格子气的声振荡衰减

采用格子气数值方法模拟了共振腔中气体声振荡衰减过程．计算结果表明：格子气中声振荡衰减的规律和经典理论结果一致；衰减系数随频率增加而减小，并且随密度增加而减小．该结果可以用来说明一些大学统计物理教科书中的一个经典例子存在不完善之处．本中采用了一种新的扭转9-bit格子气模型和并行计算方法，这些结果对今后研究格子气中的热声问题有参考价值．     

The meaning of the Kelly-Lochbaum acoustic-tube model

The scattering equations of the Kelly-Lochbaum segmented tube, including the time-varying extension by Strube, are originally based on the assumption of uniform spatial segments and stepwise time update of the acoustic impedances. Here, it is shown that the same equations can be derived without these assumptions for a nonuniform time-varying tube from the discretization of space and time derivatives by the bilinear z transform or by centered differences along the rotated coordinates ct+/-x. Moreover, the same equations also hold for a chain of lattice circuits (or equivalents) with appropriate parameters, if time derivatives are discretized by the bilinear z transform. These circuits can also be extended to simulate uniform segments of varying length.     

Phase-field models for moving boundary problems: Controlling metastability and anisotropy

We introduce a variant of a recently proposed method of rotated lattices for numerical treatment of moving boundary problems. The usual lattice introduced for numerical computation of phase-field models gives rise to unphysical metastable states and anisotropy. In the present case we rotate and shift the lattice by random angles and fractions of a lattice constant. We show that a twelve point interpolation formula is adequate to keep numerical interpolation errors sufficiently localized. This removes the unphysical metastabilities and makes the model fully isotropic. This is demonstrated by a few example-calculations for dendritic pattern formation.     

Lattice Boltzmann Simulation of Free-Surface Temperature Dispersion in Shallow Water Flows

We develop a lattice Boltzmann method for modeling free-surface temperature dispersion in the shallow water flows. The governing equations are derived from the incompressible Navier-Stokes equations with assumptions of shallow water flows including bed frictions, eddy viscosity, wind shear stresses and Coriolis forces. The thermal effects are incorporated in the momentum equation by using a Boussinesq approximation. The dispersion of free-surface temperature is modelled by an advection-diffusion equation. Two distribution functions are used in the lattice Boltzmann method to recover the flow and temperature variables using the same lattice structure. Neither upwind discretization procedures nor Riemann problem solvers are needed in discretizing the shallow water equations. In addition, the source terms are straightforwardly included in the model without relying on well-balanced techniques to treat flux gradients and source terms. We validate the model for a class of problems with known analytical solutions and we also present numerical results for sea-surface temperature distribution in the Strait of Gibraltar.     

An Asymptotic Limit of a Navier–Stokes System with Capillary Effects

A combined incompressible and vanishing capillarity limit in the barotropic compressible Navier–Stokes equations for smooth solutions is proved. The equations are considered on the two-dimensional torus with well prepared initial data. The momentum equation contains a rotational term originating from a Coriolis force, a general Korteweg-type tensor modeling capillary effects, and a density-dependent viscosity. The limiting model is the viscous quasi-geostrophic equation for the “rotated” velocity potential. The proof of the singular limit is based on the modulated energy method with a careful choice of the correction terms.     

Six-vertex model with rotated boundary conditions

We investigate the six-vertex model on a square lattice rotated through an arbitrary angle with respect to the coordinate axes, a model recently introduced by Litvin and Priezzhev. Auxiliary vertices are used to define an inhomogeneous system which leads to a one-parameter family of commuting transfer matrices. A product of commuting transfer matrices can be interpreted as a transfer matrix acting on zigzag walls in the rotated system. Using an equation for commuting transfer matrices, we calculate their eigenvalues. Finite-size properties of the model are discussed from the viewpoint of the conformal field theory.     

Surface structure of an ultrathin alumina film on Ni3Al(111): a dynamic scanning force microscopy study

The surface structure of an ultrathin alumina film on a Ni3Al(111) substrate has been studied by dynamic scanning force microscopy. The alumina film exhibits a hexagonal superstructure with a lattice parameter of 4.14 nm and a (1/sqrt[3] x 1/sqrt[3])R30 degrees substructure. Two domains rotated by 24 degrees are present. The film is terminated by a hexagonal lattice of oxygen ions with a lattice parameter of 0.293 nm, which is rotated by 30 degrees with respect to the substrate lattice. The nodes of the 4.14 nm superstructure and the 2.39 nm substructure are pinned on points of the substrate lattice, where the surface atomic lattice is almost commensurable. The oxygen lattice is perfectly hexagonal close to these nodes and disordered in the surrounding regions.     

