Capillary surfaces in a cone

We show that a capillary surface in a solid cone, that is, a surface that has constant mean curvature and for which the surface boundary meets the boundary of the cone at a constant angle, is radially graphical if the mean curvature is non-positive with respect to the Gauss map pointing towards the domain bounded by the surface and the boundary of the cone. In the particular case in which the cone is circular, we prove that the surface is a spherical cap or a planar disc. The proofs are based on an extension of the Alexandrov reflection method using inversions about spheres.     

High order numerical approximation of minimal surfaces

We present an algorithm for finding high order numerical approximations of minimal surfaces with a fixed boundary. The algorithm employs parametrization by high order polynomials and a linearization of the weak formulation of the Laplace–Beltrami operator to arrive at an iterative procedure to evolve from a given initial surface to the final minimal surface. For the steady state solution we measure the approximation error in a few cases where the exact solution is known. In the framework of parametric interpolation, the choice of interpolation points (mesh nodes) is directly affecting the approximation error, and we discuss how to best update the mesh on the evolutionary surface such that the parametrization remains smooth. In our test cases we may achieve exponential convergence in the approximation of the minimal surface as the polynomial degree increases, but the rate of convergence greatly differs with different choices of mesh update algorithms. The present work is also of relevance to high order numerical approximation of fluid flow problems involving free surfaces.     

Cu 表面性质的第一性原理分析

采用第一性原理赝势平面波方法, 计算并详细分析了面心立方Cu晶体及其 (100), (110) 和 (111) 这3个低指数表面的原子结构、 表面能量及表面电子态密度. 表面能的计算结果表明, Cu (111) 表面的结构稳定性最好, Cu (100) 表面次之, Cu (110)表面的结构稳定性最差. 3个表面的表面原子弛豫量随着层数的增加而逐渐减弱. Cu (110) 表面的最表层原子相对收缩最大, Cu (100)表面次之, Cu (111) 表面的最表层原子相对收缩最小. 表面原子弛豫不仅引起表面几何结构的变化, 而且使表面层原子的电子态密度峰形相对晶体内部发生变化, 这是表面能产生的主要原因, 而Cu (110)表面相对于Cu (100)与Cu (111)表面具有高表面活性的主要原因则源于其表面层原子电子态密度在高能级处的波峰相对晶体内部显著的升高. 关键词： Cu 晶体 表面结构 表面能 态密度     

驻波激光场中囚禁离子内外自由度熵的演化特性

从描述囚禁离子与驻波激光场相互作用的Jaynes-Cummings（J-C）模型出发,导出了囚禁离子谐振动单量子共振激发相互作用的非线性J-C模型。通过求解这一模型下系统态和离子系统熵的演化规律,数值研究了囚禁离子的熵演化与Lamb-Dick参数  、离子在驻波激光场中的位置以及初始声子强度之间的关系。结果表明,离子熵的演化呈现非周期性的振荡。随着参数  的增大,囚禁离子熵演化的振荡频率变大,囚禁离子内外自由度退纠缠的时间变短。当离子质心的位置从驻波激光场的波节移向波腹,囚禁离子熵演化的振荡频率变小,离子与声子自由度退纠缠的时间变长。如果初始声子场强度较小,离子熵随时间的演化强烈地表现为不规则的振荡,且振荡频率较大;随着初始声子场强度变大,离子熵的演化类似于J-C模型中的场熵演化,不规则的振荡频率逐渐变小。     

Inequalities for the Casorati Curvature of Totally Real Spacelike Submanifolds in Statistical Manifolds of Type Para-Kähler Space Forms

The purpose of this article is to establish some inequalities concerning the normalized δ-Casorati curvatures (extrinsic invariants) and the scalar curvature (intrinsic invariant) of totally real spacelike submanifolds in statistical manifolds of the type para-Kähler space form. Moreover, this study is focused on the equality cases in these inequalities. Some examples are also provided.     

