Effects of Field Orientation on the Driven Lattice Gas

Steady states of the driven lattice gas (DLG) on triangular, hexagonal and square lattices with the field at several fixed orientations to the principal lattice vectors were studied by Monte Carlo simulation. In most cases a strong field suppressed change to a low-temperature ordered phase. On each lattice, one field orientation that caused nonequilibrium ordering was identified. On triangular and hexagonal lattices, dependence of energy and anisotropy on field strength was studied at those orientations. Anisotropic ordering along the field developed at intermediate temperatures under weak fields. Partial ordering along the field persisted to low temperature under strong fields.     

An improvement of the lattice theory of dislocation for a two-dimensional triangular crystal

The structure of dislocation in a two-dimensional triangular crystal has been studied theoretically on the basis of atomic interaction and lattice statics. The theory presented in this paper is an improvement to that published previously.Within a reasonable interaction approximation, a new dislocation equation is obtained, which remedies a fault existing in the lattice theory of dislocation. A better simplification of non-diagonal terms of the kernel is given. The solution of the new dislocation equation asymptotically becomes the same as that obtained in the elastic theory, and agrees with experimental data. It is found that the solution is formally identical with that proposed phenomenologically by Foreman et al, where the parameter can be chosen freely, but cannot uniquely determined from theory. Indeed, if the parameter in the expression of the solution is selected suitably, the expression can be well applied to describe the fine structure of the dislocation.     

Diffusion in Lorentz lattice gas cellular automata: The honeycomb and quasi-lattices compared with the square and triangular lattices

We study numerically the nature of the diffusion process on a honeycomb and a quasi-lattice, where a point particle, moving along the bonds of the lattice, scatters from randomly placed scatterers on the lattice sites according to strictly deterministic rules. For the honeycomb lattice fully occupied by fixed rotators two (symmetric) isolated critical points appear to be present, with the same hyperscaling relation as for the square and the triangular lattices. No such points appear to exist for the quasi-lattice. A comprehensive comparison is made with the behavior on the previously studied square and triangular lattices. A great variety of diffusive behavior is found, ranging from propagation, superdiffusion, normal, quasi-normal, and anomalous, to absence of diffusion. The influence of the scattering rules as well as of the lattice structure on the diffusive behavior of a point particle moving on the all lattices studied so far is summarized.     

晶格振动简正坐标的具体表述及其讨论

在明确简正坐标定义的基础上，分析了一维单原子链简正坐标的具体表述，并给出了一种新的表达式。     

求解非线性Poisson方程的格子演化算法

非线性Poisson方程在化学、化工及生物等领域有着广泛的应用。本文发展了一种基于格子演化的新算法-格子Poisson方法(LPM),并且给出了Dirichlet边界条件和Neumann边界条件的实现方法。本方法不需要对方程进行线化处理,直接求解非线性方程,适用范围广泛。Dirichlet边界与Neumann边界的数值模拟结果与多重网格法等结果符合很好,验证了该方法在求解非线性Poisson方程的正确性与有效性。本方法非常适合并行计算,并方便扩展到三维情况。     

Wave models of non-crystallographic structures

Combinations of oscillations with incommensurate periods are utilized to generate discrete planar structures with non-crystallographic symmetries. Some previously known tilings and results are reconsidered in this context. A new kind of decagonal tiling, its relations with the Penrose tilings, and some experimental reports are discussed.     

Explicit solutions for a nonlinear model on the honeycomb and triangular lattices

We study a simple nonlinear model de?ned on the honeycomb and triangular lattices. We propose a bilin-earization scheme for the ?eld equations and demonstrate that the resulting system is closely related to the well-studied integrable models, such as the Hirota bilinear difference equation and the Ablowitz-Ladik system. This result is used to derive the two sets of explicit solutions: the N-soliton solutions and ones constructed of the Toeplitz determinants.     

光频支格波对晶格热容的贡献

讨论晶格的光频支格波对晶格热容的贡献，得到了这部分的热容的表达式。在低温极限情况下,光频支格波对晶格热容的贡献很小，可以忽略，只有频率较低的声频支格波对晶格热容有重要贡献；在高温情况下，复式 和中光频支格波对晶格热容有重要贡献，高温情况下的结果与杜隆－珀蒂定律给出的经典数值一致，该定律在高温时与实际实验符合得很好。     

Status of the lattice and τ decay determinations of α_s

The two highest precision determinations of α s (M 2 Z ),that based on the analysis of short-distancesensitive lattice observables,and that based on an analysis of hadronic τ decay data,have,until very recently,given results which are not in good agreement.I review new versions of these analyses which bring the two determinations into excellent agreement,and discuss prospects for additional future improvements.     

Review: Gas of Wormholes: A Possible Ground State of Quantum Gravity

In order to gain insight into the possible Ground State of Quantized Einstein's Gravity, we have derived a variational calculation of the energy of the quantum gravitational field in an open space, as measured by an asymptotic observer living in an asymptotically flat space-time. We find that for Quantum Gravity (QG) it is energetically favourable to perform its quantum fluctuations not upon flat space-time but around a "gas" of wormholes of mass m _p, the Planck mass (m _p 10¹⁹ GeV) and average distance l _p, the Planck length a _p(a _p 10^–33 cm). As a result, assuming such configuration to be a good approximation to the true Ground State of Quantum Gravity, space-time, the arena of physical reality, turns out to be well described by Wheeler's quantum foam and adequately modeled by a space-time lattice with lattice constant l _p, the Planck lattice.     

