The Size of a Political Club

We investigate the size of a political club that admits new members according to a rule that if only a few members vote against admission the candidate joins, but the members who voted against admission leave. For the simplest ergodic case, we use a modified Bessel function to give the generating function for the invariant distribution of the club size. This also allows us to give asymptotics for the moments as the probability of voting for admission approaches 1 and to prove global and local central limit theorems. We also calculate the mean recurrent time and determine formulas for calculating first passage times. We then show that for an expanded set of cases the club size process approaches the Ornstein-Uhlenbeck process as the probability of voting for admission approaches 1. This means that the club size will approach a Gaussian distribution for a wide set of formal and informal admission rules. Finally, we show a comparison between theoretical results and simulation runs for two cases.     

粗糙度对4种聚氨酯弹性体粘着性能的影响

采用生物摩擦磨损试验台测定了4种聚氨酯的弹性模量，研究了表面粗糙度和法向力对粘着力的影响．结果表明：4种聚氨酯的弹性模量在55～1206kPa之间，粘着力由高到低的排序同其弹性模量排序相反，弹性模量较低的试样的饱和粘着力达到15kPa，且表面粗糙度对粘着力的影响不明显；弹性模量较大的试样的粘着力仅为1．5kPa，随弹性模量增加，表面粗糙度的影响增大；试样之间的接触形式同粘着力密切关系，相当于单个凸峰接触的蓝宝石球对聚氨酯试样的粘着力不受法向力的影响，而在平面接触情况下粘着力先随法向力增加而增大，当法向力超过一定(10～15kPa)值后，粘着力增加趋缓并达到饱和值．     

Nuclear spin relaxation and magnetic shielding tensors of atoms constituting cyanogen bromide molecule

The temperature dependence of the correlation time describing reorientation kinetics of cyanogen bromide in CDCl₃ solution has been determined on the basis of the linewidths of the ¹⁴N NMR signal. It has been found that the longitudinal spin relaxation of the ¹⁵N nucleus occurs by shielding anisotropy and spin-rotation mechanisms, whereas for the ¹³C nucleus these mechanisms are of lesser importance. In the latter case the scalar relaxation of the second kind due to carbon-bromine coupling is the predominant relaxation mechanism. The parameter values: ¹ J(¹³C—⁷⁹Br) = 349 ± 10 Hz, T ₁ (⁷⁹Br, 303 K) = 2.31 ± 0.22 × 10^?7 s, Δσ(¹⁵N) = 565 ± 16 ppm and Δσ(¹³C) = 276 ± 120 ppm have been determined from the relaxation data analysis. The shielding anisotropy parameters Δσ(¹⁵N) = 580 ± 50 ppm and Δσ(¹³C) = 274 ± 9 ppm have been independently determined using ¹³C and ¹⁵N NMR in liquid crystalline solvent. The experimentally determined shielding tensors for sp-hybridized atoms in the investigated compound and in a series of bromoacetylenes have been compared with the results of quantum mechanical calculations [GIAO, DFT B3LYP/6-311 + +G(2d,p)]. The ‘heavy atom effect’ shielding bromine-bonded carbons is of the order of — 25 ppm and concerns mainly the σ⊥ component.     

The bridge function of hard spheres by direct inversion of computer simulation data

The bridge function of the hard sphere fluid has been calculated from our new highly accurate Monte Carlo and molecular dynamics simulation data on the radial distribution function using the (inverted) Ornstein-Zernike equation. Both the systematic errors (finite size, grid size, tail) and statistical errors are analysed in detail and ways to suppress them are proposed. Uncertainties in the resulting values of B(r) are about 0.001. In contrast with many previous findings the bridge function is both positive and negative.     

An integral equation and Monte Carlo study of homo- and hetero- nuclear square-well diatomic fluids

Square-well homo-nuclear and hetero-nuclear diatomic fluids are studied using the Ornstein-Zernike equation and the recently proposed RHNC-VM closure. Monte Carlo canonical simulations have been performed to complete recent literature simulation data. The integral equation thermodynamic and structural results are compared with these and literature simulation data at three elongations over a large range of densities and temperatures. The RHNC-VM theory agrees excellently with the simulation thermodynamic and structural results. Its accuracy revealed slight errors in simulation data in work by Lisal and Nezbeda [1999, Molec. Phys., 96, 335]. The data have been re-simulated.     

Calculation of elementary diagrams using a Metropolis-like simulation method

A method for the evaluation of higher order elementary diagrams is proposed. It utilizes symbolic algebra programming and automatic code generation. The method is used to calculate elementary diagrams for hard spheres up to the fifth. The obtained values are fitted to suitable functions of interparticle distance. The resulting truncated density expansion is compared with recent values of the bridge function calculated directly from the simulated pair distribution function. The method can be straightforwardly extended to hard-body systems and their mixtures.     

Magnetic shielding tensors of carbon nuclei in 3,5-dichlorophenylacetylene,a theoretical ab initio and experimental study

Ab initio GIAO-CHF and DFT(B3LYP) molecular geometry optimization and magnetic shielding tensor calculations of carbon nuclei of 3,5-dichlorophenylacetylene have been performed using 6–311G?? and 6–311+G(2d,p) basis sets. The isotropic ¹³C chemical shifts, needed for comparison, have been measured in C₆D₁₂ solution. The principal elements of the shielding tensor of the carbon nuclei in the investigated molecule in the solid state have been determined from an intensity analysis of the spinning sidebands in ¹H-¹³C CP/MAS NMR spectra. Shielding anisotropy parameters of the acetylenic carbons have been independently determined using the method based on proton-coupled ¹³C nematic phase spectra as well as from the interpretation of the ¹³C longitudinal relaxation rates. The latter data have been analysed assuming the molecular reorientation to be the rotational diffusion of an asymmetrical top, which has provided, apart from the diffusion coefficients, an additional check on the reliability of the theoretical calculation of the shielding tensors. In general, satisfactory agreement between the theoretical and experimental results has been achieved.