Enumeration of plane partitions and the algebraic Bethe anzatz

We establish a relation between an exactly solvable boson model and plane partitions, i.e., three-dimensional Young diagrams enclosed in a box of finite size, which allows representing the partition generating functions as correlation functions of an integrable model and deriving the MacMahon formulas for enumerating partitions using the quantum inverse scattering method. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 2, pp. 193–203, February, 2007.     

Soluble models for dynamics driven by a super-diffusive noise

We explicitly discuss scalar Langevin type of equations where the deterministic part is linear, but where the integrated noise source is a non-linear diffusion process exhibiting superdiffusive behavior. We calculate transient and stationary probabilities and study the possibility of noise induced transitions from a unimodal to a bimodal probability shape. Illustrations from finance and dynamical systems are given.     

结构可靠度分析非线性抗力函数线性化问题的研究

本文研究了非线性抗力函数线性化处理方法，以简化极限状态方程代替实际极限 状态方程对可靠度分析的影响。文中以钢筋混凝土两种实际构件为例，用实际极限状 态方程作了可靠度计算，并与简化方程作了对比分析．     

Structural and electrical characterization of SxSe100−x thin films

Thin films of samples of the glassy S_xSe_100−x system with 0 ≤ x ≤ 7.28 have been prepared by thermal evaporation technique at room temperature (300 K). X-ray investigations show that the structure of pure selenium (Se) does change seriously by the addition of small amount of sulphur S ≤7.28%. The lattice parameters were determined as a function of sulphur content. Results of differential thermal analysis (DTA) of the glassy compositions of the system S_xSe_100−x were discussed. The characteristic temperatures (T_g, T_c and T_m) were evaluated. Dark electrical resistivities, ρ, of S_xSe_100−x thin films with different thicknesses from 100 to 500 nm, were measured in the temperature range from 300 to 423 K. Two distinct linear parts with different activation energies were observed. The variation of electrical resistivity of examined compositions has been discussed as a function of the film thickness, temperature and the sulphur content. The application of Mott model for the phonon assisted hopping of small polarons gave the same two activation energies obtained from the resistivity temperature calculations.     

Two-Dimensional Coulomb Systems on a Surface of Constant Negative Curvature

We study the equilibrium statistical mechanics of classical two-dimensional Coulomb systems living on a pseudosphere (an infinite surface of constant negative curvature). The Coulomb potential created by one point charge exists and goes to zero at infinity. The pressure can be expanded as a series in integer powers of the density (the virial expansion). The correlation functions have a thermodynamic limit, and remarkably that limit is the same one for the Coulomb interaction and some other interaction law. However, special care is needed for defining a thermodynamic limit of the free energy density. There are sum rules expressing the property of perfect screening. These generic properties can be checked on the Debye–Hückel approximation, and on two exactly solvable models, the one-component plasma and the two-component plasma, at some special temperature.     

An investigation of the 2D attractive Hubbard model

We present an investigation of the 2D attractive Hubbard model, considered as an effective model relevant to superconductivity in strongly interacting electron systems. We use both hybrid Monte-Carlo simulations and existing hopping parameter expansions to explore the low temperature domain. The increase of the static S-wave pair correlation with decreasing temperature, which depends weakly on the band filling in the explored temperature range, is analyzed in terms of an expected Kosterlitz-Thouless superconducting transition. Using both our data and previously published results, we show that the evidence for this transition is weak: If it exists, its temperature is very low. The number of unpaired electrons remains nearly constant with temperature at fixed attractive potential strength. In contrast, the static magnetic susceptibility decreases fast with temperature, and cannot be related only to pair formation. We introduce a method by which the Padé approximants of the existing series for the susceptibility give sensible results down to rather low temperature region, as shown by comparison with our numerical data. Received: 30 October 1996 / Revised: 23 October 1997 / Accepted: 29 January 1998     

Monte Carlo simulation of cluster kinetics in three-dimensional Ising model

Simulations in lattices of size 100³ at the critical point of the three-dimensional Glauber kinetic Ising model indicate that the 1935 Becker-Doring equation no longer works there: The growth rates decay in time. These conclusions confirm those in two dimensions.     

Discrete storage processes and their Poisson flow and fluid flow approximations

Consider discrete storage processes that are modulated by environmental processes. Environmental processes cause interruptions in the input and/or output processes of the discrete storage processes. Due to the difficulties encountered in the exact analysis of such discrete storage systems, often Poisson flow and/or fluid flow models with the same modulating environmental processes are proposed as approximations for these systems. The analysis of Poisson flow and fluid flow models is much easier than that of the discrete storage processes. In this paper we give sufficient conditions under which the content of the discrete storage processes can be bounded by the Poisson flow and the fluid flow models. For example, we show that Poisson flow models and the fluid flow models developed by Kosten (and by Anick, Mitra and Sondhi) can be used to bound the performance of infinite (finite) source packetized voice/data communication systems. We also show that a Poisson flow model and the fluid flow model developed by Mitra can be used to bound the buffer content of a two stage automatic transfer line. The potential use of the bounding techniques presented in this paper, of course, transcends well beyond these examples.Supported in part by NSF grant DMS-9308149.     

An evolutionary method for optimization of plate buckling resistance

Optimization of plate buckling resistance is very complicated, because the in-plane stress resultants in the prebuckled state of a plate are functions of thickness distribution. This paper discusses the problem of finding the optimum thickness distribution of isotropic plate structures, with a given volume and layout, that would maximise the buckling load. A simple numerical method using the finite-element analysis is presented to obtain the optimum thickness distribution. Optimum designs of compression-loaded rectangular plates with different boundary conditions and plate aspect ratios are obtained by using the proposed method. Optimum designs from earlier studies and the methods of buckling analysis used to attain these results are discussed and compared with the designs from the proposed method. This paper also examines the reliability of the optimality criterion generally used for plate buckling optimization, which is based on the uniform strain energy density.     

A numerical method to compute exactly the partition function with application toZ(n) theories in two dimensions

I present a new method to exactly compute the partition function of a class of discrete models in arbitrary dimensions. The time for the computation for ann-state model on anL ^d lattice scales like . I show examples of the use of this method by computing the partition function of the 2D Ising and 3-state Potts models for maximum lattice sizes 10×10 and 8×8, respectively. The critical exponentsv and and the critical temperature one obtains from these are very near the exactly known values. The distribution of zeros of the partition function of the Potts model leads to the conjecture that the ratio of the amplitudes of the specific heat below and above the critical temperature is unity.