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。     

Extremality and the global Markov property II: The global markov property for non-FKG maximal Gibbs measures

We give a condition on a Gibbs measure for an attractive Markov specification, which assures extremality and the global Markov property. As an example of application we consider the class of attractive Markov specifications defined on a compact configuration space over a two-dimensional lattice by the interaction Hamiltonians (assumed to have a finite set of periodic ground configurations) satisfying Peierl's condition. We prove that each extremal Gibbs measure for such a specification, at sufficiently low temperature, has the global Markov property.On leave of absence from the Institute of Theoretical Physics, University of Wrocaw, Poland.     

Lattice Compatibility Theory LCT investigations on physical and optical constants of antimony processed antimonite nano-films

Antimonite (Sb₂S₃) thin films have been synthesized through an annealing process in sulfur vapors at 300 °C of Sb thermal evaporated films. Deposited films have been characterized by X-ray diffraction, scanning electron microscopy and UV–vis–NIR spectroscopy. X-ray diagrams of these films have confirms that they were well crystallized in orthorhombic structure and some parameters such as the lattice parameter, crystallite size, microstrain and degree of preferred orientation have been reported and correlated with the effect of crystallite size. Optical properties of Sb₂S₃ films have been characterized by solid-state UV–visible absorption spectroscopy, and the band gap E_g was between 1.75 and 2.23 eV. Moreover, additional opto-thermal investigation and analyses within the framework of the Lattice Compatibility Theory provided plausible explanation for thickness-dependent incorporation of sulfur element inside antimony elaborated matrices.     

Traffic dispersion induced by noise in off-lattice model

We study the dispersion of vehicles induced by speed fluctuation on a single-lane highway under open boundary. We extend the cellular automaton model on one-dimensional lattice to the real-variable model on off-lattice (continuous-in space model) in order to take into account the fluctuation of vehicular speed. Vehicles extend over the highway when moving forward. The characteristics of traffic dispersion are derived. It is shown that vehicular traffic exhibits scaling property. When a vehicle accelerates for following the vehicle ahead, vehicles move forming a cluster without dispersion. The relationship between the width of vehicular cluster and acceleration rate is clarified.     

Lattice-BGK approach to simulating granular flows

Many continuum theories for granular flow produce an equation of motion for the fluctuating kinetic energy density (granular temperature) that accounts for the energy lost in inelastic collisions. Apart from the presence of an extra dissipative term, this equation is very similar in form to the usual temperature equation in hydrodynamics. It is shown how a lattice-kinetic model based on the Bhatnagar-Gross-Krook (BGK) equation that was previously derived for a miscible two-component fluid may be modified to model the continuum equations for granular flow. This is done by noting that the variable corresponding to the concentration of one species follows an equation that is essentially analogous to the granular temperature equation. A simulation of an unforced granular fluid using the modified model reproduces the phenomenon of clustering instability, namely the spontaneous agglomeration of particles into dense clusters, which occurs generically in all granular flows. The success of the continuum theory in capturing the gross features of this basic phenomenon is discussed. Some shear flow simulations are also presented.     

Structural phase transitions in ionic molecular solids

An overview is presented of our studies on the nature of structural instabilities in relatively complex ionic solids. These are based on parameter-free interionic potentials based on the Gordon-Kim modified electron gas formalism extended to molecular ions.

We describe the manner in which there emerge from these studies quite general concepts of “size” and “shape” as structural determinants. In particular, we discuss how these, and the approximate symmetries that they can produce, can provide a relatively simple structure-based explanation of the origins of incommensurate phases in these systems. However, we also emphasize that the existence of such symmetries does not guarantee an incommensurate phase. This can only be realized if long-range correlations are sufficiently strong to overcome random local disordering. Thus, either the molecular units are partially linked and/or there exist long-range Coulomb interactions between individual units.     

Dynamical linked cluster expansions with applications to disordered systems

Dynamical linked cluster expansions are linked cluster expansions with hopping parameter terms endowed with their own dynamics. We discuss physical applications to systems with annealed and quenched disorder. Examples are the bond-diluted Ising model and the Sherrington-Kirkpatrick spin glass. We derive the rules and identify the full set of graphs that contribute to the series in the quenched case. This way it becomes possible to avoid the vague extrapolation from positive integer n to n = 0, that usually goes along with an application of the replica trick. Received 13 December 2001 Published online 25 June 2002     

Flow to strong coupling in the two-dimensional Hubbard model

We extend the analysis of the renormalization group flow in the two-dimensional Hubbard model close to half-filling using the recently developed temperature flow formalism. We investigate the interplay of d-density wave and Fermi surface deformation tendencies with those towards d-wave pairing and antiferromagnetism. For a ratio of next nearest to nearest neighbor hoppings, t'/t = - 0.25, and band fillings where the Fermi surface is inside the Umklapp surface, only the d-pairing susceptibility diverges at low temperatures. When the Fermi surface intersects the Umklapp surface close to the saddle points, d-wave pairing, d-density wave, antiferromagnetic and, to a weaker extent, d-wave Fermi surface deformation susceptibilities grow together when the interactions flow to strong coupling. We interpret these findings as indications for a non-trivial strongly coupled phase with short-ranged superconducting and antiferromagnetic correlations, in close analogy with the spin liquid ground state in the well-understood two-leg Hubbard ladder. Received 23 January 2002