Study of one-dimensional nonlinear lattice

In this article a brief review of the theory of one-dimensional nonlinear lattice is presented. Special attension is paid for the lattice of particles with exponential interaction between nearest neighbors (the Toda lattice). The historical exposition of findings of the model system, basic equations of motion, special solutions, and the general method of solutions are given as chronologically as possible. Some reference to the Korteweg-de Vries equation is also given. The article consists of three parts. Firstly, the idea of dual system is presented. It is shown that the roles of masses and springs of a harmonic linear chain can be exchanged under certain condition without changing the eigenfrequencies. Secondly, the idea is applied to the anharmonic lattice and an integrable lattice with exponential interaction force between adjacent particles is obtained. Special solutions to the equations of motion and general method of solution are shown. In the last part, some studies on the Yang-Yang’s thermodynamic formalism is given.     

Star-triangle relations in the exactly solvable statistical models

A regular method for analysis of lattice spin models with a nearest neighbour interaction is proposed. Star-triangle relations in the form of functional equations are used. Parametric families of transfer matrices commuting due to star-triangle relations are constructed. The eigenvalues of transfer matrices as functions of the spectral parameter are shown to obey two functional equations. The solution of these equations for the maximal eigenvalue yields the partition function of the model. The method is applied for evaluation of the partition function of the critical Potts models, the Ising model, the Ashkin-Teller model equivalent to the eight-vertex model.     

辐射传输的格子Boltzmann模拟

辐射动力学理论是描述辐射传输是重要手段,基于此,本文建立了辐射能和辐射动量守恒方程,并基于Chapman-Enskog多尺度展开方法实现了从辐射传输Boltzmann方程到宏观方程的推导,进而建立了适于一维辐射传输的2分量格子Boltzmann模型。数值结果与精确解吻合较好,表明本文提出的LBM方法具有很好的准确性和稳...     

Kinetics of multilayer adsorption and desorption

The equations describing the nonequilibrium kinetics of multilayer adsorption and desorption are derived. The method is based on a generalized lattice gas model and includes the mobility of adsorbate particles and their mutual interactions. For the two layer adsorbate having the structure of a square lattice the isothermal adsorption characteristics are calculated.     

Lattice model with power-law spatial dispersion for fractional elasticity

A lattice model with a spatial dispersion corresponding to a power-law type is suggested. This model serves as a microscopic model for elastic continuum with power-law non-locality. We prove that the continuous limit maps of the equations for the lattice with the power-law spatial dispersion into the continuum equations with fractional generalizations of the Laplacian operators. The suggested continuum equations, which are obtained from the lattice model, are fractional generalizations of the integral and gradient elasticity models. These equations of fractional elasticity are solved for two special static cases: fractional integral elasticity and fractional gradient elasticity.     

Spatial confinement of ferromagnetic resonances in honeycomb antidot lattices

We report on a theoretical investigation of the magnetic static and dynamic properties of a thin ferromagnetic film with honeycomb lattice of circular antidots using micromagnetic simulations and analytical calculations. The theoretical model is based on the Landau–Lifshitz equations and directly accounts for the effects of the magnetic state nonuniformity. A direct calculation of local dynamic susceptibility tensor yields that the resonance spectra consist of four different quasi-uniform modes of the magnetization precession related to the confinement of magnetic domains by the hole mesh. Three of four resonant modes follow a two-fold variation with respect to the in-plane orientation of the applied magnetic field. The easy axes of these modes are mutually rotated by 60° and combine to yield the apparent six-fold configurational anisotropy. Additionally, a mode with intrinsic six-fold symmetry behavior exists, as well. Micromagnetic calculations of the local dynamic susceptibility tensor allow identifying the magnetic unit cell areas/domains responsible for each resonance mode.     

A multiple-relaxation-time lattice Boltzmann method for high-speed compressible flows

This paper presents a coupling compressible model of the lattice Boltzmann method. In this model, the multiplerelaxation-time lattice Boltzmann scheme is used for the evolution of density distribution functions, whereas the modified single-relaxation-time(SRT) lattice Boltzmann scheme is applied for the evolution of potential energy distribution functions. The governing equations are discretized with the third-order Monotone Upwind Schemes for scalar conservation laws finite volume scheme. The choice of relaxation coefficients is discussed simply. Through the numerical simulations,it is found that compressible flows with strong shocks can be well simulated by present model. The numerical results agree well with the reference results and are better than that of the SRT version.     

