Calculations of partition functions for internal rotation of molecules

A simple numerical method for calculations of torsional energy for barriers of arbitrary forms was suggested. Within the framework of the Wigner-Kirkwood approximation, an analytic equation was derived for the partition function of a hindered top, which was used for interpretation and a comparison with numerically exact results.     

A general approach to association using cluster partition functions

A systematic and fundamental approach to associating mixtures is presented. It is shown how the thermodynamic functions may be computed starting from a partition function based on the cluster concept such as occurs in chemical theory. The theory provides a basis for and an extension of the existing chemical theory of (continuous) association. It is applicable to arbitrary association schemes. Analysis of separate cases is not necessary. The assumptions that were made to allow the development were chosen such as to make the principle of reactivity valid. It is this same principle that links various theories: the chemical theory of continuous association, the lattice fluid hydrogen bonding model, and first-order perturbation theory. The equivalence between these theories in appropriate limits is shown in a general and rigorous way. The theory is believed to provide a practical framework for engineering modeling work. Binary interaction parameters can be incorporated. The association scheme is accounted for by a set of generic equations, which should facilitate robust implementation in computer programs.     

Classical bounds on quantum partition functions

Explicit bounds on the quantum partition functions are given in terms of classical partition functions, incorporating effective pair potentials, which account for Fermi- and Bose-statistics, respectively. The bounds may be used for the limit 0 and eventually for showing the interchangeability of the classical with the thermodynamic limit. A simple derivation of the thermodynamic limit for free particles with general dispersions is given.Work supported in part by Fonds zur Förderung der wissenschaftlichen Forschung in Österreich, Project No. 3569.     

Geometric partition functions of cellular systems: Explicit calculation of the entropy in two and three dimensions

A method is proposed for the characterisation of the entropy of cellular structures, based on the compactivity concept for granular packings. Hamiltonian-like volume functions are constructed both in two and in three dimensions, enabling the identification of a phase space and making it possible to take account of geometrical correlations systematically. Case studies are presented for which explicit calculations of the mean vertex density and porosity fluctuations are given as functions of compactivity. The formalism applies equally well to two- and three-dimensional granular assemblies.     

Attempt to calculation of delayed neutron emission probabilities using simple statistical model considerations

Delayed neutron emission probabilities,P _n , have been calculated using usual nuclear statistical model considerations. The influence of the incident parameters on the calculatedP _n -values is discussed. The observed systematic deviation from the experimental neutron emission probabilities may be explained by the persistence of nuclear structure effects not contained in a simple statistical model.     

Incremental expansion of the classical partition functions

The incremental expansion of the canonical partition function of a classical many-particle system is obtained. The incremental expansion coefficients are calculated for the case of a pair interaction potential. The results are used to derive the incremental expansion of the system free energy.     

Ferrocene partition calculation in a biodiesel/water interface using electrochemical methods

This work is a continuation of previous studies concerning the behaviour of ferrocene in a mixture of two insoluble liquids. In this paper, the system reached partition equilibrium after approximately 175 min. Electroanalytical studies were executed, and a high reproducibility was observed in a range of concentrations from 2 to 14?×?10^?5 mol L^?1 of ferrocene that escaped from the oil to the aqueous phase. Because ferrocene most likely occurs only in the monomeric form in both the oil and aqueous phases, it was possible to predict a partition coefficient (log P_(oil/water)) of ferrocene of approximately 2.4.     

Exact partition functions and correlation functions of multiple Hamiltonian walks on the Manhattan lattice

This is a general and exact study of multiple Hamiltonian walks (HAW) filling the two-dimensional (2D) Manhattan lattice. We generalize the original exact solution for a single HAW by Kasteleyn to a system ofmultiple closed walks, aimed at modeling a polymer melt. In 2D, two basic nonequivalent topological situations are distinguished. (1) the Hamiltonian loops are allrooted andcontractible to a point:adjacent one to another, and, on a torus,homotopic to zero. (2) the loops can encircle one another and, on a torus, canwind around it. Forcase 1, the grand canonical partition function and multiple correlation functions are calculated exactly as those of multiple rooted spanningtrees or of a massive 2Dfree field, critical at zero mass (zero fugacity). The conformally invariant continuum limit on a Manhattantorus is studied in detail. The melt entropy is calculated exactly. We also consider the relevant effect of free boundary conditions. The number of single HAWs on Manhattan lattices with other perimeter shapes (rectangular, Kagomé, triangular, and arbitrary) is studied and related to the spectral theory of the Dirichlet Laplacian. This allows the calculation of exact shape-dependent configuration exponents y. An exact surface critical exponent is obtained. Forcase 2, nested and winding Hamiltonian circuits are allowed. An exact equivalence to thecritical Q-state Potts model exists, whereQ ^1/2 is the walk fugacity. The Hamiltonian system is then always critical (forQ<-4). The exact critical exponents, in infinite numbers, are universal and identical to those of theO(n=Q ^1/2) model in its low-temperature phase, i.e. are those of dense polymers. The exact critical partition functions on the torus are given from conformai invariance theory. These models 1 and 2 yield the two first exactly solved models of polymer melts.     

