Mechanical fabrication of metal nano-contacts showing conductance quantization under electrochemical potential control

We have mechanically fabricated Ni and Cu nano-constrictions in solution to study their quantized conductance behavior under electrochemical potential control. Conductance quantization was observed at both metals in solution at room temperature for the first time. The conductance of Cu nano-constriction was quantized in units of G₀(=2e²/h). A sharp 1G₀ peak was observed in the conductance histogram. For Ni, a rather broad peak at 1–1.5G₀ was observed in the histogram. The conductance quantization behavior was discussed by comparing previously documented results of nano-constrictions fabricated in air or ultra-high vacuum conditions, with those fabricated in solution.     

Eigenvalues and eigenfunctions of the Fokker-Planck equation for the extremely underdamped Brownian motion in a double-well potential

The eigenvalues and eigenfunctions of the Fokker-Planck equation describing the extremely underdamped Brownian motion in a symmetric double-well potential are investigated. By transforming the Fokker-Planck equation to energy and position coordinates and by performing a suitable averaging over the position coordinate, a differential equation depending only on energy is derived. For finite temperatures this equation is solved by numerical integration, whereas in the weak-noise limit an analytic result for the lowest nonzero eigenvalue is obtained. Furthermore, by using a boundary-layer theory near the critical trajectory, the correction term to the zero-friction-limit result is found.     

Zn-Mg合金的长程Finnis-Sinclair势

通过拟合Mg的晶格能、晶格常数、弹性常数,并将其与前人的结果相比较后获得了描述Mg的最优长程Finnis-Sinclair(F-S)势函数参数,使用同样方法并引入修正因子后得到了Zn的长程F-S势参数.基于单质Zn,Mg的F-S势参数,进一步拟合合金Mg₂₁Zn₂₅,MgZn₂,Mg₂Zn₁₁的晶格常数、晶格能获得Zn-Mg原子对的F-S势参数,构建了整套描述Zn-Mg合金的长程F-S势参数.在此 关键词： 长程Finnis-Sinclair势 Zn-Mg合金 分子动力学模拟     

HNO分子基态的结构与解析势能函数研究

应用群论及原子分子反应静力学的方法, 导出了HNO分子基态电子态和合理的离解极限.利用优选出的密度泛函理论B3LYP方法结合6-311G **优化计算了HNO分子基态的平衡结构和谐振频率.计算结果表明基态HNO分子稳定态为C_S构型,电子组态为X¹A',平衡核间距分别为R_H-N=0.1065 nm,R_N-O=0.1200 nm,键角∠H-N-O=108.60°,离解能D_e=15.379 eV.基态简正振动频率分别为:弯曲振动频率ν₁=1575.6351 cm^-1,对称伸缩振动频率ν₂=1673.2890 cm^-1,反对称伸缩振动频率ν₃=2837.7856 cm^-1.在此基础上,应用多体项展式理论导出了基态HNO分子的全空间解析势能函数,该势能函数等值势能图准确再现了HNO分子平衡结构和离解能. 关键词： 势能函数 光谱常数 密度泛函方法     

Brownian motion of nonlinear oscillators: The projection operator method and its application to a double-well-potential oscillator

A projection operator method is presented, which provides the most efficient way for calculating the stationary behavior of nonlinear Brownian motion. A continued-fraction expansion of the Fourier-Laplace transform of the displacement correlation function or the spectral density is used. This method utilizes a successive optimization procedure on the nonlinear terms and includes the method of statistical linearization as the lowest order approximation. A systematic way to calculate the continued fraction numerically up to sufficient order for convergence is developed, which enables us to obtain the spectral density of a system previously uncomputable.Numerical computations of the spectral density of a nonlinear oscillator with a double-well potential are presented and compared with the results obtained by statistical linearization.This work was supported in part by the National Science Foundation under Grant CHE 75-20624.     

空间轴对称变形界面裂纹尖端的应力奇异性分析

假定位移场,并将位移势函数展开成一系列的特征函数,代入空间轴对称变形的基本方程,推得界面裂纹的特征值理论。把这一理论应用到单向增强的连续纤维复合材料上,建立了纤维断裂、基体开裂等模型下应力奇异性的特征方程,分析了界面裂纹尖端的应力奇异性。     

Ne同位素替代下Ne-HF碰撞截面的理论计算

采用Huxley势函数拟合QCISD(T)/ aug-cc-pVTZ计算的相互作用势能面,通过精确度较高的密耦近似方法计算了E=100 meV时,氖原子的三种同位素 ¹⁶Ne, ²⁰Ne, ³⁴Ne与HF分子碰撞系统的微分截面和分波截面.探讨了Ne的同位素替代引起的Ne-HF碰撞激发 截面的变化规律.     

Probability theory and polymer physics

This study applies the theory of stochastic processes to the equilibrium statistical physics of polymers in solution. The topics treated include random copolymers and randomly branching polymers, with self-consistent mean field effects. A new and more natural way of dealing with Boltzmann weighting is discussed, which makes it possible from the beginning of a calculation to consider only the physical polymer conformations. We also show that in general the random copolymer problem can be reduced to the ordinary polymer problem, and treat the self-consistent field problem for a general branching polymer.     

Convergence rates of a global optimization algorithm

Second order conditions for the (pseudo-) convexity of a function restricted to an affine subspace are obtained by extending those already known for functions on ⁿ . These results are then used to analyse the (pseudo-) convexity of potential functions of the type introduced by Karmarkar.This research was completed while the first author was on sabbatical leave at the Département d'Informatiques et de Recherche Opérationelle, Université de Montréal, and supported by NSERC (grant Q015807). This research was also supported by NSERC (grants A8312 and A5408) and la Coopération franco-québécoise (project 20-02-13).     

On a class of singular biharmonic problems involving critical exponents

This paper deals with the following class of singular biharmonic problems