三维精确可解统计模型──Baxter–Bazhanov模型的可积性条件

从手征Potts模型推导出三维精确可解Baxter-Bazhanov模型的“可逆性”及“星一方”关系,从而说明其可积性条件──四面体方程是手征Potts模型星──三角关系的一个结论.若把玻尔兹曼权参变数表示为Zamolodchikov角变量形式,其附加条件自然成立.值得指出的是,由本文处理方法可以得出三维可解统计模型的星-三角关系,它包含了Bazhanov和Baxter的结论.     

三维精确可解统计模型──Baxter－Bazhanov模型的可积性条件

从手征Ｐｏｔｔｓ模型推导出三维精确可解Ｂａｘｔｅｒ－Ｂａｚｈａｎｏｖ模型的“可逆性”及“星一方”关系,从而说明其可积性条件──四面体方程是手征Ｐｏｔｔｓ模型星──三角关系的一个结论．若把玻尔兹曼权参变数表示为Ｚａｍｏｌｏｄｃｈｉｋｏｖ角变量形式,其附加条件自然成立．值得指出的是,由本文处理方法可以得出三维可解统计模型的星－三角关系,它包含了Ｂａｚｈａｎｏｖ和Ｂａｘｔｅｒ的结论．     

一个新的精确可解的三维解析势

提出了一种新的精确可解的三维解析势函数,即环形非球谐振子。势函数为V（γ,θ）=1/2mω^2γ^2 h^2/2mA/γ^2 h^2/2mb/γ^2sin^2θ。将环形非球谐振子势的Schroedinger方程在球坐标系中进行变量分离,得到了角向方程和径向方程,给出了精确的能谱方程,获得了用普遍的associated-Legendre多项式表示的归一化的角向波函数和用合流超几何函数表示的归一化的径向波函数。球谐振子、非球谐振子和环形振子的有关结果均作为特例包含在本文的一般结论之中。     

三维十五点格子Boltzmann模型仿真

格子气和格子Ｂｏｌｔｚｍａｎｎ方法的迅速发展提供了一类求解流体力学问题的新方法。格子Ｂｏｌｔｚｍａｎｎ方法在保留了格子气模型优点的同时,克服了它的不足之处。本文讨论了一种三维十五点格子Ｂｏｌｔｚｍａｎｎ模型,通过选择适当的平衡分布及参数,并用Ｃｈａｐｍａｎ－Ｅｎｓｋｏｇ展开和多尺度技术导出了Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程．在微机上模拟了工程中比较常见的管排绕流问题,并与实验观察到的结果进行了比较,结果表明该模型能较好的模拟复杂流动现象,并具有较好的工程应用背景。     

基于SIFT特征点的三维点云模型盲水印算法

为提高三维模型版权信息的安全性和鲁棒性,提出了一种基于尺度不变特征转换的三维点云模型水印算法。首先对三维点云模型进行主成分分析,然后将模型中的点到模型中心的距离r进行一定的排序,形成一个m×n的矩阵。对该矩阵进行尺度不变特征提取,找到其稳健的特征点。在选取合适的特征点后对其邻域进行Contourlet变换,将水印嵌入其低频部分,然后进行Contourlet逆变换,即可生成带水印的三维点云模型。实验表明,该算法对几何攻击以及噪声、裁切、简化等攻击具有较强的鲁棒性。该算法可用于实际三维模型的版权认证。     

一种三维环流模型及其应用

本文建立了一种广泛适用于大陆架浅海的三维环流模型。模型的支配方程是具有自由面的三维非线性瞬态Navier-Stokes方程。支配方程经σ坐标变换后与边界条件一起在空间交错网格系统上用差分法求解。为提高计算效率,基于问题的物理性质引入过程分裂概念没计了计算框架:将三维流动过程分成长重力波的传播(外模式)和速度的垂向剪变(内模式)两大组成部分,对每个部分分别选用最适宜各自物理特性和数值行为的数值方法求解。最后做为本模型的应用实例,计算了渤海三维潮流,获得了很好的结果。     

模型参数对奇异星性质的影响

用有效质量口袋模型描述奇异夸克物质,研究了耦合常数和口袋常数的选取对奇异夸克物质的状态方程及奇异星性质的影响.结果表明,随着耦合常数和口袋常数的增大,奇异夸克物质的状态方程变软,相应的奇异星的引力质量和对应的半径均变小.当耦合常数从0.5增大到2.0时,奇异星的质量从1.43M_⊙(M_⊙=1.99×10³⁰ kg)减小到1.25M_⊙,相应的半径由8.3 km减小到7.7 km;当口袋常数B^1/4由160 MeV增大到175 MeV时,奇异星的质量和半径分别由1.47M_⊙和8.6 km减小到1.22M_⊙和7.4 km.这说明奇异夸克物质及奇异星的性质明显依赖于模型参数的取值. 关键词： 模型参数 奇异星 状态方程 质量-半径关系     

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     

非接触三维测量全场结构关系模型分析及系统开发

研究开发了一种基于光栅投影和主动式三角法的高精度三维测量系统。分析了系统的全场结构关系模型及镜头失真对系统的影响,给出了空间三维坐标的详细算法。试验结果表明,系统的测量误差小于0.04mm,测量精度约为0.03mm。多视角测量的拼合结果表明,系统具有良好的360°测量精度,测量精细表面纹理效果好。该系统在反求工程及质量控制等领域具有良好的工业应用前景。     

格点Schwinger模型的一组准确解

本文找到了Naive格点Schwinger模型的一组准确解,讨论了其连续极限行为,证实Naive格点,化不能切断Schwinger模型的高能非物理状态.     

