偏序集上的滤子极大理想

在偏序集上引入并考察了滤子极大理想的概念,证明了相应的存在性定理。引入并考察了伪极大元和伪既约元的概念,利用图表的形式对连续格中各种类型的既约元和素元之间的关系进行了归纳总结,完善了文献《Continuous Lattices and Domains》(作者:G.Gierz,et al)中的一个图表的相关内容,填补了在分配的连续格情形该图表的一个未知内容,部分地回答了该文献中的一个问题。     

分配格的分式扩张

首先借助整数扩充为有理数的办法构作一个分配格对它的滤子的分式扩张,然后用泛映射性质来刻画由任意分配格所构作的分式扩张,最后讨论了这种扩张的理想结构。     

A lattice gas model for thermohydrodynamics

The lattice gas model is extended to include a temperature variable in order to study thermohydrodynamics, the combination of fluid dynamics and heat transfer. The compressible Navier-Stokes equations are derived using a Chapman-Enskog expansion. Heat conduction and convection problems are investigated, including Bénard convection. It is shown that the usual rescaling procedure can be avoided by controlling the temperature.     

Theoretical and numerical analysis for the quasi-continuum approximation of a material particle model

In many applications materials are modeled by a large number of particles (or atoms) where any one of particles interacts with all others. Near or nearest neighbor interaction is expected to be a good simplification of the full interaction in the engineering community. In this paper we shall analyze the approximate error between the solution of the simplified problem and that of the full-interaction problem so as to answer the question mathematically for a one-dimensional model. A few numerical methods have been designed in the engineering literature for the simplified model. Recently much attention has been paid to a finite-element-like quasicontinuum (QC) method which utilizes a mixed atomistic/continuum approximation model. No numerical analysis has been done yet. In the paper we shall estimate the error of the QC method for this one-dimensional model. Possible ill-posedness of the method and its modification are discussed as well.

     

剩余格与FI代数的可嵌入性

给出剩余格可嵌入于全序剩余格的乘积的充要条件。还给出定义在格上的FI代数可嵌入于全序FI代数的乘积的充要条件。     

SCDA for 3D lattice gases with repulsive interaction

The selfconsistent diagram approximation (SCDA) is generalized for three-dimensional lattice gases with nearest neighbor repulsive interactions. The free energy is represented in a closed form through elementary functions. Thermodynamical (phase diagrams, chemical potential and mean square fluctuations), structural (order parameter, distribution functions) as well as diffusional characteristics are investigated. The calculation results are compared with the Monte Carlo simulation data to demonstrate high precision of the SCDA in reproducing the equilibrium lattice gas characteristics. It is shown that similarly to two-dimensional systems the specific statistical memory effects strongly influence the lattice gas diffusion in the ordered states. Received 7 August 2002 / Received in final form 22 January 2003 Published online 24 April 2003     

Optical phonon modes and structure of ZnGa2Se4 and ZnGa2S4

We present the infrared and Raman study of the optical phonon modes of the defective compounds ZnGa₂Se₄ and ZnGa₂S₄. Most of the compounds have been found to crystallize in the thiogallate structure (defect chalcopyrite) with space group where all cations and vacancies are ordered. For some Zinc compounds a partially disordered cationic sublattice with various degrees of cation and vacancy statistical distribution, which lead to the higher symmetry (defect stannite), has been reported. For ZnGa₂Se₄ we have found three modes of A symmetry, showing Raman activity only. In addition, we have observed each five modes of B and E symmetry, showing infrared as well as Raman activity. The number of modes and their symmetry assignment, based on polarized measurements, clearly indicate space group for the investigated crystals of ZnGa₂Se₄.Regarding ZnGa₂S₄ we have found three modes exclusively showing Raman activity (2A⊕1B₁), and only eight modes showing infrared as well as Raman activity (3B₂⊕5E). The assignment of the modes has been derived by analyzing the spectral positions of the vibrational modes in comparison to a number of compounds. From the number and symmetry assignment of the optical phonon modes we confirm that ZnGa₂S₄ most likely crystallizes in space group .     

Finite-Size Effects for the Potts Model with Weak Boundary Conditions

Using the Pirogov–Sinai theory, we study finite-size effects for the ferromagnetic q-state Potts model in a cube with boundary conditions that interpolate between free and constant boundary conditions. If the surface coupling is about half of the bulk coupling and q is sufficiently large, we show that only small perturbations of the ordered and disordered ground states are dominant contributions to the partition function in a finite but large volume. This allows a rigorous control of the finite-size effects for these weak boundary conditions. In particular, we give explicit formulæ for the rounding of the infinite-volume jumps of the internal energy and magnetization, as well as the position of the maximum of the finite-volume specific heat. While the width of the rounding window is of order L ^–d , the same as for periodic boundary conditions, the shift is much larger, of order L ^–1. For strong boundary conditions—the surface coupling is either close to zero or close to the bulk coupling—the finite size effects at the transition point are shown to be dominated by either the disordered or the ordered phase, respectively. In particular, it means that sufficiently small boundary fields lead to the disordered, and not to the ordered Gibbs state. This gives an explicit proof of A. van Enter's result that the phase transition in the Potts model is not robust.     

Phase diagram of the extended hubbard model with pair hopping interaction

A one-dimensional model of interacting electrons with on-site U, nearest-neighbor V, and pair-hopping interaction W is studied at half-filling using the continuum limit field theory approach. The ground state phase diagram is obtained for a wide range of coupling constants. In addition to the insulating spin-density wave (SDW) and charge-density wave (CDW) phases for large U and V, respectively, we identify a bond-charge-density-wave (BCDW) phase W < 0, | U - 2V| < | 2W| and a bond-spin-density-wave (BSDW) for W > 0, | U - 2V| < W. The possibility of bond-located ordering results from the site-off-diagonal nature of the pair-hopping term and is a special feature of the half-filled band case. The BCDW phase corresponding to an enhanced Peierls instability in the system. The BdSDW is an unconventional insulating magnetic phase, characterized by a gapless spin excitation spectrum and a staggered magnetization located on bonds between sites. The general ground state phase diagram including insulating, metallic, and superconducting phases is discussed. A transition to the η-superconducting phase at | U - 2V| ≪ 2t?W is briefly discussed. Received 20 February 2002 / Received in final form 11 April 2002 Published online 19 July 2002     

Size dependence of self-diffusion in the hard-square lattice gas

A striking size dependence of the mean-square displacement of diffusing particles in the two-dimensional lattice gas of hard squares has been observed by Monte Carlo simulation. It is shown that the size effect is due to the formation of a stable cage structure in small lattices when the particle concentration is high. The formation of cages is governed by a new type of percolation problem related to bootstrap percolation.