Scaling Behavior of an Aggregation-Migration Model

We study the kinetic behavior of a two-species aggregation-migration model in which an irreversible aggregation occurs between any two clusters of the same species and a reversible migration occurs simultaneously between two different species. For a simple model with constant aggregation rates and with the migration rates K_A(i;j)=K'_A(i;j) ∝ij^v₁ and K_B(i;j)=K'_B(i;j) ∝ij^v₂, we find that the evolution behavior of the system depends crucially on the values of the indexes v₁ and v₂. The aggregate size distribution of either species obeys a conventional scaling law for most cases. Moreover, we also generalize the two-species system to the multi-species case and analyze its kinetic behavior under the symmetrical conditions.     

射频辉光放电CH4等离子体一维流体动力学模拟

完整建立一个关于射频辉光放电CH₄等离子体的流体动力学模型.模型包括基于迁移-扩散近似的粒子平衡方程、电子能量平衡方程,共包含了20种粒子(环境气体粒子,激发态粒子,离子和电子)和49类化学反应(电子-中性环境粒子、离子-中性环境粒子、激发态粒子-激发态粒子(中性环境粒子)).结果表明,在强电场区域有较高的电子反应率系数;等离子体中除源气体CH₄外,H₂,C₂H₆,C₃H₈,C₂H₄和C₂H₂也有较高的密度含量;激发态粒子中,CH₃含量最高,密度约为10¹⁹m^-3;在较低放电压力时(如18 Pa),CH₅⁺在离子成分中密度含量最高,当放电压力较高时(如67Pa),C₂H₅⁺在离子成分中占主导地位;除C₂H₅⁺外,其它各离子和激发态粒子在极板上的粒子流量随功率的增大逐渐升高.     

缔合流体在高温高压下的自扩散系数研究

在统计力学理论基础上,本文提出了一个考虑氢键对自扩散系数影响的方程．这个方程为非氢键贡献部分与氢键贡献部分之积,其中自扩散系数的非氢键部分由Ｌｅｎｎａｒｄ－Ｊｏｎｅｓ链模型求得,而一个分子中的平均氢键数随温度和密度的变化关系使用统计缔合流体理论得到。链节之间的相互作用能量参数由粘度的关联式获得,其它四个参数则由扩散系数的实验数据获得。对７个典型的缔合流体在相当宽的温度压力范围内计算的平均相对百分误差为５．９８％。     

多相非牛顿流体驱替过程的格子Boltzmann模拟

将非牛顿流体模型引入多相格子Boltzmann方法（LBM）,研究多相非牛顿流体的驱替过程.首先以牛顿流体驱替过程作对照,比较非牛顿流体的驱替特性.然后基于简单结构模型,分析不同界面张力下,非牛顿流体的驱替能力和驱替过程中被驱替相的形态变化规律,揭示界面张力的影响机理.结果表明：界面张力在驱替过程中起阻碍作用,其它参数相同情况下,界面张力越低,流体的驱替能力越强.最后,结合四参数随机生长（QSGS）结构生成方法,模拟不同压差、不同界面张力以及不同润湿性条件下多孔复杂结构内的非牛顿多相驱替过程,分析这些参数对过程的影响.     

等效折射率模型研究光子晶体光纤的色散特性

应用等效折射率模型对折射率导模光子晶体光纤的群速度色散特性进行了详细的讨论。由于光子晶体光纤由单一材料(SiO2)制成,光纤的波导色散决定了总色散,因此讨论中将群速度色散分解为波导色散和材料色散,研究了波导色散与光子晶体光纤的结构参量孔距∧、相对孔径f的关系。分析表明,在f一定的情况下,光子晶体光纤的波导色散与孔距∧的关系符合麦克斯韦方程的比例性质;而在孔距∧确定的情况下,光子晶体光纤的波导色散的零点、极小值点位置与f在所讨论的波长范围内存在线性关系。最后举例说明了通过调整光子晶体光纤的结构参量,可以灵活地设计其色散特性。     

Scaling properties of models of nonequilibrium phenomena

The renormalization group method proposed by 't Hooft is developed for the study of scaling properties of some models of nonequilibrium phenomena. For one of two models studied in detail, the Langevin equation for the random variables contains a bilinear streaming velocity and the stationary probability distribution is Gaussian. The time-dependent Ginzburg-Landau model is chosen as a second example because it illustrates the advantage of the 't Hooft method of not having to specify a particular renormalization point. The scaling exponents for a model of the liquid-gas phase transition are calculated in lowest order to illustrate application of the method to a multifield system.     

