自旋玻璃的二维随机格点模型模拟

本文对自旋玻璃CuMn进行了二维随机格点模型的蒙特卡罗研究。同时提出了一种快速产生二维随几格点的方法。用这个模型对CuMn进行了磁化热,磁化率等物理量的模拟测量,并对模型的有限大小问题进行了探讨。     

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     

二维三角格点系统中的拓扑陈数

利用紧束缚模型对二维三角周期格点中各能带的陈数分布进行研究.通过严格对角化方法得到体系能量本征值和对应的本征态,再利用Kubo公式计算出量子化的霍尔电导、态密度及各扩展态对应的陈数.在傅里叶变换下将哈密顿量转换到k空间从而得到体系的能谱分布.研究表明：次近邻格点之间的跳跃积分t'的不同取值影响体系各能带对应的陈数分布,计算得到当t'=1/2时体系三个能带从低到高对应的陈数分布为{-4,5,-1},t'=-1/2时其对应陈数分布变化为{2,-4,2},而t'=±1/4时对应的陈数分布都为{2,-1,-1}.同时发现：能谱帯隙的宽度和对应霍尔平台的宽度一致,并且k空间的能带越平坦,其对应的在霍尔电导跳跃处的态密度峰就越高越尖锐,而该处霍尔电导跳跃就越陡峭.     

一种颗粒底部压力不趋向饱和的粮仓系统

随着深度的增加竖直圆筒容器中的颗粒物质会把自己的重量逐渐转移到容器的侧墙壁上,使容器底部的压力出现不随筒中颗粒材料高度的增加而增加的饱和现象.但值得注意的是,圆筒中的颗粒柱体并不总是表现为这个称为粮仓效应的力学状态.例如当改变侧墙壁的力学环境使其无法承担颗粒的重量时,柱底部的压力显然将随其高度的增加而线性地增加.本文分析讨论了Janssen模型假设对这类处于静力平衡下,但违反粮仓效应的颗粒系统的行为预测. 关键词： 颗粒物质 粮仓 静摩擦 应力     

格点Schwinger模型中<ψψ>的变分计算

本文利用格点规范理论的变分方法,计算Schwinger模型中Naive格点费米子的真空凝聚参数<ψψ>,得到较好的标度行为.     

格点QCD中有限体积下形状因子的内插计算

在格点QCD的框架下,讨论了计算强子的形状因子的过程中,有限体积效应对所得结果的影响,并且给出了计算连续动量空间上形状因子数值的内插算法.本文以π介子的形状因子为例,介绍了从格点QCD中得到的三点关联函数出发计算π介子的形状因子的方法,并说明有限体积效应使得计算结果只能在分立动量上给出.本文探讨了一种保持旋转对称性的内...     

二维晶格颗粒堆积中侧壁的压力分布与转向系数

颗粒物质是大量颗粒聚集在一起的软凝聚态物质, 其微观结构与宏观力学性质的联系非常复杂. 本文用实验的方法观测了二维竖直晶格堆积颗粒, 在竖直方向外加正压力作用下其侧壁的受力分布情况, 根据实验结果详细讨论和分析了颗粒体系中正压力的转向行为. 实验结果表明: 在缓慢压缩颗粒体系的过程中, 正压力的变化呈现非线性和线性两段不同的规律; 对于确定堆积结构的颗粒体系, 竖直方向施加的正压力通过颗粒力链转向, 且水平方向不同堆积高度处所受压力值不同, 中部的压力大于顶部和底部的压力; 转向系数k的饱和值随堆积角θ 的增大而减小. 对颗粒堆的几何结构与受力情况进行分析, 给出了转向系数与堆积角之间的数学表达式, 理论值与实验值符合较好.     

2+1维U(1)格点规范场论中真空态的研究

对2+1维U(1)格点规范场论真空态进行研究,仔细推导出连续极限下真空谈函数中参数μ₀和μ₂的普适表达式,并用截断本征方程法进行数值计算.     