Exactly Solvable Model of Quantum Diffusion

We study the transport property of diffusion in a finite translationally invariant quantum subsystem described by a tight-binding Hamiltonian with a single energy band. The subsystem interacts with its environment by a coupling expressed in terms of correlation functions which are delta-correlated in space and time. For weak coupling, the time evolution of the subsystem density matrix is ruled by a quantum master equation of Lindblad type. Thanks to the invariance under spatial translations, we can apply the Bloch theorem to the subsystem density matrix and exactly diagonalize the time evolution superoperator to obtain the complete spectrum of its eigenvalues, which fully describe the relaxation to equilibrium. Above a critical coupling which is inversely proportional to the size of the subsystem, the spectrum at given wave number contains an isolated eigenvalue describing diffusion. The other eigenvalues rule the decay of the populations and quantum coherences with decay rates which are proportional to the intensity of the environmental noise. An analytical expression is obtained for the dispersion relation of diffusion. The diffusion coefficient is proportional to the square of the width of the energy band and inversely proportional to the intensity of the environmental noise because diffusion results from the perturbation of quantum tunneling by the environmental fluctuations in this model. Diffusion disappears below the critical coupling     

A Solvable Decorated Ising Lattice Model

A decorated lattice is suggested and the Ising model on it with three kinds of interactions K₁, K₂, and K₃ is studied. Using an equivalent transformation, the square decorated Ising lattice is transformed into a regular square Ising lattice with nearest-neighbor, next-nearest-neighbor, and four-spin interactions, and the critical fixed point is found at K₁=0.5769, K₂=-0.0671, and K₃=0.3428, which determines the critical temperature of the system. It is also found that this system and the regular square Ising lattice, and the eight-vertex model belong to the same universality class.     

Exactly Solvable Model of Reactions on a Random Catalytic Chain

In this paper we study a catalytically-activated A+A0 reaction taking place on a one-dimensional regular lattice which is brought in contact with a reservoir of A particles. The A particles have a hard-core and undergo continuous exchanges with the reservoir, adsorbing onto the lattice or desorbing back to the reservoir. Some lattice sites possess special, catalytic properties, which induce an immediate reaction between two neighboring A particles as soon as at least one of them lands onto a catalytic site. We consider three situations for the spatial placement of the catalytic sites: regular, annealed random, and quenched random. For all these cases we derive exact results for the partition function, and the disorder-averaged pressure per lattice site. We also present exact asymptotic results for the particles' mean density and the system's compressibility. The model studied here furnishes another example of a 1D Ising-type system with random multisite interactions which admits an exact solution.     

Surface Tension of a Metal-Electrolyte Boundary: Exactly Solvable Model

An ideal conductor electrode in contact with a semi-infinite two-dimensional two-component plasma in an external potential is considered. The model is mapped onto an integrable sine-Gordon theory with Dirichlet boundary conditions. The information gained from the mapping provides an explicit form of the surface tension in the plasma-stability regime.     

Remarks on Exactly Solvable Noncommutative Quantum Field

We study exactly the solvable noncommutative scalar quantum field models of （2n） or （2n ＋ 1） dimensions. By writing out an equivalent action of the noncommutative field, it is shown that the special condition B. 0 = 4-1 in field theoretic context means the full restoration of the maximal U（∞） gauge symmetries broken due to kinetic term. It is further shown that the model can be obtained by dimensional reduction of a 2n-dimensional exactly solvable noncommutative φ4 quantum field model closely related to the 1＋1-dimensional Moyal/matrix-valued nonlinear Schr6dinger （MNLS） equation. The corresponding quantum fundamental commutation relation of the MNLS model is also given explicitly.     

An Exactly Solvable Model of Disordered System

An exactly solvable model of disordered system with infinite-ranged interaction is solved. We find that almost every eigenvector is localized.     

Surface Tension of an Ideal Dielectric-Electrolyte Boundary: Exactly Solvable Model

The model under consideration is a semi-infinite two-dimensional two-component plasma (Coulomb gas), stable against bulk collapse for the dimensionless coupling constant <2, in contact with a dielectric wall of dielectric constant =0. The model is mapped onto an integrable sine-Gordon theory with a free Neumann boundary condition. Using recent results on a reflection relationship between the boundary Liouville and sine-Gordon theories, an explicit expression is derived for the surface tension at a rectilinear dielectric – Coulomb gas interface. This expression reproduces the Debye-Hückel 0 limit and the exact result at the bulk collapse border, the free-fermion point =2, where the surface tension keeps a finite value. The surface collapse, identified with the divergence of the surface tension, occurs at =3.     

Z_n格点模型的量子仿射变形代数

应用两种不同的星三角关系及其对应的Ｂｏｌｔｚｍａｎｎ面权，通过反对称聚合，构造出了在椭圆情形下的ｑ变形仿射代数．     

Three-Dimensional Vertex Model Related BCC Model in Statistical Mechanics

In this paper, a three-dimensional vertex model is obtained. It is a duality of the three-dimensional integrable lattice model with N states proposed by Boos, Mangazeev, Sergeev and Stroganov. The Boltzmann weight of the model is dependent on four spin variables, which are the linear combinations of the spins on the corner sites of the cube, and obeys the modified vertex-type tetrahedron equation. This vertex model can be regarded as a deformation of the one related to the three-dimensional Baxter-Bazhanov model. The constrained conditions of the spectrums are discussed in detail and the symmetry properties of weight functions of the vertex model are presented.