硅熔化特性的分子动力学模拟–-不同势函数的对比研究

分别采用Stillinger-Weber (SW)势、修正的成熟原子嵌入模型(MEAM)势、 Tersoff势和HOEP (highly optimized empirical potential)势来描述硅原子间相互作用, 运用分子动力学方法对比模拟研究了四种势函数的硅晶体的体熔化和表面熔化特性. 结果表明: 四种势函数均能反映出硅的热膨胀、高温熔化和熔化时吸热收缩等基本物理规律. 但综合对比发现, Tersoff势和MEAM势相对更适合描述硅的熔化和凝固过程, SW势次之, HOEP势则不适合描述硅的熔化和凝固过程. 关键词： 硅 势函数 熔化 分子动力学     

刚性多原子分子的正则系综分子动力学算法

通过将Nose所定义的扩展系统哈密顿量推广到刚性多原子分子系统中，严格地推导了刚性多原子分子在正则系综下的运动方程.在此基础上，证明了依靠所给出的运动方程能得到平衡态的正则分布，并给出了该方程所对应的可逆而守恒的积分格式. 关键词： 刚性多原子分子 正则系综 分子动力学算法     

A stabilization theorem for dynamics of continuous opinions

A stabilization theorem for processes of opinion dynamics is presented. The theorem is applicable to a wide class of models of continuous opinion dynamics based on averaging (like the models of Hegselmann–Krause and Weisbuch–Deffuant). The analysis detects self-confidence as a driving force of stabilization.     

A molecular dynamics model for nuclear clusterization

We present a newly developed Nuclear Molecular Dynamics model aiming at the dynamical simulations of intermediate-energy heavy-ion collisions. This is a quasi-classical approach reducing a complex many-body dynamics to the propagation of Gaussian nucleons in a nuclear mean field and stochastic two-body scattering. We describe in detail main ingredients of the model including the Hamiltonian, scattering algorithm and initialization procedure. We show how the model describes isolated nuclei and the nuclear matter equation of state. The limitation of the model in reproducing the fermionic nature of nuclei is also demonstrated. The main emphasis in the paper is put on the study of the fragment formation dynamics. The backtracing method is applied to investigate the time evolution of subsets of nucleons which finally organize themselves into clusters. The non-equilibrium features of the clusterization process are demonstrated by several examples.     

两种势下硅锗合金熔体快速凝固过程的分子动力学模拟

分别采用S-W势和Tersoff势来描述硅锗原子间相互作用,运用分子动力学方法对比模拟研究了硅锗合金熔体的快速凝固过程。通过对径向分布函数、静态结构因子、键角分布函数、配位数、Voronoi多面体以及宏观密度的研究,综合对比发现,Tersoff 势和S-W势相比更适合描述硅锗合金的快速凝固过程。     

两种势下硅锗合金熔体快速凝固过程的分子动力学模拟

分别采用S-W势和Tersoff势来描述硅锗原子间相互作用,运用分子动力学方法对比模拟研究了硅锗合金熔体的快速凝固过程。通过对径向分布函数、静态结构因子、键角分布函数、配位数、Voronoi多面体以及宏观密度的研究,综合对比发现,Tersoff 势和S-W势相比更适合描述硅锗合金的快速凝固过程。     

A continuous model of human dynamics

Ideas and tools from statistical physics have recently been applied to the investigation of human dynamics. The timing of human activities, in particular, has been studied both experimentally and analytically. Empirical data show that, in many different situations, the time interval separating two consecutive tasks executed by an individual follows a heavy-tailed probability distribution rather than Poisson statistics. To account for this data, human behaviour has been viewed as a decision-based queuing system where individuals select and execute tasks belonging to a finite list of items as an increasing function of a task priority parameter. It is then possible to obtain analytically the empirical result P(τ)∼1/τ, where P(τ) is the waiting time probability distribution.Here a continuous model of human dynamics is introduced using instead an infinite queuing list. In contrast with the results obtained by other models in the finite case we find a waiting time distribution explicitly depending on the priority distribution density function ρ. The power-law scaling P(τ)∼1/τ is then recovered when ρ is exponentially distributed.     

