Some Observations on the Early History of Equilibrium Statistical Mechanics

The article begins with some personal comments by the author on the outstanding contributions of Michael Fisher to statistical mechanics and critical phenomena. Its major aim is to trace the contributions of a number of pioneering personalities to the early history of equilibrium statistical mechanics. Four different areas are considered: (1) Classical Statistical Mechanics, (2) Quantum Statistical Mechanics, (3) Interacting Systems, and (4) The Ising Model. The article is concerned with the development and applications of statistical mechanics when certain basic assumptions are made. It does not deal with the justification of these assumptions which is a sophisticated discipline of its own.     

C6H6分子振动能谱的涨落统计特征

分析了C6 H6 分子振动能谱的涨落统计特征 .研究结果显示 ,C6 H6 分子振动能谱的涨落统计特征属于低Poisson型 ,即谱刚度值大于Poisson型与Wigner型 ,而能谱分维函数值则小于Poisson型与Wigner型 ,这是一种与通常的Poisson型、Wigner型完全不同的类型 ,该特性在一定程度上反映了C6 H6 分子结构的特殊性 .     

Bimodalities: A survey of experimental data and models

Bimodal distributions of some chosen variables measured in nuclear collisions were recently proposed as a non-ambiguous signature of a first-order phase transition in nuclei. This section presents a compilation of both theoretical and experimental studies on bimodalities performed so far, in relation with the liquid-gas phase transition in nuclear matter.     

Decay of correlations and related sum rules in a layered classical plasma

Summary The asymptotic behaviours of particle correlation functions and the related sum rules are discussed for a layered classical plasma withe ²/r interactions in the fluid state, in dependence on the number of layers. These properties derive from consistency conditions imposed by screening on the hierarchical equations, as already treated by A. Alastuey and P. A. Martin (J. Stat. Phys.,39, 405 (1985)) for various Coulomb fluids. The main results concern i) the type of clustering of correlations needed for the validity of multipolar sum rules at various orders, ii) the proof that the pair correlation function in a finite multilayer may carry an electric dipole moment and the calculation of its partioning among the layers, and iii) the dimensionality crossover in an infinitely extended or periodically repeated multiplayer with varying interlayer spacing and wave vector.     

Statistical analysis of the effect of dielectric barrier discharge (DBD) operating parameters on the surface processing of poly(methylmethacrylate) film

A dielectric barrier discharge (DBD) plasma, operating in air at atmospheric pressure, has been used to induce changes in the surface properties of poly(methylmethacrylate) (PMMA) films. The relative effects that key DBD operating parameters, specifically: discharge power, electrode gap and duration of exposure have on producing chemical and microstructural changes in the polymer surface region have been investigated. The approach taken involves the application of an orthogonal array experimental design and statistical analysis methodology. The various data sets obtained from these analyses have been used to develop an equation in which induced changes in the surface properties of the DBD modified PMMA films are expressed in terms of the effectiveness of the various processing parameters in producing them.In general, the results obtained clearly indicate that DBD plasma processing is an effective method for the controlled surface modification of PMMA. Relatively short exposures to the atmospheric pressure discharge produces a significant amount of oxygen incorporation at the surface as indicted by a pronounced reduction in water contact angle. Analysis of the role of each of the operating parameters concerned shows that they do indeed have selective effectiveness for inducing resultant surface modification. Duration of exposure to the DBD plasma, expressed here as the number of treatment cycles at a given speed of specimen transit through the electrode gap, was found to play a major role in decreasing the surface wettability of PMMA. Conversely, the magnitude of the discharge power was not a significant parameter in this regard. In contrast, the value of the applied power played the dominant role in achieving the observed enrichment of the surface oxygen abundance, as measured by XPS, with the duration of exposure to the discharge playing a secondary role in this case.The nature and scale of the induced surface changes that originate from the various processing conditions employed have been further considered to determine if an interrelationship exists between them. Non-parametric data analysis indicates that no significant correlation exists between the observed changes in measured polymer wettability and the attendant surface oxygen enrichment. This result suggests that the increase in surface wettability caused by DBD processing, as manifested in a reduced contact angle, is not merely attributable to changes in the surface chemistry. As such, it is postulated that changes in the surface microstructure may also contribute to this change in surface wettability.     

Dynamic critical properties of a one-dimensional probabilistic cellular automaton

Dynamic properties of a one-dimensional probabilistic cellular automaton are studied by Monte Carlo simulation near a critical point which marks a second-order phase transition from an active state to an effectively unique absorbing state. Values obtained for the dynamic critical exponents indicate that the transition belongs to the universality class of directed percolation. Finally the model is compared with a previously studied one to show that a difference in the nature of the absorbing states places them in different universality classes. Received: 6 February 1998 / Revised and Accepted: 17 February 1998     

控制图判断准则的显著性检验

徐哲，段晓江．控制图判断准则的显著性检验．数理统计与管理，１９９８，１７（３），４５～４８．利用控制图判断生产过程的状态是一种统计判断，必然犯两种错误。本文在规定“小概率事件”标准的基础上，对休哈特控制图判断准则假设检验的显著性水平进行了分析，并直观解释了各种异常情况的系统性变化特点，最后简述了计算机辅助质量控制图的应用     

Entanglement and phase

Entanglement is the cornerstone of all new technological implications of quantum mechanics, which meanwhile extend into the realm of theoretical chemistry. In this contribution, the relation between entanglement and phase factors is investigated in terms of statistical operators. After the introduction of a simplified definition of the separability of a statistical operator, a new way to obtain phase information from experiments is presented, and the emergence of separability from non-separability is explained by the loss of a special phase operator containing the quantum part of the system's information. Dedicated to my doctoral adviser, Prof. Dr. Karl Jug, Hannover, in honor of his 65th birthday     

Molecular thermodynamic model for equilibria in solution II. Statistical microscopic properties of ensembles

A statistical thermodynamic model for the interpretation of the equilibria in solution is based on the principle that the representative statistical ensembles can be characterized by two types of molecular distribution, one for non-reacting systems and another for reacting ones, respectively. Non-reacting and reacting ensembles correspond at the molecular level to one or a couple of potential curves, respectively. The properties of the thermodynamic model for solutions can be set up following some rules. These concern the statistical extension of the microscopic model to the whole ensemble and the successive averaging to get a mean partition function. The mean partition function is linked to the experimental domain of concentrations, dilutions and equilibrium constants (probability space) and to that of calorimetry, chemical work, and potentiometry (thermodynamics space). The formal connection between probability and thermodynamic space and the conformity of thermal equivalent dilution with the formulations of statistical thermodynamics are also shown.     

Interactions of He atoms with Xe plated graphite: unified treatment of scattering and adsorbate dynamics based on method of coupled channels

Interactions of He atoms with surfaces have been in the focus of surface scientists for more than seventy years. Depending on the types of the studied problems, and on the algorithms available for their assessment, the accuracy of model calculations aiming at the interpretations of the various aspects of He-atom scattering and dynamics in the adsorbed phase have greatly varied during that period. In this article, we describe the application of a numerical algorithm based on the coupled-channel method that proves very accurate in the calculations of eigen-states and eigen-energies of He atoms interacting with strongly corrugated surfaces. The algorithm is applied to compute diffraction spectra characteristic of thermal energy He-atom scattering from a monolayer of Xe atoms adsorbed on (0 0 0 1) surface of graphite, and the thermodynamical quantities describing a quasi-two-dimensional gas of He atoms adsorbed on the same surface. The usefulness of the developed approach is illustrated in comparisons of the theoretical results with the available experimental data.