Phonon Dispersion and Thermodynamics Properties of CaF2 via Shell Model Molecular Dynamics Simulations

The phonon and thermodynamics properties of face-centered cubic CaF2 at high pressure and high temperature are investigated by using the shell model interatomic pair potential within General Utility Lattice Program （GULP）. The phonon dispersion curves and the corresponding density of state （PDOS） in this work are consistent with the experimental data and other theoretical results. The transverse optical （TO） and longitudinal optical （LO） mode splitting as well as heat capacity at constant volume Cv and entropy S versus pressure and temperature are also obtained.     

Scaling theory of transient phenomena near the instability point

A general scaling theory of transient phenomena is formulated near the instability point for the moments of the relevant intensive macrovariable, for the generating function, and for the probability distribution function. This scaling theory is based on a generalized scale transformation of time. The whole range of time is divided into three regions, namely the initial, scaling, and final regions. The connection procedure between the initial region and the scaling region is studied in detail. This scaling treatment has overcome the difficulty of divergence of the variance for a large time which was encountered in the -expansion, and this scaling theory yields correct values of moments to order unity for an infinite time. Some instructive examples are discussed for the purpose of clarifying the concepts of the scaling theory.     

矩形网格上VOF运动界面重构的流体体积分数保持法

针对处理运动界面问题的流体体积函数(VOF)法,提出一种新的流体体积分数保持界面重构算法.该方法在单个网格内用斜线段近似运动界面,并要求相邻网格内的斜线段在公共边上的交点重合,通过保持网格内的流体体积分数不变,在边界网格上建立非线性方程组,通过求解非线性方程组,确定运动界面边界线与网格线的交点位置,最终重构出运动界面的形状.应用算例模拟结果表明,该方法能够高精度,较少尖点地重构运动界面,证实了该方法的有效性和可行性.     

Magnetic Properties of Transverse Ising Model under a Time Oscillating Longitudinal Field

A transverse Ising spin system, in the presence of time-dependentlongitudinal field, is studied by the effective-field theory (EFT). Theeffective-field equations of motion of the average magnetization are givenfor the simple cubic lattice (Z = 6) and the honeycomb lattice (Z = 3).The Liapunov exponent λ is calculated for discussing the stability of the magnetization and it is used to determine the phase boundary. Thedynamic phase transition diagrams in h₀/ ZJ -Γ/ZJ plane and in h₀/ZJ-T/ZJ plane have been drawn, and there is no dynamical tricritical point on the dynamic phase transition boundary. The effect of the thermal fluctuations upon the dynamic phase boundary has been discussed.     

磁场中非广延相对论费米系统的统计性质

基于广义外势中的非广延统计理论,运用理论解析与数值模拟方法,研究磁场中非广延极端相对论费米气体的热力学性质,给出总能、热容量、化学势的解析式,分析非广延参数、极端相对论效应、磁场及温度对系统热力学性质的影响机理.研究显示,非广延参数不仅对热力学性质有直接的影响,而且也影响着磁场的物理效应. 随温度的升高,非广延参数及磁场对热力学性质的影响均被放大.极端相对论效应对化学势及热容量有特别显著的影响.     

Nonlinear Exact Solutions of the 2-Dimensional Rotational Euler Equations for the Incompressible Fluid

In this paper, the Clarkson–Kruskal direct approach is employed to investigate the exact solutions of the2-dimensional rotational Euler equations for the incompressible fluid. The application of the method leads to a system of completely solvable ordinary differential equations. Several special cases are discussed and novel nonlinear exact solutions with respect to variables x and y are obtained. It is of interest to notice that the pressure p is obtained by the second kind of curvilinear integral and the coefficients of the nonlinear solutions are solitary wave type functions like tanh(kt/2)and sech(kt/2) due to the rotational parameter k = 0. Such phenomenon never appear in the classical Euler equations wherein the Coriolis force arising from the gravity and Earth's rotation is ignored. Finally, illustrative numerical figures are attached to show the behaviors that the exact solutions may exhibit.     