Comparison between lattice Boltzmann method and Navier–Stokes high order schemes for computational aeroacoustics

Computational aeroacoustic (CAA) simulation requires accurate schemes to capture the dynamics of acoustic fluctuations, which are weak compared with aerodynamic ones. In this paper, two kinds of schemes are studied and compared: the classical approach based on high order schemes for Navier–Stokes-like equations and the lattice Boltzmann method. The reference macroscopic equations are the 3D isothermal and compressible Navier–Stokes equations. A Von Neumann analysis of these linearized equations is carried out to obtain exact plane wave solutions. Three physical modes are recovered and the corresponding theoretical dispersion relations are obtained. Then the same analysis is made on the space and time discretization of the Navier–Stokes equations with the classical high order schemes to quantify the influence of both space and time discretization on the exact solutions. Different orders of discretization are considered, with and without a uniform mean flow. Three different lattice Boltzmann models are then presented and studied with the Von Neumann analysis. The theoretical dispersion relations of these models are obtained and the error terms of the model are identified and studied. It is shown that the dispersion error in the lattice Boltzmann models is only due to the space and time discretization and that the continuous discrete velocity Boltzmann equation yield the same exact dispersion as the Navier–Stokes equations. Finally, dispersion and dissipation errors of the different kind of schemes are quantitatively compared. It is found that the lattice Boltzmann method is less dissipative than high order schemes and less dispersive than a second order scheme in space with a 3-step Runge–Kutta scheme in time. The number of floating point operations at a given error level associated with these two kinds of schemes are then compared.     

The concept of “incompatibility” for a simple model of a crystal lattice

A system of equations is derived for a simple model of a crystal lattice disturbed by a dislocation. The model is represented by two rows of atoms. The system of equations is analogous to that describing a singular dislocation in the theory of the continuous distribution of crystal imperfections. The method of solving the derived system of equations is given.     

Elastic Constants of Superconducting MgB2 from Molecular Dynamics Simulations with Shell Model

The elastic constants of superconducting MgB₂ are calculated using a molecular dynamics method (MD) with shell model. The lattice parameters, five independent elastic constants, equations of state (EOS), Debye temperature, and bulk modulus of MgB₂ are obtained. Meanwhile, the dependence of the bulk modulus B, the lattice parameters a and c, and the unit cell volume V on the applied pressure are presented. It is demonstrated that the method introduced here can well reproduce the experimental results with a reasonable accuracy.     

用格子Boltzmann模型模拟可压缩完全气体流动

采用一种新的格子Boltzmann模型模拟超音速流动。在这种模型中,粒子的速度不受限制,可以取得很广。而平衡分布函数的支集却相对集中,使模型得以简化。粒子速度的这种自适应特性允许流体以较高的马赫数流动。通过引入粒子的势能使得该模型适用于具有任意比热比的完全气体。利用Chapman-Enskog方法,从BGK型Boltzmann方程推导出Navier-Stokes方程。在六边形网格上模拟了马赫数为3的前台阶绕流,得到了合理的结果。     

二维棋盘格子复式晶格的完全光子带隙研究

设计了一种棋盘格子复式晶格的二维光子晶体：在二维正方形格子中，把截面为正方形的柱子旋转45°，同时在每个原胞中心引入一个圆形截面的柱子构成的光子晶体结构. 用平面波展开计算棋盘格子复式晶格的完全光子带隙，结果表明：棋盘格子复式晶格的完全光子带隙的Δω/ω比值几乎是普通棋盘格子的5倍，完全光子带隙的个数也增加. 与其他复式结构相比较，发现其最佳的Δω/ω比值是一类粗锐复合结构光子晶体的2.1倍. 关键词： 二维光子晶体 复式晶格 完全光子带隙     

一个镶嵌稀释双键Potts模型的严格解

本文研究在一个镶嵌正方形格子上的一个稀释双键Potts模型,模型中既包含铁磁作用,也包含反铁磁作用。得到了非常一般的和某些特殊情况下的临界行为的严格解及相图。特别是,我们的结果中展示出在二维情况下,当q≤3时,稀释反铁磁Potts模型也如同正规(非稀释)模型一样,存在着特殊的低温相。 关键词：