The role of reconstruction in self-assembly of alkylthiolate monolayers on coinage metal surfaces

Through a combination of standard laboratory-based surface science methods, together with synchrotron radiation-based normal incidence X-ray standing wave (NIXSW) experiments, the interface structure of simple alkylthiolate ‘self-assembled monolayers’ on Cu(1 1 1), Ag(1 1 1) and Au(1 1 1) has been investigated over the last ∼15 years. A key conclusion is that in all cases the adsorbate produces a substantial, density-lowering, reconstruction of the outermost metal layer, although the nature of these reconstructions is quite different on the three metals. The main results of these investigations are briefly reviewed and contrasted.     

On the role of electron-hole pair excitation in the kinetics of atom recombination at metal surfaces

The dynamics of energy relaxation of the adspecies in exoergic processes at metal surfaces has been modeled by means of the master equation approach. The effect of energy disposal to the solid via electron-hole (e-h) pair excitation on the rate of adatom recombination, has been investigated in the case of a discrete set of vibrational levels of the adspecies. The kinetics is solved, analytically, for two recombination channels and by taking into account two energy dissipation pathways of the adspecies. It is shown that dissipation pathways, characterized by a sizable energy transfer per scattering event, affect the kinetics leading to enhanced recombination rates. The kinetic model has been applied to describe experimental data on H(D)-adatom abstraction and recombination at metal surfaces. The rate coefficient of the process is shown to be proportional to the energy power transferred to the solid, owing to the reaction exothermicity, and correlates to the surface electron density.     

Atomic force microscopy analysis of wool fibre surfaces in air and under water

Wool fibre surfaces have been treated by solvent cleaning which leaves the native covalently bound surface lipid layer intact, and by alcoholic alkali which removes the lipid layer. The resultant surfaces have been analysed by atomic force microscopy (AFM), with particular emphasis on force–distance (F–d) methods. Methodologies were developed for investigation in situ in water of both the surface topography and the characteristics of the lipid layer. Longitudinal surface texturing was resolved in images of wool fibre surfaces in air; the texturing remained prominent after exposure to water. High resolution F–d curves revealed features associated with the lipid layer. A simple formalism was used to show that the layer had a thickness of a few nm, and an effective stiffness of some 0.12±0.01 N/m. Strong adhesive interactions, equivalent to a pressure of 0.1 MPa, acted on the tip at the tip-to-substrate interface. The methodology and formalism are likely to be relevant in the broad field of thin-film analysis and for fibre technology.     

Adatom lifetime in film growth at solid surfaces in the framework of the Johnson–Mehl–Avrami–Kolmogorov model

On the basis of the quasi-static approximation and for simultaneous nucleation the adatom lifetime, τ, during film growth at solid surfaces has been computed by Monte Carlo (MC) simulation. The quantity DN₀τ, N₀ and D being respectively the cluster density and the adatom diffusion coefficient, is found to depend upon the portion of surface covered by clusters and, very weakly, on N₀. Moreover, a stochastic approach based on the Johnson–Mehl–Avrami–Kolmogorov (JMAK) theory has been developed to obtain the analytical expression of the MC curve. The collision factor of the mean island has been calculated and compared with those previously obtained from the uniform depletion approximation and the lattice approximation.     

粗糙表面相关结构对远场散斑相位差统计性质的影响

假设弱散射体粗糙表面高度起伏服从高斯统计，在表面高度起伏分别服从高斯相关，指数相关，圆形相关的情况下，分析了由弱射体产生的远场高斯斑场相位差的条件统计分析。     

A Geometric Interpretation of the Second-Order Structure Function Arising in Turbulence

We primarily deal with homogeneous isotropic turbulence and use a closure model for the von Kármán-Howarth equation to study several geometric properties of turbulent fluid dynamics. We focus our attention on the application of Riemannian geometry methods in turbulence. Some advantage of this approach consists in exploring the specific form of a closure model for the von Kármán-Howarth equation that enables to equip a model manifold (a cylindrical domain in the correlation space) by a family of inner metrics (length scales of turbulent motion) which depends on time. We show that for large Reynolds numbers (in the limit of large Reynolds numbers) the radius of this manifold can be evaluated in terms of the second-order structure function and the correlation distance. This model manifold presents a shrinking cylindrical domain as time evolves. This result is derived by using a selfsimilar solution of the closure model for the von Kármán-Howarth equation under consideration. We demonstrate that in the new variables the selfsimilar solution obtained coincides with the element of Beltrami surface (or pseudo-sphere): a canonical surface of the constant sectional curvature equals − 1.      

