Dynamic properties,scaling and related freezing criteria of two- and three-dimensional colloidal dispersions

The static and dynamic properties of 2- and 3-dimensional dispersions of strongly interacting colloidal spheres are examined. Quasi-2-dimensional dispersions of particles interacting by long range electrostatic and dipolar magnetic forces, respectively, are investigated using Brownian dynamics computer simulations with hydrodynamic interactions included. The dynamics of 3-dimensional bulk dispersions of charge-stabilized and neutral colloidal spheres is determined from a fully self-consistent mode-coupling scheme. For systems with long range repulsive interactions the dynamic correlation functions are shown to obey dynamic scaling in terms of a characteristic relaxation time related to the mean particle distance. Hydrodynamic interactions introduce a second characteristic length scale, and they lead to more restricted scaling behaviour with an enhancement of self-diffusion and, for 2-dimensional systems, to the divergence of the short-time collective diffusion coefficient. As a consequence of dynamic scaling, a dynamic criterion for the onset of colloidal freezing related to long-time self-diffusion is shown to be equivalent to a static freezing criterion related to the 2- and 3-dimensional static structure factors. Alternative freezing criteria are given in terms of the long-time and the mean collective diffusion coefficients.     

Analytical representations for the radial distribution functions of mixtures of adhesive spheres

A study has been made of the pole topology of the Laplace transforms of the pair distribution functions (PDFs) of a binary mixture of adhesive hard spheres (AHS) both for the Percus-Yevick equation and the mean spherical model (MSM). Expressions are given that describe how the distribution of the poles in the left half of the complex plane varies with the system parameters for the special case of the MSM for symmetric binary AHS mixtures. The locations of the poles closest to the imaginary axis are known to determine the asymptotic form of the PDFs, i.e. either exponentially monotonic or exponentially oscillatory decaying. As a byproduct of this inquiry analytical r space representations of the PDFs are derived that allow their accurate and efficient determination over the entire r range.     

用长气体靶研究22Na+α共振散射

在日本东京大学CRIB 次级束装置上,用长气体靶开展了22Na+ α共振散射的厚靶实验研究。针对长气体靶实验中的两体运动学重构问题,提出了一套包括构建空间复杂几何关系、计算能量损失以及反应运动学的逐事件分析方法;对22Na+α共振散射的实验数据进行了重构分析,得到了E_c.m. = 4.2 ~ 5.4 MeV 区间22Na( α,α ) 的激发函数,从实验的激发函数中观测到了复合核26Al 5 个较为明显的共振峰。鉴于26Al 共振态的衰变模式比较复杂,本工作发现的26Al新共振态的能级性质有待进一步的理论分析。The 22Na+α resonant scattering is studied via a conventional thick target inverse kinematic method with an extended gas target. A data analysis method is proposed for the two-body reaction kinematic reconstruction, in which the spatial geometry, the reaction kinematics and the energy losses are considered. The experimental data of 22Na+ αresonant scattering have been thus reconstructed, and the excitation function is obtained in the energy interval of Ec.m. =4.2~5.4 MeV. Five resonant states in 26Al are observed in the experimental excitation function. Since several decay modes coexist for the observed 26Al resonant states, multi-channel theoretical analysis is thus needed to reveal their structure and decay features.     

二分量胶体悬浮系统的短时间动力学

研究了二分量带电粒子悬浮系统的短时间平动和转动自扩散系数.由于存在静电相互作用和流体力学作用,扩散系数与两种粒子的尺寸比,它们的体积分数,以及所带的有效电荷都有关.计入了流体力学相互作用对扩散张量的二体贡献和首项三体贡献.计算结果表明,流体力学作用对于带电粒子系统的影响要小于它对硬球粒子系统的影响.扩散系数随两种粒子的尺寸比和它们的体积分数变化的关系可以用有效硬球模型来解释,而其定性结果与实验相符合.     

