Two-Point Resistance of a Cobweb Network with a 2r Boundary

We consider the problem of the two-point resistance on an m × n cobweb network with a 2r boundary,which has never been solved before. Up to now researchers just only solved the cases with free boundary or null resistor boundary. This paper gives the general formulae of the resistance between any two nodes in both finite and infinite cases using a method of direct summation pioneered by Tan [Z. Z. Tan, et al., J. Phys. A 46(2013) 195202], which is simpler and can be easier to use in practice. This method contrasts the Green's function technique and the Laplacian matrix approach, which is difficult to apply to the geometry of a cobweb with a 2r boundary. We deduce several interesting results according to our general formula. In the end we compare and illuminate our formulae with two examples. Our analysis gives the result directly as a single summation, and the result is mainly composed of the characteristic roots.     

Growth of Pt thin films on WSe2

The morphology and structure of Pt deposited on a WSe₂(0 0 0 1) van der Waals surface have been investigated by reflection high energy electron diffraction and scanning tunneling microscopy. At room temperature, the initial growth is characterized by the formation of three-dimensional fcc Pt islands with (1 1 1) orientation. In contrast, at higher temperatures of about 450 °C the formation of a novel chemically ordered Pt-Se alloy is observed. Based on the diffraction patterns, a tetragonal DO₂₂-type structure of a Pt₃Se compound is suggested. With increasing Pt thickness, this chemically ordered alloy disappears and an additional superstructure occurs, which is accompanied by the coalescence of the islands. The observed superstructure is attributed to a strong Se diffusion towards the growth surface, forming most likely a PtSe₂ alloy with the CdI₂-type layered structure on the top surface. Due to the lateral lattice mismatch between the Pt(1 1 1) layers and the PtSe₂(1 1 1) top layer, a Moiré pattern with a period of 1.1 nm is created, which might be used as a long-range atomic pattern for further nanostructure growth.     

Oscillatory zoning caused by oscillating surface relaxations

Oscillatory zoning is a spatial variation in the composition of minerals. It has been observed in many different minerals and a variety of mechanisms have been proposed to explain it. We propose an equilibrium model of oscillatory zoning in which the variations in composition stabilise a ferroelastic phase. This results in a sinusoidal variation in composition. We expect that this mechanism could account for oscillatory zoning found in minerals with oscillatory surface relaxations. Received 9 March 1999     

吴大猷先生点评《经典力学》

文章介绍了吴大猷先生对《经典力学》中一些基本问题的意见以及他的近期工作。吴先生认为,Hamilton原理是一个物理原则,而不仅仅是数学变分问题。他还对“齐次问题”和“猝变运动”作了讨论。     

Method for independent control of particle size and distance in rhodium epitaxy on TiO2(110)-(1×2) surface An STM study

A method for independent control of the particle size and distance is presented for rhodium epitaxy on TiO₂(110)-(1×2) surface. The real space imaging of the surface morphology was performed by scanning tunneling microscopy. The amount of the deposited rhodium was checked by Auger electron spectrometry. The method consists of two steps: (i) evaporation of 0.001–0.050 ML equivalent of rhodium at room temperature with a post-annealing at 1100 K (“seeding”); (ii) post-deposition of rhodium for growing of the Rh nanoparticles formed in step (i) (“growing”). The mechanism of this procedure is based on the large difference of the surface diffusion coefficient between Rh adatoms and Rh nanocrystallites larger than 1–2 nm. In the first step the average distance between the metal particles is controlled in the range 5–200 nm, the second step determines the particles size (2–50 nm). This work demonstrates that the diffusion processes of metal nanoparticles of different sizes and the growing modes of the crystallites can be studied in detail by application of seeded surfaces.     

二元高阶Lipschitz函数类和二重Fourier级数

利用二元函数的(r,s)阶差分和二元连续模函数定义了二元周期函数的高阶Lipschitz函数类Λr,s(ω)和λr,s(ω),并且从函数Fourier级数的系数出发,在复数域内给出了函数属于二元周期函数类的充分条件,在实数域内给出了函数属于二元周期函数类的充要条件.     

贮存条件对纤维素/大豆蛋白膜结构与性能的影响

通过流延成膜法制备一系列纤维素/大豆分离蛋白复合膜材料,分别以10%醋酸溶液、5%醋酸和5%乙醇的混合溶液、75%乙醇溶液等3种水溶液及蒸馏水为贮存体系,通过力学性能测试、扫描电镜观察、紫外测试等方法研究了不同贮存条件对纤维素/大豆分离蛋白复合膜结构与性能的影响.结果表明,10%醋酸水溶液贮存纤维素/大豆分离蛋白复合膜30d能够较好地维持其力学性能和微观结构,可作为该复合膜较为适合的贮存体系.     

强一致收敛下的初值敏感性与等度连续性

首先,举例指出了《Nonlinear Anglgsis》文中定理3.2的条件下并不能使函数序列的初值敏感性遗传至极限函数,并证明了若函数序列的敏感常数的上极限为某一正数,则在强一致收敛下,函数序列的极限函数也具有初值敏感性.其次,证明了在强一致收敛下,序列系统的等度连续性和一致几乎周期性能被极限系统所继承.     

非晶氧化钛薄膜形成过程中钛离子能量对表面结构影响的机理

研究了非晶氧化钛薄膜沉积过程中入射钛离子能量对表面结构形成机理以及薄膜特性的影响.模拟结果表明,通过提高入射钛离子能量,可以有效降低成膜表面粗糙度,从而减小薄膜表面的光学散射损耗.研究发现,当入射离子能量提高后,薄膜生长模式从"岛"状生长过渡到了"层"状生长,且离子入射点附近的平均扩散系数也有显著增加,这有利于形成更加平整的高质量薄膜表面.     

Growth and spectral properties of Yb:Ca0.28Ba0.72Nb2O6 disordered crystal

The growth, XRD patterns, spectral properties, and fluorescence decays of Yb:Ca_0.28Ba_0.72Nb₂O₆ (Yb:CBN) with doping concentration of 1 at.% and 5 at.% were studied. The peak absorption cross-section and the emission cross-section were calculated. Larger Stark splitting of Yb:CBN offers the prospect of the quasi-four level laser operation.