Non-equilibrium momentum exchange algorithm for molecular dynamics simulation of heat flow in multicomponent systems

A new non-equilibrium molecular dynamics algorithm is presented based on the original work of Müller-Plathe, (1997, J. chem. Phys., 106, 6082), for the non-equilibrium simulation of heat transport maintaining fixed the total momentum as well as the total energy of the system. The presented scheme preserves these properties but, unlike the original algorithm, is able to deal with multicomponent systems, that is with particles of different mass independently of their relative concentration. The main idea behind the new procedure is to consider an exchange of momentum and energy between the particles in the hot and cold regions, to maintain the non-equilibrium conditions, as if they undergo a hypothetical elastic collision. The new algorithm can also be employed in multicomponent systems for molecular fluids and in a wide range of thermodynamic conditions.     

Loop dynamics for gauge theories: A numerical algorithm

The loop equations defining the lattice U(N) gauge theory are recalled and a formal solution is presented (for N = 1 and N → ∞). Wilson's expectation function W(C) for a loop C is expressed as a matrix element of a resolvent in the space of all the loops between C and 0 (no loop). It is shown that such a solution provides a new numerical algorithm to compute physical quantities. This is based on a Ulam-von Neumann type of method for computing inverse matrix elements by introducing importance sampling for the paths in the space of the matrix indices, which in this case are the loops. As a result W(C) is obtained by summing over important paths in the loop space connecting C to 0. A Monte Carlo program is presented, for the N → ∞ case, where a very simple form for the importance sampling is introduced so that the computer time for each step in the construction of the path is minimized. The rates for successful paths (i.e. path C → 0 within a given finite number of steps) are computed for D = 2 and D = 4. Both rates and computer time involved encourage us to attempt a large scale calculation. Here the numerical studies of the convergence and of the fluctuations are presented only for D = 2. Convergence is rather fast, but specially in the weak-coupling region rare and large fluctuations appear thus suggesting that a better tuning for the importance sampling is needed.     

耗散粒子动力学处理复杂固体壁面的一种有效方法

耗散粒子动力学(dissipative particle dynamics,DPD)作为一种介观尺度拉格朗日型粒子方法,已经成功地应用于微纳米流动和生化科技的研究中.复杂固体壁面的处理和壁面边界条件的实施一直是DPD方法发展及应用的一个障碍.提出了处理复杂固体壁面的一种新的方法.复杂固体区域通过冻结随机分布并且达到平衡状态的DPD粒子代表;所冻结的DPD粒子位于临近流动区域的一个截距内;在靠近固体壁面的流动区域中设置流动反弹层,当流动DPD粒子进入此流动层后反弹回流动区域.应用这种固体壁面处理方法对简单流动区域的Poiseuille流动和复杂多孔介质内的流动进行了分析.研究表明,这种新的固体壁面处理方法能够有效模拟复杂固体区域,准确实施壁面边界条件.     

A molecular dynamics study on iridium

In this study, molecular dynamics simulations are performed by using a modified form of Morse potential function in the framework of the Embedded Atom Method (EAM). Temperature-and pressure-dependent behaviours of bulk modulus, second-order elastic constants (SOEC), and the linear-thermal expansion coefficient is calculated and compared with the available experimental data. The melting temperature is estimated from 3 different plots. The obtained results are in agreement with the available experimental findings for iridium.      

