Fractal behavior in trapping and reaction: A random walk study

We investigate the trapping of a random walker in fractal structures (Sierpinski gaskets) with randomly distributed traps. The survival probability is determined from the number of distinct sites visited in the trap-free fractals. We show that the short-time behavior and the long-time tails of the survival probability are governed by the spectral dimensiond. We interpolate between these two limits by introducing a scaling law. An extension of the theory, which includes a continuous-time random walk on fractals, is discussed as well as the case of direct trapping. The latter case is shown to be governed by the fractal dimensiond.     

Thermodynamic evaluation of a partial charge model assumptionfor the dissolved silica system

The Partial Charge Model was developed to predict the hydroxylation, polymerization, and precipitation of ions. The purpose of this study is to evaluate the Partial Charge Model for describing the polymerization of silica in aqueous solutions. The Partial Charge Model predicts the stability of ions and complexes based on the assumption that the stable species will have the same electronegativity as the mean electronegativity of the solution. The silica system was chosen for model validation because of the rare availability of self-consistent thermodynamic data on many dissolved but polymerized silicate anions, including both linear and cyclical species. The electronegativity of each species was calculated using the Partial Charge Model and the results were plotted against the stability constants for the ions. The silicate anions segregated into groups on the plot based on the number of charges per silicon atom in the polymer. Plots of the log of the stability constant versus the change in electronegativity produced a linear relationship for the silica polymers containing one negative charge per silicon atom, which resulted in an r ² of 0.9978. Thus, the Partial Charge Model successfully describes the thermodynamics of silica polymerization in aqueous solution for species that are sufficiently alike, but was not accurate for all silica species.     

Determination of Aggregation Parameters of Hexadecyltrimethylammonium Bromide from Probe Absorption

The mean aggregation number (n) and the critical micelle concentrations (CMC) of reverse micelles formed by hexadecyltrimethylammonium bromide have been determined by means of an optical absorption probe (acridine orange). The procedure to obtain these quantities from absorption spectrophotometric measurements is described. The CMC and mean aggregation number are in satisfactory agreement with published results obtained from more sophisticated methods.     

Spectral density distribution moments of a Hamiltonian of N coupled Morse oscillators: The large‐N limit

The expressions for moments of spectral density distribution of a Hamiltonian representing a system of N coupled Morse oscillators are reduced to the large‐N limit. The effect of the values of coupling constants on the spectral density distribution is analyzed. For the values of coupling constants within the pertinent range for real molecules, the relations between moments appear to be close to those for a Gaussian distribution. Outside this range, the deviations from the normal distribution are substantial. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

A method for correcting the contact angle from the θ/2 method

The θ/2 method, a widely used technique on measuring the contact angle of a sessile drop, assumes that the drop profile is part of a sphere. However, the shape profile of a sessile drop is governed by the Young–Laplace equation and is different from a sphere, especially for drops with a large bound number (e.g. large volume or small surface tension). The spherical assumption, therefore, causes errors on evaluating the contact angles. The deviation of contact angle from the θ/2 method is evaluated from a theoretical calculation in this work. A simple means is given for correcting the measurement error. The corrected angle results from the drop volume, surface tension, liquid density and the contact angle from θ/2 method. An algorithm for finding the correct contact angle without knowing the density and surface tension is also given. At the end, two examples of pendant drops are given for the illustration.     

Molecular electrostatic potentials as input for the alignment of HIV-1 integrase inhibitors in 3D QSAR

Comparative molecular similarity indices analysis (CoMSIA), a three-dimensional quantitative structure activity relationship (3D QSAR) paradigm, was used to examine the correlations between the calculated physicochemical properties and the in vitro activities (3'-processing and 3'-strand transfer inhibition) of a series of human immunodeficiency virus type 1 (HIV-1) integrase inhibitors. The training set consisted of 34 molecules from five structurally diverse classes: salicylpyrazolinones, dioxepinones, coumarins, quinones, and benzoic hydrazides. The data set was aligned using extrema of molecular electrostatic potentials (MEPs). The predictive ability of the resultant model was evaluated using a test set comprised of 7 molecules belonging to a different structural class of thiazepinediones. A CoMSIA model using an MEP-based alignment showed considerable internal as well external predictive ability (r2(cv) = 0.821, r2(pred) = 0.608 for 3'-processing; and r2(cv) = 0.759, r2(pred.) = 0.660 for 3'-strand transfer).     

Iminophosphanes: Unconventional Compounds of Main Group Elements

The large number of known stable compounds in which phosphorus has a low coordination number makes it clear that such compounds can no longer be regarded as “exotic” in main group chemistry. While the rich chemistry of P? C multiply bonded systems makes clear their affinity to their organic congeners, iminophosphanes in particular are also of increasing importance. The linkage of a phosphinidine fragment with an imine fragment via a multiple bond gives rise to a class of compounds with an unusually wide range of structural types. This in turn leads to a broad spectrum of chemical behavior which makes iminophosphanes extremely useful synthetic building blocks in organoelement chemistry.     

A central limit theorem for age- and density-dependent population processes

Consider a population consisting of one type of individual living in a fixed region with area A. In [8], we constructed a stochastic population model in which the death rate is affected by the age of the individual and the birth rate is affected by the population density P_A(t), i.e., the population size divided by the area A of the given region. In [8], we proposed a continuous deterministic model which in general is a nonlinear Volterra type integral equation and proved that under appropriate conditions the sequence P_A(t) would converge to the solution P(t) of our integral equation in the sense that

$\text{lim}\text{→∞}\text{P}\text{sup}\text{0?s?t}\text{|P}{}_{\mathrm{A}}\text{(s) ? P(s)|>ε}\text{=0}\text{for every}\text{ε > 0}$

.In this paper, we obtain a “central limit theorem” for the random element √A(P_A(t)?P(t)). We prove that under appropriate conditions √A(P_A(t)?P(t)) will converge to a Gaussian process. (See Theorem 3.4 for the explicit formula of this Gaussian process.)     

样品价态对激光气化产生Cu/Cl团簇的组成和稳定性的影响

研究团控的形成条件、形成机理是目前团簇科学中的一个热点领域［‘］．产生气相团簇的方法主要有Knudsen高温炉扩散法、粒子溅射法、激光气化／分子束法、直接激光气化法·因为不需要另加缓冲气体，直接激光气化法【刀具有对体系真空要求较低，装置简单，容易和飞行时间质谱结