Discrete breathers in a two-dimensional Morse lattice with an on-site harmonic potential

Two-dimensional discrete breathers in a two-dimensional Morse lattice with on-site harmonic potentials are investigated. Under the harmonic approximation, the linear dispersion relations for the triangular and the square lattices are discussed. The existence of discrete breathers in a two-dimensional Morse lattice with on-site harmonic potentials is proved by using local inharmonic approximation and the numerical method. The localization and amplitude of two-dimensional discrete breathers correlate closely to the Morse parameter a and the on-site parameter κ.     

Dimer problem on the cylinder and torus

We obtain explicit expressions of the number of close-packed dimers and entropy for three types of lattices (the so-called 8.8.6, 8.8.4, and hexagonal lattices) with cylindrical boundary condition and the entropy of the 8.8.6 lattice with toroidal boundary condition. Our results and the one on 8.8.4 and hexagonal lattices with toroidal boundary condition by Salinas and Nagle [S.R. Salinas, J.F. Nagle, Theory of the phase transition in the layered hydrogen-bonded SnCl²⋅2H₂O crystal, Phys. Rev. B 9 (1974) 4920-4931] and Wu [F.Y. Wu, Dimers on two-dimensional lattices, Inter. J. Modern Phys. B 20 (2006) 5357-5371] imply that the 8.8.6 (or 8.8.4) lattices with cylindrical and toroidal boundary conditions have the same entropy whereas the hexagonal lattices have not. Based on these facts we propose the following problem: under which conditions do the lattices with cylindrical and toroidal boundary conditions have the same entropy?     

Application of Rational Expansion Method for Differential-Difference Equation

In this paper, we applied the rational formal expansion method to construct a series of soliton-like and period-form solutions for nonlinear differential-difference equations. Compared with most existing methods, the proposed method not only recovers some known solutions, but also finds some new and more general solutions. The efficiency of the method can be demonstrated on Toda Lattice and Ablowitz-Ladik Lattice.     

Ferromagnetism in the Hubbard model: instability of the Nagaoka state on the triangular,honeycomb and kagome lattices

In order to analyse the lattice dependence of ferromagnetism in the two-dimensional Hubbard model we investigate the instability of the fully polarised ferromagnetic ground state (Nagaoka state) on the triangular, honeycomb and kagome lattices. We mainly focus on the local instability, applying single spin flip variational wave functions which include majority spin correlation effects. The question of global instability and phase separation is addressed in the framework of Hartree-Fock theory. We find a strong tendency towards Nagaoka ferromagnetism on the non-bipartite lattices (triangular, kagome) for more than half filling. For the triangular lattice we find the Nagaoka state to be unstable above a critical density of n = 1.887 at U = ∞, thereby significantly improving former variational results. For the kagome lattice the region where ferromagnetism prevails in the phase diagram widely exceeds the flat band regime. Our results even allow the stability of the Nagaoka state in a small region below half filling. In the case of the bipartite honeycomb lattice several disconnected regions are left for a possible Nagaoka ground state.     

对流扩散方程的格点模型

推广流体力学的格点法解一般的数学物理方程,建立了一维对流扩散方程的简单和复杂的格点模型,并利用此模型模拟了几种不同初边值条件下的对流扩散方程     

On the area of square lattice polygons

We consider the generating function of self-avoiding square lattice polygons grouped by both area and perimeter. The generating function for polygons of arean is found to diverge atx _c =0.251834, with an exponent of zero. The mean perimeter of polygons with arean is found to be proportional ton, while the mean area of polygons with perimetern is found to be proportional ton ^1.5.     

长程作用下Gauss系统的临界温度

利用傅里叶变换的方法，严格求解了d维(d=1，2和3)超立方晶格和二维三角晶格上具有长程 相互作用的Gauss模型(这里考虑的长程作用有幂指数、指数和对数三种形式).得到了这些情 况下系统的临界点(温度)，并对不同形式的长程作用对临界点的影响进行了比较.结果表明 ，长程相互作用的存在，使得系统的临界温度有了一定程度的升高，它们对系统临界温度的 影响与其衰减的快慢有关. 关键词： Gauss模型 临界点 超立方晶格 三角晶格     

Quantum diffusion in semi-infinite periodic and quasiperiodic systems

This paper studies quantum diffusion in semi-infinite one-dimensional periodic lattice and quasiperiodic Fibonacci lattice. It finds that the quantum diffusion in the semi-infinite periodic lattice shows the same properties as that for the infinite periodic lattice. Different behaviour is found for the semi-infinite Fibonacci lattice. In this case, there are still C（t） - t^-δ and d（t） - t^β. However, it finds that 0 〈δ 〈 1 for smaller time, and δ = 0 for larger time due to the influence of surface localized states. Moreover, β for the semi-infinite Fibonacci lattice is much smaller than that for the infinite Fibonacci lattice. Effects of disorder on the quantum diffusion are also discussed.     

纳米晶体线的晶格动力学格林函数及晶格振动

通过求解差分方程,推导了纳米晶体线的晶格动力学格林函数,分析了其晶格振动,并推导了声子数表象中的原子位移及晶格振动哈密顿公式.研究结果表明,纳米晶体线的晶格振动能带分裂为一系列的子带,格波只能沿纳米晶体线的纵向传播,沿纳米晶体线的横截面只存在驻波.     

Surface adsorption and collapse transition of linear polymer chains

The critical behaviour of surface adsorption and collapse transition of a flexible self-attracting self-avoiding polymer chain is examined. Depending upon the underlying lattice and space dimensionality, phase diagrams that exhibit many different universality domains of critical behavior are found. We discuss these phase diagrams and the values of the critical exponents found from different theoretical methods.