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101.
Michael K. -H. Kiessling 《Journal of statistical physics》1990,59(5-6):1157-1186
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. 相似文献
102.
Yosihiko Ogata 《Annals of the Institute of Statistical Mathematics》1990,42(3):403-433
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. 相似文献
103.
P. J. Forrester 《Journal of statistical physics》1989,56(5-6):767-782
The vicious random walker problem on a line is studied in the limit of a large number of walkers. The multidimensional integral representing the probability that thep walkers will survive a timet (denotedP
t
(p)
) is shown to be analogous to the partition function of a particular one-component Coulomb gas. By assuming the existence of the thermodynamic limit for the Coulomb gas, one can deduce asymptotic formulas forP
t
(p)
in the large-p, large-t limit. A straightforward analysis gives rigorous asymptotic formulas for the probability that after a timet the walkers are in their initial configuration (this event is termed a reunion). Consequently, asymptotic formulas for the conditional probability of a reunion, given that all walkers survive, are derived. Also, an asymptotic formula for the conditional probability density that any walker will arrive at a particular point in timet, given that allp walkers survive, is calculated in the limittp. 相似文献
104.
An intrinsic principle of least action is presented for the intrinsic dynamism of chemical reactions. Then, as the stationary trajectory, a meta-IRC (intrinsic reaction coordinate) draws a geodesic curve in a rigged Riemannian space. This establishes a geodesic law for the intrinsic dynamism. Moreover, a diagrammatic perturbation theory is formulated for the intrinsic dynamism, and a dynamical interaction between a chemically reacting system and a background system is investigated. Then, the structural stability of the system is discussed using a new concept of the dynamical potential field. An example is given in order to elucidate the present theory.Dedicated to Prof. Hermann Hartmann on the occasion of his 65th birthday. 相似文献
105.
Summary The complete error potential is used for the study of the correlation of molecules. The correlation can be seen as a relaxation of the electrons and a relaxation of the nuclei. From the Fermi sea, the electronic relaxation gives rise to a partial excitation of each orbital which collectively generates a linear, a surface or a volume pressure; the resulting forces acting on the nuclei are defined in a general theory of the intramolecular forces. H3, H
3
+
, the diatoms and the hydrid of the first nine elements are taken as examples. 相似文献
106.
多电解质溶液中带电胶体粒子的电势分布由球形Poisson-Boltzmann方程(PBE)描述.PBE是一个非线性的微分方程,且难以求得其解析解.本文采用非线性P-B积分方程,计算电势分布的数值解.首先,根据静电场和热力学系统中的物理定理,导出描述电势分布的P-B积分方程(PBIE);其次,用迭代方法求PBIE的数值解.最后,计算了在3-1型电解液中无量纲半径κa分别为0.12和0.22,无量纲表面电势ξ分别为1,2,4,6时球形胶体粒子外部的电势值.为了检验数值解的精度,计算了表面电荷密度,并与Loeb(1961)和Oshima(1995)等人的结果比较,本文结果的相对误差小于1%,优于Oshima的结果. 相似文献
107.
The Fermi and Coulomb holes of the 21
S state of the helium isoelectronic sequence are investigated. Several interesting differences between the results obtained and those which might be expected on the basis of the corresponding 23
S state are pointed out and discussed. 相似文献
108.
Zou JW Jiang YJ Guo M Hu GX Zhang B Liu HC Yu QS 《Chemistry (Weinheim an der Bergstrasse, Germany)》2005,11(2):740-751
Ab initio calculations have been performed on a series of complexes formed between halogen-containing molecules and ammonia to gain a deeper insight into the nature of halogen bonding. It appears that the dihalogen molecules form the strongest halogen-bonded complexes with ammonia, followed by HOX; the charge-transfer-type contribution has been demonstrated to dominate the halogen bonding in these complexes. For the complexes involving carbon-bound halogen molecules, our calculations clearly indicate that electrostatic interactions are mainly responsible for their binding energies. Whereas the halogen-bond strength is significantly enhanced by progressive fluorine substitution, the substitution of a hydrogen atom by a methyl group in the CH(3)X...NH(3) complex weakened the halogen bonding. Moreover, remote substituent effects have also been noted in the complexes of halobenzenes with different para substituents. The influence of the hybridization state of the carbon atom bonded to the halogen atom has also been examined and the results reveal that halogen-bond strengths decrease in the order HC triple bond CX > H(2)C=CHX approximately O=CHX approximately C(6)H(5)X > CH(3)X. In addition, several excellent linear correlations have been established between the interaction energies and both the amount of charge transfer and the electrostatic potentials corresponding to an electron density of 0.002 au along the R-X axis; these correlations provide good models with which to evaluate the electron-accepting abilities of the covalently bonded halogen atoms. Finally, some positively charged halogen-bonded systems have been investigated and the effect of the charge has been discussed. 相似文献
109.
Polymer electrolyte systems were prepared for the first time by dissolution of amidomagnesium chlorides in poly(ethylene oxide),
(PEO). For the preparation, solutions of (hexamethyldisilylamido)magnesium chloride, (dimethylpyrrolyl)magnesium chloride,
(diisopropylamido)magnesium chloride, piperidinomagnesium chloride and morpholinomagnesium chloride were chosen. The composition
of these polymer electrolyte systems corresponds to the general formula R2NMgCl·P(EO)n·THF. Most work has been done with the system (hexamethyldisilylamido)magnesium chloride in PEO, (Me3Si)2NMgCl·P(EO)n·THF, with n= 3, 4, 5, or 7. The electrolytes have a soft rubber-like consistency. At 30 °C, electrical conductivities of 10−6–10−5 S/cm were found. The conductivities were measured in the temperature range 20–60 °C. Within this temperature range a linear
dependence of the logarithms of the conductivity on the inverse temperature was found and activation energies for the conducting
process of 30–60 kJ/mol were calculated. Using those polymer electrolytes with a high content of the amidomagnesium compound,
a reversible magnesium deposition takes place by cathodic reduction at potentials below −1.9 V vs. a Ag/AgCl reference electrode.
These polymer electrolytes were found to be stable against oxidation up to about −0.3 V vs. Ag/AgCl.
Electronic Publication 相似文献
110.
J. C. Lpez V. A. L. Rivera Yu. F. Smirnov A. Frank 《International journal of quantum chemistry》2002,88(2):280-295
The calculation of Franck–Condon factors between different 1‐D Morse potential eigenstates using a formula derived from the Wigner function is discussed. Our numerical calculations using a simple program written in Mathematica are compared with other calculations. We show that our results have a similar accuracy as those calculations performed with more sophisticated methods. We discuss the extension of our method to include non‐Condon effects in the calculation. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem 88: 280–295, 2002 相似文献