Magnetic resonance studies of the properties of water in cellulose acetate membranes

The properties of water in various cellulose acetate (CA) membranes have been investigated by magnetic resonance techniques. It has been observed that the longitudinal (T₁) relaxation time of ¹⁷O in CA membranes containing H₂ ¹⁷O is considerably shorter (by a factor of 5 to 6) than the corresponding value in pure water. The T₁ values of ²³Na ions contained in these membranes were, however, shorter than the corresponding values observed in measurements of the aqueous mother solution by a factor smaller than 2. The EPR spectra of Mn²⁺ and of Cr³⁺ contained in CA membranes were practically identical to the spectra of the pure aqueous solution.

The data suggest the existence, in the CA membrane, of two “types” of water; a small fraction of highly immobilized “bound” water and the remaining large fraction of “free” water displaying properties almost identical to those of pure bulk water. This model is supported by measurements of the longitudinal relaxation rates of H₂ ¹⁷O in CA membranes which were gradually dehydrated from their water.     

石墨烯能带中的重叠矩阵效应:Tight-Binding方法在模拟中的研究

采用紧束缚方法计算了石墨烯的价带(π)和导带(π*),考虑了非正交基矢下重叠矩阵效应,重叠积分参量s越小,导带越靠近费米面,而价带越远离费米面.在重叠积分参量s≤0.1时,基本保持了原子在实际空间中重叠所引起的能带的改变,太大(s=0.4)则会导致物理上失效.计算了石墨烯的能态密度,在费米面ε=0处(对应Dirac点)的能态密度为零,并且在Dirac点附近呈线性变化.     

182Os 核yrast带相继SU(3)–U(5)–SU(3)结构相变势能曲面的一种可能理解

基于联合实施微观相互作用玻色子模型的最大F旋方案 (sdIBM-F_max)与γ射线能量-自旋曲线 (γ-ray energy over spin curves, E-GOS)方案, 成功描述了¹⁸²Os核yrast带相继的SU(3)–U(5)–SU(3)结构相变, 由于缺少直观解释而显得抽象. 本文借助微观sdIBM-F_max的微观参数与Bohr哈密顿量的势能曲面方程之间存在的泛函关系, 几何地给出了对这种相继相变途径的另外一种可能理解; 并阐述了在完全变形核的高角动量态中, 由于量子效应在高激发态与低激发态之间生成高简并的临界区, 提供了γ振动能量会变得低于转动能量的一个可能途径, 从而实现了SU(3)–U(5)的相变. 关键词： yrast带结构演化 势能曲面 相变临界区 182Os核')" href="#">¹⁸²Os核     

Fluctuations at the domain edges of nematic liquid crystals in two dimensions

Capillary waves and director fluctuations reduce the surface tension of a non-anchoring unbound nematic surface by comparable amounts. These are relatively small effects in three dimensions, but in two dimensions they become more significant. We examine the conditions in two dimensions under which they dominate explicitly within the framework of a model of the Maier-Saupe type. We find that for reasonable physical parameters of the model the onset of the fluctuation dominated regime generally preempts the nematic-isotropic transition. We conclude that processes which are sensitive to line tension, such as Ostwald ripening during two-dimensional liquid-gas phase separation, are much more strongly coupled to anisotropic molecular interactions and associated nematic ordering than in three dimensions. Received 10 February 1999 and Received in final form 29 March 1999