Comments on the mean spherical approximation for hard-core and soft potentials and an application to the one-component plasma

The thermodynamic properties of the mean spherical (MSA), Percus-Yevick (PY), and hypernetted-chain (HNC) approximations are derived by a simple and unified approach by considering the RPA free-energy functionalF and employing an Ewald-type identity. It is demonstrated that with decreasing relative contribution of the hard-core insertion to the thermodynamic functions, the MSA changes its nature from PY-like to HNC-like, withF changing its role from excess pressure to excess free energy, respectively. It is found that the condition of continuity of the MSA pair functions is equivalent to a stationarity condition forF and leads to thermodynamic consistency between the virial and energy equations of state for the (thus defined) soft-MSA (SMSA), withF playing the role of the excess free energy. It is shown that the PY-compressibility and virial equations of state forD-dimensional hard spheres may be simply obtained one from the other without knowing any details of the solution of the model. Using this relation we find an indication that the PY approximation for hard spheres becomes less accurate with increasing dimensionality. A general variational formulation is presented for the application of the MSA for soft potentials, and results for the one-component plasma are discussed and extended.On sabbatical leave from the Nuclear Research Center-Negev, P.O. Box 9001, Beer Sheva, Israel.     

Exact short time dynamics for steeply repulsive potentials

The autocorrelation functions for the force on a particle, the velocity of a particle and the transverse momentum flux are studied for the power law potential v(r)=ε(σr)^ν (soft spheres). The latter two correlation functions characterize the Green–Kubo expressions for the self-diffusion coefficient and shear viscosity. The short-time dynamics is calculated exactly as a function of ν. The dynamics is characterized by a universal scaling function S(τ), where τ=t/τ_ν and τ_ν is the mean time to traverse the core of the potential divided by ν. In the limit of asymptotically large ν this scaling function leads to delta function in time contributions in the correlation functions for the force and momentum flux. It is shown that this singular limit agrees with the special Green–Kubo representation for hard-sphere transport coefficients. The domain of the scaling law is investigated by comparison with recent results from molecular dynamics simulation for this potential.     

A molecular dynamics method for simulations in the canonical ensemble

A molecular dynamics simulation method which can generate configurations belonging to the canonical (T, V, N) ensemble or the constant temperature constant pressure (T, P, N) ensemble, is proposed. The physical system of interest consists of N particles (f degrees of freedom), to which an external, macroscopic variable and its conjugate momentum are added. This device allows the total energy of the physical system to fluctuate. The equilibrium distribution of the energy coincides with the canonical distribution both in momentum and in coordinate space. The method is tested for an atomic fluid (Ar) and works well.     

基于分子动力学模拟的主链型液晶聚合物的新模型

在传统的Gay-Berne (GB)/Lennard-Jones (LJ)模型的基础上，发展了一种用于模拟半刚性主链型液晶聚合物(LCP)的分子级模型，命名为Solo-LJ-SP-GB 模型.单一的LJ联合体和非线性弹簧被用于描述LCP分子中的间隔体.用分子动力学模拟半刚性主链型LCP系统(该系统由169条分子链组成，每两个刚性体之间的间隔体个数为6)时，该模型所需的计算时间不到传统的GB/LJ 模型所需时间的十分之一，大大地提高了计算效率.通过采用该模型模拟半刚性主链型LCP的相变问题，观察到了与半刚性主链型LCP分子中间隔体个数相关的热力学的奇偶效应以及从等方相到向列相的相转变过程.这些模拟结果与当前的试验结果相当符合，从而表明了该模型可以较为准确地描述出半刚性主链型LCP的结构特性. 关键词： Solo-LJ-SP-GB模型 液晶聚合物 分子动力学模拟     

A simple and effective Verlet-type algorithm for simulating Langevin dynamics

We present a revision to the well known Störmer–Verlet algorithm for simulating second order differential equations. The revision addresses the inclusion of linear friction with associated stochastic noise, and we analytically demonstrate that the new algorithm correctly reproduces diffusive behaviour of a particle in a flat potential. For a harmonic oscillator, our algorithm provides the exact Boltzmann distribution for any value of damping, frequency and time step for both underdamped and overdamped behaviour within the usual stability limit of the Verlet algorithm. Given the structure and simplicity of the method, we conclude that this approach can trivially be adapted for contemporary applications, including molecular dynamics with extensions such as molecular constraints.