A complementary thermodynamic limit for classical Coulomb matter

The canonical equilibrium measure of classical two-component Coulomb matter with regularized interactions is analyzed in a finite volume. It is shown that, in the mean-field regime, the one-particle density is inhomogeneous on a new characteristic length scale _inh. For a system ofN positive andN negative particles, _inh and the characteristic length scale of correlations _corr (=Debye screening length) are related via _inh=(2N)^1/2 _corr. The major conceptual conclusion that is drawn from this is that one needs two nontrivial complementary thermodynamic limits to define the equilibrium thermodynamics of two-component Coulomb systems. One of them is the standard thermodynamic limit (infinite volume), where one takesN, _corr fixed. Its complementary limit is characterized byN, _inh fixed, and is a finite-volume inhomogeneous mean-field limit. The most prominent new feature in the mean-field thermodynamic limit, which is absent in the standard thermodynamic limit, is an anomalous first-order phase transition where the Coulomb system explodes or implodes, respectively. The phase transition is connected with the existence of a metastable plasma phase far below the ionization temperature.     

A Monte Carlo method for an objective Bayesian procedure

This paper describes a method for an objective selection of the optimal prior distribution, or for adjusting its hyper-parameter, among the competing priors for a variety of Bayesian models. In order to implement this method, the integration of very high dimensional functions is required to get the normalizing constants of the posterior and even of the prior distribution. The logarithm of the high dimensional integral is reduced to the one-dimensional integration of a cerain function with respect to the scalar parameter over the range of the unit interval. Having decided the prior, the Bayes estimate or the posterior mean is used mainly here in addition to the posterior mode. All of these are based on the simulation of Gibbs distributions such as Metropolis' Monte Carlo algorithm. The improvement of the integration's accuracy is substantial in comparison with the conventional crude Monte Carlo integration. In the present method, we have essentially no practical restrictions in modeling the prior and the likelihood. Illustrative artificial data of the lattice system are given to show the practicability of the present procedure.     

Stochastic flows on a countable set: Convergence in distribution

Consider a sequenceF ₁,F ₂,... of i.i.d. random transformations from a countable setV toV. Such a sequence describes a discrete-time stochastic flow onV, in which the position at timen of a particle that started at sitex isM _n(x), whereM _n =F _n F _n–1 F ₁. We give conditions on the law ofF ₁ for the sequence (M _n) to be tight, and describe the possible limiting law. an example called the block charge model is introduced. The results can be formulated as a statement about the convergence in distribution of products of infinite-dimensional random stochastic matrices. In practical terms, they describe the possible equilibria for random motions of systems of particles on a countable set, without births or deaths, where each site may be occupied by any number of particles, and all particles at a particular site move together.     

Transient bimodality in interacting particle systems

We consider a system of spins which have values ±1 and evolve according to a jump Markov process whose generator is the sum of two generators, one describing a spin-flipGlauber process, the other aKawasaki (stirring) evolution. It was proven elsewhere that if the Kawasaki dynamics is speeded up by a factor ^–2, then, in the limit 0 (continuum limit), propagation of chaos holds and the local magnetization solves a reaction-diffusion equation. We choose the parameters of the Glauber interaction so that the potential of the reaction term in the reaction-diffusion equation is a double-well potential with quartic maximum at the origin. We assume further that for each the system is in a finite interval ofZ with ^–1 sites and periodic boundary conditions. We specify the initial measure as the product measure with 0 spin average, thus obtaining, in the continuum limit, a constant magnetic profile equal to 0, which is a stationary unstable solution to the reaction-diffusion equation. We prove that at times of the order ^–1/2 propagation of chaos does not hold any more and, in the limit as 0, the state becomes a nontrivial superposition of Bernoulli measures with parameters corresponding to the minima of the reaction potential. The coefficients of such a superposition depend on time (on the scale ^–1/2) and at large times (on this scale) the coefficient of the term corresponding to the initial magnetization vanishes (transient bimodality). This differs from what was observed by De Masi, Presutti, and Vares, who considered a reaction potential with quadratic maximum and no bimodal effect was seen, as predicted by Broggi, Lugiato, and Colombo.     

La（NCS）3.4.5H2O和B15C5在乙醇中的相平衡及热化学研究

采用半微量相平衡方法测定了三元体系Ｌａ（ＮＣＳ）３．４．５Ｈ２Ｏ－Ｂ１５Ｃ５－Ｃ２Ｈ５ＯＨ在２９８．１５Ｋ的溶解度，测定了各饱和溶液的折光率。     

Reliable evaluation of temperature-independent parameters in correlation of vapour–liquid equilibrium data

A new algorithm/program has been elaborated for simultaneous processing of different sets of vapour–liquid equilibrium data. The program was tested with six binary hexane + isomeric pentanol systems, each of them measured at three different isobaric conditions and one isothermal system of tert-butyl-methyl-ether + 2-methyl-2-propanol measured at three different temperatures. The correlation uses the maximum likelihood method, taking into account real behaviour of vapour phase. The parameters obtained are valid within the whole temperature range of the data, and are consistent in comparison with those obtained from individual correlations of isobars or isotherms. Results are presented for the Wilson and NRTL equations.     

General application of jäntti's method for the fast calculation of sorption equilibrium

On the basis of a molecular model for adsorption kinetics Jäntti introduced a method to calculate equilibriums shortly after a change of the pressure of the sorptive gas. In the present paper we show that this method is useful in many more situations than those intended originally.     

关于meso—四苯基卟啉在冰醋酸中的存在形式

前言卟啉在生物化学、分析化学、药物化学等领域有着广泛研究和重要应用［１～３］。近年来虽然对卟啉类化合物的研究报道很多［４～６］，但对卟啉在酸性介质中的研究很少。较早期的研究工作认为卟啉类化合物在酸性介质中仅以其二酸形式存在［７］。本文实验结果显示ｍｅ...     

Phase Analysis of the Binary System of Cryolite (Na3AlF6) and Sodium Metasilicate (Na2SiO3)

The phase analysis of cryolite (Na₃AlF₆) and sodium metasilicate (Na₂SiO₃) was performed by thermal analysis. The eutectic system with a region of two immiscible substances at a concentration of Na₂SiO₃ between 42.8 and 46.3 mol‐% was identified and the eutectic temperature determined to (886±2) °C. Based on the results of mass‐loss measurements, it was assumed that the introduced Na₂SiO₃ reacts with Na₃AlF₆ due to the formation of some nonvolatile stable compounds. The stable reaction products were identified by X‐ray diffraction analysis and IR spectroscopy of the spontaneously cooled samples, which established the formation of NaF and stable amorphous aluminosilicate compounds.