Effects of Thermal Radiation on a 3D Sisko Fluid over a Porous Medium Using Cattaneo-Christov Heat Flux Model

This paper investigates the three-dimensional flow of a Sisko fluid over a bidirectional stretching sheet, in a porous medium. By using the effect of Cattaneo-Christov heat flux model, heat transfer analysis is illustrated. Using similarity transformation the governing partial differential equations are transferred into a system of ordinary differential equations that are solved numerically by applying Nachtsheim-Swigert shooting iteration technique along with the 6-th order Runge-Kutta integration scheme. The effect of various physical parameters such as Sisko fluid, ratio parameter, thermal conductivity, porous medium, radiation parameter, Brownian motion, thermophoresis, Prandtl number, and Lewis number are graphically represented.     

The Properties of Voronoi Tessellations for 2D Ising Fluid Near the Second-Order Magnetic Phase Transition

The topological and geometrical properties of Voronoi cells generated for 2D fluid of hard disks with Ising-like spins near the second-order phase transition from the paramagnetic to ferromagnetic phase are described for different disk densities. The comparison with Voronoi cells generated for the random hard disk system is given.     

高频感应等离子体流动模型与微型电推进器流场特性分析

微型射频离子推力器具有结构简单、 工作寿命长、 推力动态范围大、 性能调节响应灵敏等特点,是国际微电推进领域的研究热点之一.射频离子推力器电离室内的感性耦合放电等离子体特性和推力器的性能密切相关.为此,文章建立了低气压、小尺寸微型射频离子推力器电离室内感性耦合等离子体流体模型,开展了电磁场、流场、化学反应浓度场的多物理...     

壁面在展向作周期运动的槽道湍流的大涡模拟

分别采用3种亚格子模式:传统的Smagorinsky模式、动力Smagorinsky模式和Cui(2004)基于Kolmogorov方程所提出的新模式,对壁面在展向作周期运动的槽道湍流进行了大涡模拟,以考察这3种模式对平均运动为三维、非定常的湍流流动的模拟能力.通过对湍流基本统计量的分析,发现动力模式和新模式都可以较好地预测这种三维非定常的湍流流动;对相位平均的湍流统计量,动力模式的结果略优于新模式;传统的Smagorinsky模式对这种流动的预测结果是最差的.     

Analytic Solutions for Asymmetric Model of a Rod in a Lattice Fluid

We consider the problem of determining analytically some exact solutions of the concentration u(x, y, t) of particles moving by diffusion and advection or drift. It is assumed that the advection is nonlinear. The driven diffusive flow is impeded by an impenetrable obstacle (rod) of length L. The exact solutions for u are evaluated for small and big values of vL/D, where v is the drift velocity and D is the diffusion coefficient. The results show that in some regions in the (x, y) plane the concentration first increases (or decreases) monotonically and then is nearly constant after some critical length L. The location at which u is nearly constant depends on the nature of the driving field v/D. This problem has relevance for the size segregation of particulate matter which results from the relative motion of different-size particles induced by shaking. Methods of symmetry reduction are used in solving the nonlinear advection-diffusion equation in (2+1) dimensions.     

Ballistic Deposition模型孔洞生长标度行为的数值模拟

为研究表面界面粗化生长中孔洞的标度行为,在对Ballistic Deposition(BD)模型进行数值模拟的基础上,对模型中孔洞的模拟生长情况进行统计和分析.结果表明,BD模型中孔洞数目随模型生长时间的变化从初始阶段的高于线性而渐趋近于线性,并对该规律进行理论分析.     

Fluid Simulation of a Cusped Field Thruster

The cusped field thruster is a kind of newly developed electric propulsion device. The electric field at the channel exit and the low frequency oscillation were measured by former experiments. While the formation mechanism of them have not been fully interpreted yet. Through studying two distinguishing typical electron paths in the thrusters, a fluid model is built up along two electron paths, and then the model is completed by synthetically analyzing the effect of two electron paths. Time‐averaged electric potential distribution, anode current oscillation curve and time‐synchronized atom density and ion density distribution are obtained by simulation. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Gradient theory of fluid microstructures

The general gradient theory of fluid microstructures is outlined. This theory reduces the determination of fluid microstructures to a boundary value problem. The density and pressure tensor profiles and the tension of planar thin films and layered structures in one-component fluids are investigated. The boundary conditions determining these structures are given a geometric interpretation in the free energy-density diagram. Discussed are the implications of the theory for the validity of Antonov's rule, the duplex film hypothesis, and the asymptotic theory of disjoining pressure and of the origin of a characteristic length scale in spinodal decomposition.This work was supported financially by the U.S. Department of Energy and the National Science Foundation.