个振动组分的频域光谱和总加和光谱. 此外还利用低频拉曼光谱技术测量了离子液体[bmim][PF6]的低频光谱, 并和飞秒光学外差光学克尔效应实验的结果进行对比, 发现两种方法获得的低频光谱相近. 实验结果表明Brownian振子时间相关函数的精确表达式可用来解析离子液体体系中低频振动的时间演化行为.     

Two analytic methods applied to radiative transfer in the linear-anisotropic scattering medium with graded index and diffuse gray boundaries

The curved ray-tracing method is extended to radiative transfer in the graded index medium with diffuse gray boundary conditions instead of black boundary conditions and the pseudo-source adding method is extended to the case of the linear-anisotropic scattering medium with graded index from non-scattering medium. Furthermore, the equivalence of the two methods is verified by formulation derivation. As exact analytical solutions, both the methods have high accuracy and fast computational speed. The predicted temperature distributions and dimensionless radiative heat flux at radiative equilibrium are determined by the proposed methods, and the numerical results are compared with the data in references. The results show that the present methods have a good accuracy. Influences of various combinations of refractive index and boundary emissivities on the temperature distributions and dimensionless radiative heat flux are also investigated.     

Curved ray tracing method for one-dimensional radiative transfer in the linear-anisotropic scattering medium with graded index

The curved ray tracing method (CRT) is extended to radiative transfer in the linear-anisotropic scattering medium with graded index from non-scattering medium. In this paper, the CRT is presented to solve one-dimensional radiative transfer in the linear-anisotropic scattering gray medium with a linear refractive index and two black boundaries. The predicted temperature distributions and radiative heat flux at radiative equilibrium are determined by the proposed method, and numerical results are compared with the data in references. The results show that the CRT has a good accuracy for radiative transfer in the linear-anisotropic scattering medium with graded index and the dimensionless emissive power and dimensionless radiative heat flux depend on the dimensionless refractive index gradient. It can also be seen that the dimensionless refractive index gradient has important effects on the temperature discontinuity at the boundaries.