ON THE COADJOINT ORBITS OF MAXIMAL UNIPOTENT SUBGROUPS OF REDUCTIVE GROUPS

Let G be a simple algebraic group defined over an algebraically closed field of characteristic 0 or a good prime for G. Let U be a maximal unipotent subgroup of G and \( \mathfrak{u} \) its Lie algebra. We prove the separability of orbit maps and the connectedness of centralizers for the coadjoint action of U on (certain quotients of) the dual \( \mathfrak{u} \)* of \( \mathfrak{u} \). This leads to a method to give a parametrization of the coadjoint orbits in terms of so-called minimal representatives which form a disjoint union of quasi-affine varieties. Moreover, we obtain an algorithm to explicitly calculate this parametrization which has been used for G of rank at most 8, except E₈.When G is defined and split over the field of q elements, for q the power of a good prime for G, this algorithmic parametrization is used to calculate the number k(U(q); \( \mathfrak{u} \)*(q)) of coadjoint orbits of U(q) on \( \mathfrak{u} \)*(q). Since k(U(q), \( \mathfrak{u} \)*(q)) coincides with the number k(U(q)) of conjugacy classes in U(q), these calculations can be viewed as an extension of the results obtained in [11]. In each case considered here there is a polynomial h(t) with integer coefficients such that for every such q we have k(U(q)) = h(q). We also explain implications of our results for a parametrization of the irreducible complex characters of U(q).     

LINEAR INSTABILITY OF THE ANNULAR HAGEN-POISEUILLE FLOW WITH SMALL INNER RADIUS BY A CHEBYSHEV PSEUDOSPECTRAL METHOD

Abstract

A new eigenvalue search procedure using the Chebyshev pseudospectral technique has been developed for the solution of the Orr-Sommerfeld equations. It can deal accurately and flexibly with various velocity profiles. The axisymmetric linear instability characteristics oflhe annular Hagen-Poiseuille Bow have been studied with this procedure. Neutral curves were obtained for 1 > R = R₁/R₀ > 0.06 where R_l is the inner radius and R₀ is the outer radius. When R = 1 which is the plane Poiseuille flow, the corresponding critical Reynolds number is 5772.22 α_r; = 1.0209. As R decreases to 0.06, the critical Reynolds number increases to 2.6 × 10₆ and the wave speed decreases to 0.0573. The wavenumber first decreases gradually from a, = 1.0209 at R = 1.0 to α _r, = 0.90 at R = 0.3. and then it increases rapidly to α _r, = 1.73 at R = 0.06.     

Structure and thermodynamic properties of a polydisperse fluid in contact with a polydisperse matrix

We present expressions that allow the determination of the structural and thermodynamic properties of a polydisperse liquid mixture in contact with a polydisperse matrix; polydispersity of the fluid and of the matrix are described by distribution functions f ^f(σ) and f m (σ), where σ and σ characterize the size of the fluid and of the matrix particles. The formalism is based on the replica trick (to describe the properties of a fluid in contact with a matrix) and on the expansion of size-dependent functions in terms of orthogonal polynomials associated with the distribution functions f _f(σ) and f _m (σ). In our expressions structural and thermodynamic properties are calculated from coefficient functions (of these expansions) which are obtained from a numerical solution of the generalized replica Ornstein-Zernike equations, solved along with a suitable closure relation.     

An efficient method for calculating the pair distribution functions of a ternary hard-sphere system in r space within the Percus-Yevick approximation

We present a direct method which allows an accurate and—at the same time—economical calculation of the pair distribution functions (PDFs) g_ij (r) of an additive ternary hard-sphere system within the Percus—Yevick approximation. The approach is based on the fact that for this approximation the Laplace transforms [?_ij (s)] of the PDFs are known analytically, so that the inversion of the ?_ij (s) into r space can be performed exactly. The expressions presented here allow the determination of the ?_ij (r) for r values up to 8R ₁, R ₁ being the diameter of the smallest species; this range in r space should be sufficient for applications in standard algorithms of liquid state theory, such as thermodynamic perturbation theories or integral-equation approaches.     

Effect of surface modification on the pore condensation of fluids: experimental results and density functional theory

The physisorption and pore condensation of a polar fluid (CHF₃) in a series of MCM-41 type mesoporous silica materials with native and chemically modified pore walls has been studied over the temperature range 168–293 K, corresponding to reduced temperatures T/T_c in the range 0.56-0.98, where T_c is the critical temperature of the fluid. Chemical modification of the pore walls by attachment of Si(CH₃)₃ groups causes a shift in pore condensation to higher relative pressures p/p0. This effect is most pronounced for materials with narrow pores (2.9 nm) at low temperatures. In the theoretical part of the work density functional theory based on a simple cubic lattice model of the confined fluid has been used to analyse the combined effect of a reduced pore width and weaker fluid-wall interaction caused by the surface coating. For realistic values of the model parameters it is found that the effect of the lower pore width is outweighed by the opposing effect of the lower fluid-wall interactions. The weaker temperature dependence of the pore existence curve observed experimentally for the surface modified materials can be traced back to a crossover from a two-step to a single-step process of pore filling predicted by the model.