基于边缘方向投影的棋盘格角点亚像素细化

随着视觉测量技术在工程中的推广,越来越多的视觉标定和测量需在车间现场由非专业人员执行,这会造成拍摄的棋盘格图像中包含较多的噪声。为了实现噪声下棋盘格角点稳健、精确的亚像素细化,提出一种基于边缘方向投影的棋盘格角点亚像素细化方法。首先基于非极大值抑制算法计算初始边缘方向,然后基于最小加权二乘拟合法细化边缘方向,最后基于边缘方向最大投影细化棋盘格角点的亚像素坐标。结果表明：在高质量的棋盘格图像中,所提方法的棋盘格边长测量偏差的最大值均小于0.021 mm,棋盘格边长测量偏差的均值均小于0.006 mm;在高斯噪声和角点污染的棋盘格图像中,所提方法的棋盘格边长测量偏差的最大值均小于0.05 mm,棋盘格边长测量偏差的均值均小于0.02 mm。     

巨正则量子Monte Carlo方法和二维Hubbard模型的研究

用巨正则量子Monte Carlo方法,计算了二维单带Hubbard模型的局域磁矩、磁化率、交错磁化率和内能等物理量.结果表明,用巨正则量子Monte Carlo方法能够统一地研究Hubbard模型的关联强度从弱至强区域的性质,它是处理强关联多体系统的有效方法.     

应力未饱和粮仓系统中器壁与颗粒的摩擦阻力

对于仓壁不固定的粮仓系统,其底部压力会随颗粒高度线性增加.由于没有Janssen应力饱和现象,其力学状态与通常粮仓系统显然不同.通过上拉和下压这种应力未饱和粮仓系统的仓壁,实验研究了不同顶部负载时颗粒介质与仓壁的最大静摩擦阻力.结果显示阻力随颗粒质量的增加在上拉时呈线性增长关系,但在下压时呈指数增长关系,下压阻力强度比上拉时大一个量级以上.此外阻力与顶部负载呈线性变化关系.这些测量很好地符合了基于应力转向比为常数的假设（即Janssen假设）下给出的连续力学理论计算,表明该假设对于此应力未饱和粮仓系统依然适用. 关键词： 颗粒物质 粮仓 静摩擦 应力转向比     

二维成分无序颗粒体系中法向力的分布

运用离散元法研究成分无序体系中法向力的几率分布,该体系由两种不同刚度系数的颗粒规则堆积而成, 体系的无序程度由缺陷率控制.模拟发现,无缺陷时体系的力网几乎是均匀的,而有缺陷时力网变得不均匀. 提出了主法向力与次法向力的概念,并对它们分别进行统计;随着缺陷率的增加,主法向力的分布经历了比较复杂的变化过程,而次法向力总是指数型分布.模拟结果表明,缺陷率较小时成分无序体系中的法向力分布与随机堆积体系很不相同,而缺陷率较大时得到了与随机堆积类似的结果.这些结果有助于理解力网的不均匀性与体系无序性的关系.     

A Remark on High Temperature Polymer Expansion for Lattice Systems with Infinite Range Pair Interactions

We consider the standard high temperature-small activity polymer expansion for lattice spin systems and show how, in many cases using a tree graph equality, various classical results may be improved in some cases or at least proved in a much simpler way.     

Lattice Boltzmann model for combustion and detonation

In this paper we present a lattice Boltzmann model for combustion and detonation. In this model the fluid behavior is described by a finite-difference lattice Boltzmann model by Gan et al. [Physica A, 2008, 387: 1721]. The chemical reaction is described by the Lee-Tarver model [Phys. Fluids, 1980, 23: 2362]. The reaction heat is naturally coupled with the flow behavior. Due to the separation of time scales in the chemical and thermodynamic processes, a key technique for a successful simulation is to use the operator-splitting scheme. The new model is verified and validated by well-known benchmark tests. As a specific application of the new model, we studied the simple steady detonation phenomenon. To show the merit of LB model over the traditional ones, we focus on the reaction zone to study the non-equilibrium effects. It is interesting to find that, at the von Neumann peak, the system is nearly in its thermodynamic equilibrium. At the two sides of the von Neumann peak, the system deviates from its equilibrium in opposite directions. In the front of von Neumann peak, due to the strong compression from the reaction product behind the von Neumann peak, the system experiences a sudden deviation from thermodynamic equilibrium. Behind the von Neumann peak, the release of chemical energy results in thermal expansion of the matter within the reaction zone, which drives the system to deviate the thermodynamic equilibrium in the opposite direction. From the deviation from thermodynamic equilibrium, Δ _m *, defined in this paper, one can understand more on the macroscopic effects of the system due to the deviation from its thermodynamic equilibrium.     