Derivation of tunneling probabilities for arbitrarily graded potential barriers using modified Airy functions

General expressions of tunneling probability for arbitrarily graded potential barriers are rigorously derived using the modified Airy functions. Three types of graded potential barriers for which exact solutions exist are taken as examples for comparison’s purpose. Results obtained by the proposed method are confirmed to be in fairly good agreement with exact ones, demonstrating the usefulness of the modified Airy functions method.     

Burnup calculation by the method of first-flight collision probabilities using average chords prior to the first collision

A technique to calculate the burnup of materials of cells and fuel assemblies using the matrices of first-flight neutron collision probabilities rebuilt at a given burnup step is presented. A method to rebuild and correct first collision probability matrices using average chords prior to the first neutron collision, which are calculated with the help of geometric modules of constructed stochastic neutron trajectories, is described. Results of calculation of the infinite multiplication factor for elementary cells with a modified material composition compared to the reference one as well as calculation of material burnup in the cells and fuel assemblies of a VVER-1000 are presented.     

The calculation of transition probabilities for atomic oxygen

In this contribution we present scanning tunnelling microscopy (STM) and spectroscopy (STS) investigations on isolated cobalt clusters in contact with Ge(001). Mass-filtered nanoparticles with diameters ranging from 3 to 11 nm are generated using an arc cluster ion source (ACIS) and deposited under soft landing conditions (E_kin/atom < 0.5 eV). Since the tip radius is of the same order as the nanoparticle diameters the recorded STM images are significantly affected by tip folding. By means of the “blind reconstruction method" it is possible to approximate the tip shape. After a respective deconvolution of the image structural features of the particle facets become observable. According to the equilibrium shape of the clusters being a truncated octahedron in the size range under investigation, hexagonal and rectangular features appear in the images. STS is sensitive to occupied and unoccupied states near the Fermi level and reveals the existence of distinct states in the tunnelling conductivity of the substrate as well as on the clusters. The richly structured density of states of the germanium surface serves here as tip condition test. First measurements of the tunnelling conductivity of the Co_N/Ge(001) are presented and discussed.     

二氧化硅分子配分函数的研究

在低温20K到高温6000K温度范围内,计算了¹⁶O²⁸Si¹⁶O分子稳定结构的的总配分函数.其中,转动配分函数考虑了离心扭曲修正,振动配分函数采用谐振子近似.把20—6000K的温度范围划分为五区间段,计算的总配分函数在这五个温度区间分别被拟合到一个温度T的四阶多项式,从而在每个区间均得到五个拟合系数.由这些拟合系数就可以快速、准确地获得分子在所研究温度范围内任意温度的总的配分函数. 关键词： 总配分函数 二氧化硅分子 转动配分函数 振动配分函数     

Functional integrals for the partition functions of dual strings

We show how the partition functions and helicity partition functions of the known dual strings can be obtained from functional integrals. We define these integrals using a cut-off which is essentially equivalent to Ramanujan's definition of divergent sums. This leads to a very compact algorithm.     

The classical limit of quantum partition functions

We extend Lieb's limit theorem [which asserts that SO(3) quantum spins approachS ² classical spins asL] to general compact Lie groups. We also discuss the classical limit for various continuum systems. To control the compact group case, we discuss coherent states built up from a maximal weight vector in an irreducible representation and we prove that every bounded operator is an integral of projections onto coherent vectors (i.e. every operator has diagonal form).Supported by USNSF Grant MCS-78-01885     

Zeros of partition functions via correlation inequalities

We show analyticity of the pressure for some classical ferromagnetic systems in the region ¦Im ¦ < Re of the external field. The proof, via correlation inequalities, is simpler than existing proofs for the Lee and Yang region {Re 0} and applies, without any approximation procedure, to more general continuous spin variables, e.g., distributed as , where _2n is an arbitrary real number and the other parameters are positive. It also applies directly to plane rotators in the region ¦Im ¦ ¦Re ¦ (Euclidean norms), but the proof will be given in a subsequent article, together with new inequalities between truncated correlation functions.     

Charge partition probabilities in the 32S + 27Al reaction at 37.5 MeV/nucleon analysed using the Boltzmann distribution

We apply the Boltzmann distribution to charge partition probabilities measured with the AMPHORA multidetector in the reaction ³²S + ²⁷Al at 37.5 MeV/ nucleon. Approximate corrections to the data for pre-equilibrium emission are made and modifications to the basic formalism due to detection e?ciency and evaporation are treated explicitly. The data are well reproduced with a temperature of 5.0 MeV and a freeze-out volume which corresponds to densities which are 20 times smaller than normal density.