Analysis of stresses in two-dimensional isostatic granular systems

We analyze a recently proposed continuous model for stress fields that develop in two-dimensional purely isostatic granular systems. We present a reformulation of the field equations, as a linear first-order hyperbolic system, and show that it is very convenient both for analysis and for numerical computations. Our analysis allows us to predict quantitatively the formation and directions of stress paths and, from these, trajectories and magnitudes of force chains, given the structure in terms of a particular fabric tensor. We further predict quantitatively changes of stresses along the paths, as well as leakage and branching of stress from the main paths into the cones that they make in terms of the fabric tensor. Numerical computations in both Cartesian and cylindrical coordinates verify the analytic results and illustrate the rich behavior discovered. All the phenomena predicted by our solutions have been observed experimentally, suggesting that stresses in isostatic systems can form a base model for a more developed stress theory in granular materials.     

格子Boltzmann方法应用于气动声学研究

应用格子Boltzmann方法(LBM)对不同类型的气动声学问题进行数值研究.通过模拟一维平面声波和二维点源声波的传播,得到沿传播方向的声压脉动,其振荡幅值和衰减趋势与理论值相吻合.其次进行声波衍射和干涉现象的数值模拟.最后,模拟处于流场中运动声源辐射声场的多普勒效应.模拟结果说明LBM方法能较好地模拟低马赫数下的声学问题,包括声压脉动的传播,声波的波动特性以及流动与声波间的相互作用.     

Exact Potts Model Partition Functions for Strips of the Honeycomb Lattice

We present exact calculations of the Potts model partition function Z(G,q,v) for arbitrary q and temperature-like variable v on strip graphs G of the honeycomb lattice for a variety of transverse widths equal to L _y vertices and for arbitrarily great length, with free longitudinal boundary conditions and free and periodic transverse boundary conditions. These partition functions have the form , where m denotes the number of repeated subgraphs in the longitudinal direction. We give general formulas for N _Z,G,j for arbitrary L _y . We also present plots of zeros of the partition function in the q plane for various values of v and in the v plane for various values of q. Plots of specific heat for infinite-length strips are also presented, and, in particular, the behavior of the Potts antiferromagnet at is investigated.     

Lattice Boltzmann simulation of fluid flows in two-dimensional channel with complex geometries

Boundary conditions (BCs) play an essential role in lattice Boltzmann (LB) simulations. This paper investigates several most commonly applied BCs by evaluating the relative L₂-norm errors of the LB simulations for two-dimensional (2-D) Poiseuille flow. It is found that the relative L₂-norm error resulting from FHML's BC is smaller than that from other BCs as a whole. Then, based on the FHML's BC, it formulates an LB model for simulating fluid flows in 2-D channel with complex geometries. Afterwards, the flows between two inclined plates, in a pulmonary blood vessel and in a blood vessel with local expansion region, are simulated. The numerical results are in good agreement with the analytical predictions and clearly show that the model is effective. It is expected that the model can be extended to simulate some real biologic flows, such as blood flows in arteries, vessels with stenosises, aneurysms and bifurcations, etc.     

Uniqueness Problem for Quantum Lattice Systems with Compact Spins

Quantum lattice systems with compact spins and nearest-neighbour interactions are considered. Uniqueness of the corresponding Euclidean Gibbs states is proved uniformly with respect to the temperature, in the case where the particles have a sufficiently small mass.     

格点核子-核子势在核物质中的相对论效应(英文)

利用最新的格点核子-核子势研究了核物质中的相对论效应。通过此格点核子-核子势场,首先我们构建一个包括π介子,σ介子以及ω介子的单玻色子交换势。势场中的介子-核子耦合常数以及截断动量通过拟合格点核力得到的核子-核子散射相移确定。随后采用非常成功的第一性原理多体计算方法Brueckner-Hartree-Fock模型,计算了核物质的基本性质。发现对称核物质的状态方程以及饱和性质在非相对论框架和相对论框架中有很明显的区别。在格点核力中,该相对论效应对核物质的结合能提供吸引的贡献。这与采用传统的核力计算得到的结果是相反的。The relativistic effect in nuclear matter is investigated with the latest lattice nucleon-nucleon (NN) potential. A one-boson-exchange potential (OBEP) including three mesons, pion, σ meson and ω meson was constructed based on the lattice NN potential. The meson-nucleon coupling constants and cutoff momentums are determined by fitting the phase shifts of NN scattering from lattice NN potential. The properties of nuclear matter with this OBEP from lattice potential are calculated by one very successful ab initio many-body method, Brueckner-Hartree-Fock model. The equations of state and saturation properties of symmetric nuclear matter present very obvious different behaviors in non-relativistic and relativistic frameworks. The relativistic effect plays attractive contributions with the components of S and D waves in lattice NN potential, which is opposite comparing to the relativistic effect from the conventional NN potential.